The reciprocal of a number is 1 divided by the number. By using reciprocals, division is changed into multiplication, since a/b=a/b=ax1/b. The table gives the reciprocals of all numbers expressed with three significant figures to six significant figures. By proceeding in a manner similar to that just described for powers and roots, the reciprocal of any number correct to five significant figures may be obtained. The decimal point in the result may be located as follows: If the given number has an integral part, the number of ciphers following the decimal point in the reciprocal will be one less than the number of figures in the integral part of the given number; and if the given number is entirely decimal, the number of figures in the integral part of the reciprocal will be one greater than the number of ciphers following the decimal point in the given number. For example, the reciprocal of 3370 = .000296736 and of .00348 = 287.356.

When the number whose reciprocal is desired contains more than three significant figures, express the number to six significant figures (adding ciphers, if necessary, to make six figures) and find between what two numbers in the column headed - the significant figures of the given number falls; then proceed exactly as previously described to deter mine the fourth and fifth figures.

Example

(a) The reciprocal of 379.426 =? (b)1/.0004692 =?

Solution

(a) .379426 falls between .378788 = 1/2.64 and

.380228 = 1/2.63. The first difference is 380228 - 378788 = 1440: the second difference is 380228 - 379426 = 802; 802 -4- 1440 = .557, or .56. Hence, the first five significant figures are 26356, and the reciprocal of 379.426 is .0026356, to five significant figures.

(b) .469200 falls between .469484=1 / 2.13 and .467290=1 / 2.14

The first difference is 2194; the second difference is 284; 284/

2194 = .129+, or .13. Hence, 1/.0004692 = 2131.3, correct to five significant figures.

