Standard Form

4 Key excerpts on "Standard Form"

• 

  eBook - ePub

  Basic Engineering Mechanics Explained, Volume 1

  Principles and Static Forces

  • Gregory Pastoll, Gregory Pastoll(Authors)
  • 2019(Publication Date)
  • Gregory Pastoll

    (Publisher)

  Chapter 3 Working with numbers in engineering

  • Engineering notation, as opposed to scientific or ordinary notation

  • The number of significant figures in a value

  • Required format of answers for engineering purposes

  • Loss of accuracy when rounding off numbers during a calculation

  • The units that apply to mechanical quantities in the S.I. system

  • The difference between precision and accuracy

  • The limitations of precision in a primarily practical science

  • Converting the units of quantities, e.g. miles per hour to metres per second

  • Units preferred by engineers

  An engineering student needs to know how to write and interpret numbers for the purposes of engineering. At some stage in your career, you will be writing lab and other types of investigative reports, performing calculations, and showing the results of your calculations. It is essential to get to know the conventions.

  Engineering notation, as opposed to scientific or ordinary notation Any given number can be expressed in three ways: ordinary arithmetic notation, scientific notation, and engineering notation.

  Ordinary arithmetic notation is what comes up on your calculator readout when you key in a sequence of digits. For example: 86.5 or 374.29 or 128502.972

  Scientific notation is a way of writing a number in terms of multiples of powers of ten. For example: 1.284 × 104 or 4.932 × 1017 or 7.996 × 10−6 . In scientific notation, the aim is to express the number as compactly as possible. Only one digit is allowed in front of the decimal point, and any multiple of powers of 10 can be used.

  Often, however, numbers expressed in scientific notation, though mathematically valid, are not conveniently practical for engineers to work with. For this reason, engineering notation was developed.

  Consider the number, in ordinary notation: 154 300. A scientist would write it as 1.543 x 105, whereas an engineer would write it as 154.3 x 103. If both are mathematically correct, what’s the difference, and why is there a difference?

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  eBook - ePub

  Science and Technical Writing

  A Manual of Style

  • Philip Rubens(Author)
  • 2002(Publication Date)
  • Routledge

    (Publisher)
• Place a decimal point to the right of the first nonzero digit in the number,
• Delete all nonsignificant zeros (see 7.38 ), and
• Multiply the resulting number by the power of ten required to make the product equal to the original number.
Thus:247,000,000 becomes 2.47 108 in scientific notation, and0.000014647 becomes 1.4647 10–5 .

7.29

The exponent (the power of ten) can be negative or positive depending on whether the number being represented is smaller or larger than 1 (the number 1 is equal to ten to the zero power). A factor of 100 is customarily omitted. Various examples of small or large numbers and their equivalents in scientific notation include

27.5	2.75 × 10 (not 2.75 × 101 )
1.375	1.375 (not 1.375 × 100 )
37,040,000	3.704 × 107 (assuming the trailing zeros are not significant)
2,000,000	2 × 106 (not 2.0 × 106 )(assuming the trailing zeros are not significant)
0.000715	7.15 × 10-4
0.09004	9.004 × 10-2
0.000000000145	1.45 × 10-10
10.07	1.007 × 10

7.30

The factor preceding the power of ten, the “mantissa,” is normally between one and ten, as in the preceding examples. However, there is an alternative convention of representing numbers in scientific notation so that the power of ten is a multiple of three. This practice fits the structure of the prefixes used in the International System of Units (see 7.41 ). When this convention is used, the mantissa will be between 1 and 999:149.598 × 106 km (not 1.495 98 108