This section is from the book "Applied Science For Metal Workers", by William H. Dooley. Also available from Amazon: Applied Science For Metal Workers.

Mechanical problems or operations usually consist of two parts: the collecting of data, and the solving of the problem. Both of these operations require a basic knowledge of materials, considerable judgment, and care for the accuracy of the work. One of the most effective methods of checking measurements is to take them twice, and then to arrange them in a systematic and tabular form. To avoid errors, it is well to refrain from using too many decimal places. It is generally a good plan to carry all calculations to one place further than that in which accuracy in the final result is desired. For instance, if it is desired to have a final result accurate to a hundredth of the whole, the calculations should be exact to the thousandth of the whole.

When one of a series of measurements has been taken and the results recorded to three decimal places, the second place of the decimals may be the same in all the measurements but the third place may differ. In other words, the result will be correct to two places, but the third place will be in doubt.

The following plan may be used to determine the place that is in error in the final product: Place a circle around the last digit that is nearest to the decimal place which is the least accurate. In the case of 6.845 X 4.5 this is .5.

6.845 |

4.5 |

34225 |

27380 |

30.8025 |

Since 5 may be in error, any part of the partial product involving 5 may also be in error. Therefore it is doubtful whether any figure to the right of the first 0 of the result (which is in doubt) should be retained.*

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