n

n2

n3

√n

Reciprocals 51

Reciprocals 52

Reciprocals 53

Reciprocals 54

1/n

1.01

1.0201

1 03030

1.00499

3.17805

1.00332

2.16159

4.65701

.990099

1.02

1.0404

1.06121

1.00995

3.19374

1.00662

2.16870

4.67233

.980392

1.03

1.0609

1.09273

1.01489

3.20936

1.00990

2.17577

4.68755

.970874

1.04

1.0816

1.12486

1.01980

3.22490

1.01316

2.18278

4.70267

.961539

1.05

1.1025

1.15763

1.02470

3.24037

1.01640

2.18976

4.71769

.952381

1.06

1.1236

1.19102

1.02956

3.25576

1.01961

2.19669

4.73262

.943396

1.07

1 1449

1.22504

1.03441

3.27109

1.02281

2.20358

4.74746

.934579

1.08

1.1664

1.25971

1.03923

3.28634

1.02599

2.21042

4.76220

.925926

1.09

1.1881

1.29503

1.04403

3.30151

1.02914

2.21722

4.77686

.917431

1.10

1.2100

1.33100

1.04881

3.31662

1.03228

2.22398

4.79142

.909091

1.11

1.2321

1 36763

1.05357

3.33167

1.03540

2.23070

4.80590

.900901

1.12

1.2544

1.40493

1.05830

3.34664

1.03850

2.23738

4.82028

.892857

1.13

1.2769

1.44290

1.06301

3.36155

1.04158

2.24402

4.83459

.884956

1.14

1.2996

1.48154

1.06771

3.37639

1.04464

2.25062

4.84881

.877193

1.15

1.3225

1.52088

1.07238

3.39116

1.04769

2.25718

4.86294

.869565

1.16

1.3456

1.56090

1.07703

3.40588

1.05072

2.26370

4.87700

.862069

1.17

1.3689

1.60161

1.08167

3.42053

1.05373

2.27019

4.89097

.854701

1.18

1.3924

1.64303

1.08628

3.43511

1.05672

2.27664

4.90487

.847458

1.19

1.4161

1.68516

1.09087

3.44964

1.05970

2.28305

4.91868

.840336

1.20

1.4400

1.72800

1.09545

3.46410

1.06266

2.28943

4.93242

.833333

1.21

1.4641

1.77156

1.10000

3.47851

1.06560

2.29577

4.94609

.826446

1.22

1.4884

1.81585

1.10454

3.49285

1.06853

2.30208

4.95968

.819672

1.23

1.5129

1.86087

1.10905

3.50714

1.07144

2.30835

4.97319

.813008

1.24

1.5376

1.90662

1.11355

3.52136

1.07434

2.31459

4.98663

.806452

1.25

1.5625

1.95313

1.11803

3.53553

.1.07722

2.32080

5.00000

.800000

1.26

1.5876

2.00038

1.12250

3.54965

1.08008

2.32697

5.01330

.793651

1.27

1.6129

2.04838

1.12694

3.56371

1.08293

2.33310

5.02653

.787402

1.28

1.6384

2.09715

1.13137

3.57771

1.08577

2.33921

5.03968

.781250

1.29

1.6641

2.14669

1.13578

3.59166

1.08859

2.34529

5.05277

.775194

1.30

1.6900

2.19700

1.14018

3.60555

1.09139

2.35134

5.06580

.769231

1.31

1.7161

2.24809

1.14455

3.61939

1.09418

2.35735

5.07875

.763359

1.32

1.7424

2.29997

1.14891

3.63318

1.09696

2.36333

5.09164

.757576

1.33

1.7689

2.35264

1.15326

3.64692

1.09972

2.36928

5.10447

.751880

1.34

1.7956

2.40610

1.15758

3.66060

1.10247

2.37521

5.11723

.746269

1.35

1.8225

2.46038

1.16190

3.67423

1.10521

2.38110

5.12993

.740741

1.36

1.8496

2.51546

1.16619

3.68782

1.10793

2.38696

5.14256

.735294

1.37

1.8769

2.57135

1.17047

3.70135

1.11064

2.39280

5.15514

.729927

1.88

1.9044

2.62807

1.17473

3.71484

1.11334

2.39861

5.16765

.724638

1.39

1.9321

2.68562

1.17898

3.72827

1.11602

2.40439

5.18010

.719425

1.40

1.9600

2.74400

1.18322

3.74166

1.11869

2.41014

5.19249

.714286

1.41

1.9881

2.80322

1.18743

3.75500

1.12135

2.41587

5.20483

.709220

1.42

2.0164

2.86329

1.19164

3.76829

1.12399

2.42156

521710

.704225

1.43

2.0449

2.92421

1.19583

3.78153

1.12662

2.42724

5.22932

.699301

1.44

2.0736

2.98598

1.20000

3.79473

1.12924

2.43288

5.24148

.694444

1.45

2.1025

3.04863

1.20416

3.80789

1.13185

2.43850

5.25359

.689655

1.46

| 2.1316

3.11214

1.20830

3.82099

1.13445

2.44409

5.26564

.684932

1.47

2.1609

3.17652

1.21244

3.83406

1.13703

2.44966

5.27763

.680272

1.48

2.1904

3.24179

1.21655

3.84708

1.13960

2.45520

5.28957

.675676

1.49

2.2201

3.30795

1.22066

3.86005

1.14216

2.46072

5.30146

.671141

1.50

2.2500

3.37500

1.22474

3.87298

1.14471

2.46621

5.31329

.666667

n

n2

n3

Reciprocals 55

Reciprocals 56

Reciprocals 57

Reciprocals 58

Reciprocals 59

1/n

1.51

2.2801

3.44295

1.22882

3.88587

1.14725

2.47168

5.32507

.662252

1.52

2.3104

3.51181

1.23288

3.89872

1.14978

2.47713

5.33680

.667895

1.53

14400

3.58158

1.23693

3.91152

1.15230

2.48255

5.34848

.653595

1.54

2.3716

3.65226

1.24097

3.92428

1.15480

2.48794

5.36011

.649351

1.55

2.4025

3.72388

1.24499

3.93700

1.15729

2.49332

5.37169

.645161

1.56

2.4336

3.79642

1.24900

3.94968

1.15978

2.49866

5.38321

.641026

1.57

2.4649

3.86989

1.25300

3.96232

1.16225

2.50399

5.39469

.636943

1.58

2.4964

3.94431

1.25698

3.97492

1.16471

2.50930

5.40612

.632911

1.59

2.5281

4.01968

1.26095

3.98748

1.16717

2.51458

5.41750

.628931

1.60

2.5600

4.09600

1.26491

4.00000

1.16961

2.51984

5.42884

.625000

1.61

2.5921

4.17328

140080

4.01248

1.17204

2.52508

5.44012

.621118

1.62

2.6244

4.25153

1.97170

4.02492

1.17446

2.53030

5.45136

.617284

1.68

2•6569

4.33075

1.27671

4.03733

1.17687

2.53549

5.46256

.613497

1.64

2.6896

4.41094

1.28062

4.04969

1.17927

2.54067

5.47370

.609756

1.65

2.7225

4.49213

1.28452

4.06202

1.18167

2.54582

5.48481

.606061

1.66

2.7556

4.57430

140043

4.07431

1.18405

2.55095

5. 49586

.602410

1.67

2.7889

4.65746

1.29228

4.08656

1.18642

2.55607

5.50688

.598802

1.68

2.8224

4.74163

1.29615

4.09878

1.18878

2.56116

5.51785

.595238

1.69

2.8561

4.82681

1.30000

4.11096

1.19114

2.56623

5.52877

.591716

1.70

2.8900

4.91300

1.30384

4.12311

1.19348

2.57128

640000

.588235

1.71

2.9241

5.00021

1.30767

4.13521

1.19582

2.57631

5.55050

.584795

1.72

2•9584

5.08845

1.31149

4.14790

1 19815

2.58133

5.56130

.581395

1.73

2.9929

5.17772

1.31529

4.15933

1.20046

2.58632

5.57205

.578035

1.74

3.0276

5.26802

1.31909

4.17133

1.20277

2.59129

5.58277

.574713

1.75

3.0625

5.35938

1.32288

4.18330

1.20507

2.59625

5.59344

.571429

1.76

3.0976

5.45178

1.32665

4.19524

1.20736

2.60118

5 80401

.568182

1.77

3.1329

5.54523

1. 33041

4.20714

140004

1.00010

5.61467

.564972

1.78

3.1684

5.63975

1.33417

4.21900

1.21192

2.61100

5.62523

.561798

1.79

3.2041

5.73534

1.33791

4.23084

141418

2.61588

5.63574

.558659

1.80

3.2400

5.83200

1.34164

4.24264

1.21644

2.62074

5.64622

.555556

1.81

3.2761

5.92974

1.34536

4.25441

1.21869

2.62558

5.65665

.552486

1.82

3.3124

6.02857

1.34907

4.26615

140000

2.63041

5.66705

.549451

1.83

3.3489

6.12849

1.35277

4.27785

1.22316

2.63522

5.67741

.546448

1.84

3.3586

6.22950

1.35647

4.28952

1.22539

2.64001

5.68773

.543478

1.85

3.4225

6.33163

1.36015

4.30116

1.22760

2.64479

5.69802

.540541

1.86

3.4596

6.43486

1.36382

4.31277

1.22981

2.64954

5.70827

.537634

1.87

3.4969

6.53920

1.36748

4.32435

1.23201

2.65428

5.71848

.534759

1.88

3.5344

6.64467

1.37113

4.33590

1.23420

2.65900

5.72865

.531915

1.89

3.5721

6.75127

1.37477

4.34741

1.23639

2.66371

5.73879

.529101

1.90

3.6100

6.85900

1.37840

446000

1.23856

2.66840

5.74890

.526316

1.91

3.6481

6.96787

1.38203

4.37035

1.24073

2.67307

5.75897

.523560

1.92

3.6864

7.07789

1.38564

4.38178

1.24289

2.67773

5.76900

.520833

1.93

3.7249

7.18906

1.38924

4.39318

1.24505

2.68237

5.77900

.518135

1.94

3.7636

7.30138

1.39284

4.40454

1.24719

2.68700

5.78896

.515464

1.95

3.8025

7.41488

1.39642

4.41588

144000

2.69161

6.70000

.512821

1.96

3.8416

7.52954

1.40000

4.42719

1.25146

2.69620

5.80879

.510204

1.97

8.8800

7.64607

1.40067

4.43847

1.25359

2.70078

5.81865

.507614

1.98

3.9204

7.76239

1.40712

4.44972

1.25571

2.70534

5.82848

.505051

1.99

3.9601

7.88060

1.41067

4.46094

1.25782

2.70989

5.83827

.502513

2.00

4.0000

8.00000

1.41421

4.47214

1.25992

2.71442

5.84804

.500000

n

n2

n3

Reciprocals 60

Reciprocals 61

Reciprocals 62

Reciprocals 63

Reciprocals 64

1/n

2.01

4.0401

8.12060

1.41774

4.48330

1.26202

2.71893

5.85777

.497512

2.02

4.0804

8.24241

1.42127

4.49444

1.26411

2.72343

5.86746

.495050

2.03

4.1209

8.36543

1.42478

4.50555

1.26619

2.72792

5.87713

.492611

2.04

4.1616

8.48966

1.42829

4.51664

1.26827

2.73239

5.88677

.490196

2.05

4.2025

8.61513

1.43178

4.52769

1.27033

2.73685

5.89637

.487805

2.06

4.2436

8.74182

1.43527

4.53872

1.27240

2.74129

5.90594

.485437

2.07

4.2849

8.86974

1.43875

4.54973

1.27445

2.74572

5.91548

.483092

2.08

4.3264

8.99891

1.44222

4.56070

1.27650

2.75014

5.92499

.480769

2.09

4.3681

9.12933

1.44568

4.57165

1.27854

2.75454

5.93447

.478469

2.10

4.4100

9.26100

1.44914

4.58258

1.28058

2.75893

5.94392

.476191

2.11

4.4521

9.39393

1.45258

4.59347

1.28261

2.76330

5.95334

.473934

2.12

4.4944

9.52813

1.45602

4.60435

1.28463

2.76766

5.96273

.471698

2.13

4.5369

9.66360

1.45945

4.61519

1.28665

2.77200

5.97209

.469484

2.14

4.5796

9.80034

1.46287

4.62601

1.28866

2.77633

5.98142

.467290

2.15

4.6225

9.93838

1.46629

4.63681

1.29066

2.78065

5.99073

.465116

2.16

4.6656

10.0777

1.46969

4.64758

1.29266

2.78495

6.00000

.462963

2.17

4.7089

10.2183

1.47309

4.65833

1.29465

2.78924

6.00925

.460830

2.18

4.7524

10.3602

1.47648

4.66905

1.29664

2.79352

6.01846

.458716

2.19

4.7961

10.5035

1.47986

4.67974

1.29862

2.79779

6.02765

.456621

2.20

4.8400

10.6480

1.48324

4.69042

1.30059

2.80204

6.03681

.454546

2.21

4.8841

10.7939

1.48661

4.70106

1.30256

2.80628

6.04594

.452489

2.22

4.9284

10.9410

1.48997

4.71169

1.30452

2.81051

6.05505

.450451

2.23

4.9729

11.0896

1.49332

4.72229

1.30648

2.81472

6.06413

.448431

2.24

5.0176

11.2394

1.49666

4.73286

1.30843

2.81892

6.07318

.446429

2.25

5.0625

11.3906

1.50000

4.74342

1.31037

2.82311

6.08220

.444444

2.26

5.1076

11.5432

1.50333

4.75395

1.31231

2.82728

6.09120

.442478

2.27

5.1529

11.6971

1.50665

4.76445

1.31424

2.83145

6.10017

.440529

2.28

5.1984

11.8524

1.50997

4.77493

1.31617

2.83560

6.10911

.438597

2.29

5.2441

12.0090

1.51327

4.78539

1.31809

2.83974

6.11803

.436681

2.30

5.2900

12.1670

1.51658

4.79583

1.32001

2.84387

6.12693

.434783

2.31

5.3361

12.3264

1.51987

4.80625

1.32192

2.84798

6.13579

.432900

2.32

5.3824

12.4872

1.52315

4.81664

1.32382

2.85209

6.14463

.431035

2.33

5.4289

12.6493

1.52643

4.82701

1.32572

2.85618

6.15345

.429185

2.34

5.4756

12.8129

1.52971

4.83735

1.32761

2.86026

6.16224

.427350

2.35

5.5225

12.9779

1.53297

4.84768

1.32950

2.86433

6.17101

.425532

2.36

5.5696

13.1443

1.53623

4.85798

1.33139

2.86838

6.17975

.423729

2.37

5.6169

13.3121

1.53948

4.86826

1.33326

2.87243

6.18846

.421941

2.38

5.6644

13.4813

1.54272

4.87852

1.33514

2.87646

6.19715

.420168

2.39

5.7121

13.6519

1.54596

4.88876

1.33700

2.88049

6.20582

.418410

2.40

5.7600

13.8240

1.54919

4.89898

1.33887

2.88450

6.21447

.416667

2.41

5.8081

13.9975

1.55242

4.90918

1.34072

2.88850

6.22308

.414938

2.42

5.8564

14.1725

1.55563

4.91935

1.34257

2.89249

6.23168

.413223

2.43

5.9049

14.3489

1.55885

4.92950

1.34442

2.89647

6.24025

.411523

2.44

5.9536

14.5268

1.56205

4.93964

1.34626

2.90044

6.24880

.409836

2.45

6.0025

14.7061

1.56525

4.94975

1.34810

2.90439

6.25732

.408163

2.46

6.0516

14.8869

1.56844

4.95984

1.34993

2.90834

6.26583

.406504

2.47

6.1009

15.0692

1.57162

4.96991

1.35176

2.91227

6.27431

.404858

2.48

6.1504

15.2530

1.57480

4.97996

1.35358

2.91620

6.28276

.403226

2.49

6.2001

15.4382

1.57797

4.98999

1.35540

2.92011

6.29119

.401606

2.50

6.2500

15.6250

1.58114

5.00000

1.35721

2.92402

6.29961

.400000

n

n2

n3

Reciprocals 65

Reciprocals 66

Reciprocals 67

Reciprocals 68

Reciprocals 69

1/n

2.51

6.3001

15.8133

1.58430

5.00999

1.35902

2.92791

6.30799

.398406

2.52

6 8604

16.0030

1.58745

5.01996

1.36082

2.93179

6.31636

.396825

2.53

6.4009

16.1943

1.59060

5.02991

1.36262

2.93567

6.32470

.395257

2 54

6.4516

16.3871

1.59374

5.03984

1.88441

3.80868

6.33303

.393701

2.55

6.5025

16.5814

1.59687

5.04975

148888

2.94338

6.34133

.392157

2.56

6.5536

16.7772

1.60000

5.05964

1.36798

2.94723

6.34960

.390625

2.57

6.6049

16.9746

1.60312

5.06952

1.36976

2.95106

6.35786

.389105

2.58

6.6564

17.1735

1.60624

5.07937

1.37153

2.98488

6.36610

.387597

2.59

6.7081

17.3740

1.60935

5.08920

1.37330

2.95869

6.37431

.386100

2.60

6.7600

17.5760

1.61245

5.09902

1.37507

2.96250

6.38260

.384615

2.61

6.8121

17.7796

1.61555

5.10882

1.37683

2.96629

6.39068

.383142

2.62

6.8644

17.9847

1.61864

5.11859

1.37859

2.97007

6.39883

.381679

2.63

6.9169

18.1914

1.62173

5.12835

1.38034

2.9785

6.40696

.380228

2.64

6.9696

18.3997

1.62481

5.13809

1.38208

2.97761

6.41607

.378788

2.65

7.0225

18.6096

1.62788

5.14783

1.38383

2.98137

848810

.377359

2.66

7.0756

18.8211

1.63095

6.15753

1.38557

2.98511

6.43123

.375940

2.67

7.1289

19.0342

1.63401

5.16720

1.38730

2 80008

6.43928

.374532

2.6-

7.1824

19.2488

1.63707

5.17687

1.38903

2.99257

6.44731

.373134

2.69

T.SS61

19.4651

1.64012

5.18652

1.39076

2.99629

6.45531

.371747

2.70

7.2900

19.6830

1.64317

5.19615

1.39248

3.00000

6.46330

.370370

2.71

7.3441

19.9025

1.64621

5.20577

1.39419

3.00370

6.47127

.369004

2.72

74884

20.1236

1.64924

5.21536

1.39591

3.00739

6.47922

.367647

2.73

7.4529

20.3464

1.65227

5.22494

1.39761

3.01107

6.48715

.366300

2.74

7.5076

20.5708

1.65529

5.23460

1.39932

3.01474

6.49507

.364964

2.75

7.5625

20.7969

1.65831

5.24404

1.40102

3.01841

6.50296

888008

2.76

7.6176

21.0246

1.66132

5.25357

1.40272

3.02206

6.51083

.362319

2.77

7.6729

21.2539

1.66433

5.26308

1.40441

3.02571

6.51868

.361011

2.78

7.7284

21.4850

1.66733

5.27257

1.40610

3.02934

6.52652

.359712

2.79

7.7841

21.7176

1.67033

5.28205

1.40778

3.03297

648484

.358423

2.80

7.8400

21.9520

1.67332

5.29160

1.40946

3.03659

6.54213

.357142

2.81

7.8961

22.1880

1.67631

5.30094

1.41114

3.04020

6.54991

.355872

2.82

7.9524

22.4258

1.67929

5.31037

1.41281

3.04380

6.55767

.354610

2.83

B4088

22.6652

l.68226

5.31977

1.41448

3.04740

6.56541

.353357

2.84

8.0656

22.9063

1.68523

5.32917

1.41614

3.05098

6.57314

.352113

2.86

8.1225

23.1491

1.68819

5.33864

1.41780

3.05456

6.58084

880871

2.86

8.1796

23.3937

1.69115

5.34790

1.41946

3.05813

6.58853

.349650

2.87

8.2369

23.6399

1.69411

5.36724

1.42111

3.06169

6.59620

.348432

2.88

8.2944

23.8879

1.69706

5.36656

1.42276

3 60834

6.60385

.347222

2.89

8.3521

24.1376

1.70000

5.37587

1.42440

3.06878

6.61149

.346021

2.90

8.4100

24.3890

1.70294

5.38516

l.42604

3.07232

6.61911

844808

2.91

8.4681

24.6422

1.70587

5.39444

1.42768

3.07585

6.62671

.343643

2.92

8.5264

24.8971

1.70880

5.40370

1.49801

3.07936

6.63429

.342466

2.93

8.5849

25.1538

1.71172

5.41295

1.43094

8.00987

6.64185

.341297

2.94

8.6438

25.4122

1.71464

6.42218

l.43257

3.08638

644040

.340136

2.95

8.7025

25.6724

1.71756

5.43139

l.43419

3.08987

6.65693

488808

2.96

8.7616

25.9343

1.72047

5.44069

1.43581

3.09336

6.66444

.337838

2.97

8.8209

26.1981

1.72337

5.44977

1 43743

3.09684

6.67194

.336700

2.96

8.8804

26.4636

1.72627

5.45894

1.43904

3.10031

6.67942

.335571

2.99

8.9401

26.7309

1.73205

5.46809

1 14086

3.10878

6.68688

.334448

3.00

9.0000

27.0000

1.73205

5.47723

1.44225

3.10723

6.69433

.333333

n

n2

n3

Reciprocals 70

Reciprocals 71

Reciprocals 72

Reciprocals 73

Reciprocals 74

1/n

3.01

9.0601

27.2709

1.73494

5.48635

1.44385

3.11068

6.70176

.332226

3.02

9.1204

27.5436

1.73781

5.49545

1.44545

3.11412 6.70917

.331126

3.03

9.1809

27.8181

1.74069

5.50454

1.44704

3.11755 6.71657

.330033

3.04

9.2416

28.0945

1.74356

5.51362

1.44863

3.12098 6.72395

.328947

3.05

9.3025

28.3726

1.74642

5.52268

1.45022

3.12440

6.73132

.327869

3.06

9.3636

28.6526

1.74929

5.53173

1.45180

3.12781

6.73866

.326797

3.07

9.4249

28.9344

1.75214

5.54076

1.45338

3.13121

6.74600

.325733

3.08

9.4864

29.2181

1.75499

5.54977

1.45496

3.13461

6.75331

.324675

3.09

9.5481

29.5036

1.75784

5.55878

1.45653

3.13800

6.76061

.323625

3.10

9.6100

29.7910

1.76068

5.56776

1.45810

3.14138

6.76790

.322581

3.11

9.6721

30.0802

1.76352

5.57674

1.45967

3.14475

6.77517

.321543

3.12

9.7344

30.3713

1.76635

5.58570

1.46123

3.14812

6.78242

.320513

3.13

9.7969

30.6643

1.76918

5.59464

1.46279

3.15148

6.78966

.319489

3.14

9.8596

30.9591

1.77200

5.60357

1.46434

3.15484

6.79688

.318471

3.15

9.9225

31.2559

1.77482

5.61249

1.46590

3.15818

6.80409

.317460

3.16

9,9856

31.5545

1.77764

5.62139

1.46745

3.16152

6.81128

.316456

3.17

10.0489

31.8550

1.78045

5.63028

1.46899

3.16485

6.81846

.315457

3.18

10.1124

32.1574

1.78326

5.63915

1.47054

3.16817

6.82562

.314465

3.19

10.1761

32.4618

1.78606

5.64801

1.47208

3.17149

6.83277

.313480

3.20

10.2400

32.7680

1.78885

5.65685

1.47361

3.17480

6.83990

.312500

3.21

10.3041

33.0762

1.79165

5.66569

1.47515

3.17811

6.84702

.311527

3.22

10.3684

33.3862

1.79444

5.67450

1.47668

3.18140

6.85412

.310559

3.23

10.4329

33.6983

1.79722

5.68331

1.47820

3.18469

6.86121

.309598

3.24

10.4976

34.0122

1.80000

5.69210

1.47973

3.18798

6.86829

.308642

3.25

10.5625

34.3281

1.80278

5.70088

1.48125

3.19125

6.87534

.307692

3.26

10.6276

34.6460

1.80555

5.70964

1.48277

3.19452

6.88239

.306749

3.27

10.6929

34.9658

1.80831

5.71839

1.48428

3.19779

6.88942

.305810

3.28

10.7584

35.2876

1.81108

5.72713

1.48879

3.20104

6.89643

.304878

3.29

10.8241

35.6129

1.81384

5.73585

1.48730

3.20429

6.90344

.303951

3.30

10.8900

35.9370

1.81659

5.74456

1.48881

3.20753

6.91042

.303030

3.31

10.9561

36.2647

1.81934

5.75326

1.49031

3.21077

6.91740

.302115

3.32

11.0224

36.5944

1.82209

5.76194

1.49181

3.21400

6.92436

.301205

3.33

11.0889

36.9260

1.82483

5.77062

1.49330

3.21723

6.93130

.300300

3.34

11.1556

37.2597

1.82757

5.77927

1.49480

3.22044

6.93823

.299401

3.35

11.2225

37.5954

1.83030

5.78792

1.49629

3.22365

6.94515

.298508

3.36

11.2896

37.9331

1.83303

5.79655

1.49777

3.22686

6.95205

.297619

3.37

11.3569

38.2728

1.83576

5.80517

1.49926

3.23005

6.95894

.296736

3.38

11.4244

38.6145

1.83848

5.81378

1.50074

3.23325

6.96582

.295858

3.39

11.4921

38.9582

1.84120

5.82237

1.50222

3.23643

6.97268

.294985

3.40

11.5600

39.3040

1.84391

5.83095

1.50369

3.23961

6.97953

.294118

3.41

11.6281

39.6518

1.84662

5.83952

1.50517

3.24278

6.98637

.293255

3.42

11.6964

40.0017

1.84932

5.84808

1.50664

3.24595

6.99319

.292398

3.43

11.7649

40.3536

1.85203

5.85662

1.50810

3.24911

7.00000

.291545

3 44

11.8336

40.7076

1.85472

5.86515

1.50957

3.25227

7.00680

.290698

3.45

11.9025

41.0636

1.85742

5.87367

1.51103

3.25542

7.01358

.289855

3.46

11.9716

41.4217

1.86011

5.88218

1.51249

3.25856

7.02035

.289017

3.47

12.0409

41.7819

1.86279

5.89067

1.51394

3.26169

7.02711

.288184

3.48

12.1104

42.1442

1.86548

5.89915

1.51540

3.26482

7.03385

.287356

3.49

12.1801

42.5085

1.86815

5.90762

1.51685

3.26795

7.04058

.286533

3.50

12.2500

42.8750

1.87083

5.91608

1.51829

3.27107

7.04730

.285714

n

n2

n3

Reciprocals 75

Reciprocals 76

Reciprocals 77

Reciprocals 78

Reciprocals 79

1/n

3.51

12.3201

43.2436

1.87350

5.92453

1.51974

3.27418

7.05400

.284900

3.52

12.3904

43.6142

1.87617

5.93296

1.52118

3.27729

7.06070

.284091

3.53

12.4609

43.9870

1.87883

6.84188

1.52262

3.28039

7.06738

.283286

3.54

12.5316

44.3619

1.88149

5.94979

1.52406

3.28348

7.07404

.282486

3.55

12.6025

44.7389

1.88414

5.95816

1.52549

3.28657

7.08070

.281690

3.56

12.6736

45.1180

1.88680

5.96657

1.52692

3.28965

7.08734

.280899

3.57

12.7449

46.4993

1.88944

5.97495

1.52835

3.29273

7.09397

.280112

3.58

12.8164

664037

1.89209

5.98331

1.52978

3.29580

7.10059

.279330

3.59

12.8881

46.2683

1.89473

5.99166

1.53120

3.29887

7.10719

.278552

3.60

12.9600

46.6560

1.89737

6.00000

1.53262

3.30193

7.11379

.277778

3.61

13.0321

47.0459

1.90000

6.00833

1.53404

3.30498

7.12037

.277008

3.62

13.1044

47.4379

1.90263

6.01664

1.53545

3.30803

7.12694

.276243

3.63

13.1769

47.8321

1.90526

6.02495

1.53686

3.31107

7.13349

.275482

364

13.2496

48.2285

1.90788

6.03324

1.53827

3.31411

7.14004

.274725

3.65

13.3225

48.6271

1.91050

6.04152

1.53968

3.31714

7.14657

.273973

3.66

13.3956

49.0279

1.91311

6.04979

1.54109

3.32017

7.15309

.273224

3.67

13.4689

49.4309

1.91572

6.05805

1.54249

3.32319

7.15960

.272480

3.68

13.5424

49.8360

1.91833

6.06630

1.54389

3.32621

7.16610

.271739

3.69

13.6161

50.2434

1.92094

6.07454

1.54529

3.32922

7.17258

.271003

3.70

13.6900

50.6530

1.92354

6.08276

1.54668

3.33222

7.17905

.270270

3.71

13.7641

51.0648

1.92614

6.09098

1.54807

3.33522

7.18552

.269542

$.72

18.8384

51.4788

6.09918

1.54946

3.33822

7.19197

.268817

3.73

104130

614061

1.93132

6.10737

155085

3.34120

7.19841

.268097

8.74

13.9876

52.3136

1.99391

6.11555

1.55223

3.34419

7.20483

.267380

8.75

14.0625

52.7344

1.93649

6.12372

1.55362

3.34716

7.21125

.266667

3.76

14.1376

53.1574

1.93907

6.13188

1.55500

3.35014

7.21765

.265957

3.77

14.2129

53.5826

1.94165

6.14003

1.55637

3.35310

7.22405

.265252

3.78

14.2884

54.0102

1.94422

6.14817

1.55775

3.35607

7.23043

.264550

3.79

14.3641

64.4880

1.94679

6.15630

1.55912

3.35902

7.23680

.263852

3.80

14.4400

54.8720

1.94936

6.16441

1.56049

3.36188

7.24316

.263158

3.81

14.5161

55.3063

1.95192

6.17252

1.56186

3.36492

7.24950

.262467

3.82

14.5924

55.7430

1.95448

6.18061

1.56322

3.36786

7.25584

.261780

3.83

1 4 8888

56.1819

1.95704

6.18870

1.56459

3.37080

7.26217

.261097

3.84

56.6231

l.95959

6.19677

1.56595

3.37373

7.26848

.260417

3.85

14.8225

57.06666

1.96214

6.20484

1.56731

3.37666

7.27479

.259740

3.86

14.8996

57.5125

1.96469

6.21289

1.56866

3.37958

7.28108

.259067

3.87

14.9769

57.9606

1.96723

6.22093

1..57001

3.38249

7.28736

.258398

3.88

15.0544

58.4111

l.96977

6.22896

1.57137

3.38540

7.29363

..2577322.

3.89

15.1321

58.8639

1.97231

6.23699

1.57271

3.38831

7.29989

.257069

3 90

15.2100

59.3190

1.97484

6.24500

1.57406

3.39121

7.30614

.256410

3.91

15.2881

59.7765

1.97737

6.25300

1.57541

3.39411

7.31238

.255755

3.92

15.3664

60.2363

l.97990

6.26099

l .57675

3.39700

7.31861

.255102

3.93

15.4449

60.6985

1.98242

6.26897

1.57809

3.39988

7.32483

.254453

3.94

15.5236

61.1630

1.98494

6.27694

1.57942

3.40277

7.33104

.253807

3.95

15.6025

61.6299

1.98746

6.28490

1.58076

3.40564

7.33723

.253165

3.96

15.6816

014001

1.98997

6.29285

1.58209

3.40851

7.34342

.252525

3.97

15.7609

62.5708

1.99249

6.30079

1.58342

3.41138

7.34960

.251889

3.98

164404

63.0448

1.99499

6.30872

1.58475

3.41424

7.35576

.251256

3.99

15.9201

63.5212

1.99750

6.31664

1.58608

3.41710

7.36192

.250627

4.00

16.0000

64.0000

2.00000

6.32456

1.58740

3.41995

7.36806

.250000

n

n2

n3

Reciprocals 80

Reciprocals 81

Reciprocals 82

Reciprocals 83

Reciprocals 84

1/n

4.01

16.0801

64.4812

2.00250

6.33246

1.58872

3.42280

7.37420

.249377

4.02

16.1604

64.9648

2.00499

6.34035

1.59004

3.42564

7.38032

.248756

4.03

16.2409

65.4508

2.00749

6.34823

1.59136

3.42848

7.38644

.248139

4.04

16.3216

65.9393

2.00998

6.35610

1.59267

3.43131

7.39254

.247525

4.05

16.4025

66.4301

2.01246

6.36396

1.59399

3.43414

7.39864

.246914

4.06

16.4836

66.9234

2.01494

6.37181

1.59530

3.43697

7.40472

.246305

4.07

16.5649

67.4191

2.01742

6.37966

1.59661

3.43979

7.41080

.245700

4.08

16.6464

67.9173

2.01990

6.38749

1.59791

3.44260

7.41686

.245098

4.09

16.7281

68.4179

2.02237

6.39531

1.59922

3.44541

7.42291

.244499

4.10

16.8100

68.9210

2.02485

6.40312

1.60052

3.44822

7.42896

.243902

4.11

16.8921

69.4265

2.02731

6.41093

1.60182

3.45102

7.43499

.243309

4.12

16.9744

69.9345

2.02978

6.41872

1.60312

3.45382

7.44102

.242718

4.13

17.0569

70.4450

2.03224

6.42651

1.60441

3.45661

7.44703

.242131

4.14

17.1396

70.9579

2.03470

6.43428

1.60571

3.45939

7.45304

.241546

4.15

17.2225

71.4734

2.03715

6.44205

1.60700

3.46218

7.45904

.240964

4.16

17.3056

71.9913

2.03961

6.44981

1.60829

3.46496

7.46502

.240385

4.17

17.3889

72.5117

2.04206

6.45755

1.60958

3.46773

7.47100

.239808

4.18

17.4724

73.0346

2.04450

6.46529

1.61086

3.47050

7.47697

.239234

4.19

17.5561

73.5601

2.04695

6.47302

1.61215

3.47327

7.48292

.238664

4.20

17.6400

74.880

2.04939

6.48074

1.61343

3.47603

7.48887

.238095

4.21

17.7241

74.6185

2.05183

6.48845

1.61471

3.47878

7.49481

.237530

4.22

17.8084

75.1514

2.05426

6.49615

1.61599

3.48154

7.50074

.236967

4.23

17.8929

75.6870

2.05670

6.50385

1.61726

3.48428

7.50666

.236407

4.24

17.9776

76.2250

2.05913

6.51153

1.61853

3.48703

7.51257

.235849

4.25

18.0625

76.7656

2.06155

6.51920

1.61981

3.48977

7.51847

.235294

4.26

18.1476

77.3088

2.06398

6.52687

1.62108

3.49250

7.52437

.234742

4.27

18.2329

77.8545

2.06640

6.53452

1.62234

3.49523

7.53025

.234192

4.28

18.3184

78.4028

2,06882

6.54217

1.62361

3.49796

7.53612

.233645

4.29

18.4041

78.9536

2.07123

6.54981

1.62487

3.50068

7.54199

.233100

4.30

18.4900

79.5070

2.07364

6.55744

1.62613

3.50340

7.54784

.232558

4.31

18.5761

80.0630

2.07605

6.56506

1.62739

3.50611

7.55369

.232019

4.32

18.6624

80.6216

2.07846

6.57267

1.62865

3.50882

7.55953

.231482

4.33

18.7489

81.1827

2.08087

6.58027

1.62991

3.51153

7.56535

.230947

4.34

18.8356

81.7465

2.08327

6.58787

1.63116

3.51423

7.57117

.230415

4.35

18.9225

82.3129

2.08567

6.59545

1.63241

3.51692

7.57698

.229885

4.36

19.0096

82.8819

2.08806

6.60303

1.63366

3.51962

7.58279

.229358

4.37

19.0969

83.4535

2.09045

6.61060

1.63491

3.52231

7.58858

.228833

4.38

19.1844

84.0277

2.09284

6.61816

1.63616

3.52499

7.59436

.228311

4.39

19.2721

84.6045

2.09523

6.62571

1.63740

3.52767

7.60014

.227790

4.40

19.3600

85.1840

2.09762

6.63325

1.63864

3.53035

7.60590

.227273

4.41

19.4481

85.7661

2.10000

6.64078

1.63988

3.53302

7.61166

.226757

4.42

19.5364

86.3509

2.10238

6.64831

1.64112

3.53569

7.61741

.226244

4.43

19.6249

86.9383

2.10476

6.65582

1.64236

3.53835

7.62315

.225734

4.44

19.7136

87.5284

2.10713

6.66333

1.64359

3.54101

7.62888

.225225

4.45

19.8025

88.1211

2.10950

6.67083

1.64483

3.54367

7.63461

.224719

4.46

19.8916

88.7165

2.11187

6.67832

1.64606

3.54632

7.64032

.224215

4.47

19.9809

89.3146

2.11424

6.68581

1.64729

3.54897

7.64603

.223714

4.48

20.0704

89.9154

2.11660

6.69328

1.64851

3.55162

7.65172

.223214

4.49

20.1601

90.5188

2.11896

6.70075

1.64974

3.554X6

7.65741

.222717

4.50

20.2500

91.1250

2.12132

6.70820

1.65096

3.55689

7.66309

.222222