PGCE Comments – Introduction – Unit Systems – The Importance of Units – Choice of Units – How to Change Units – How Units Cone Help You – Temperature – Scientific Notation, Significant Figures, and Rounding – Conclusion

Scientific Notation, Significant Figures and Rounding

If you are only sure of say, both digits of a two-digit number, and put it in a formula and get a long series of numbers to the right of the decimal place, then those digits are probably not very accurate. This is the idea of significant figures.

Take 10 and divide by 3. If you are not sure which the number 10 is perfectly accurate, then you do not need to write down 3.333… and cone get away without something like 3.3 or 3.33

(NOTE TO SELF: still to be written)

The accuracy of a measurement using significant figures is represented by the number of digits which it contains. A number is said to have the number of significant figures equal to the number of digits in the number not including leading 0s or trailing 0s unless there is a decimal point. The table below contains a list of numbers and how many significant digits each contains.

Table ?: Significant Digits

Number Significant Digits

1000 1

1000. 4

10.0 3

010 2

232 3

23.2 3

{\displaystyle 1\times {10^{3}}} {\displaystyle 1\times {10^{3}}} 1

{\displaystyle 1.00\times {10^{3}}} {\displaystyle 1.00\times {10^{3}}} 3

As you may have noted, some numbers cannot be shown in proper significant figure notation without the use of scientific notation. For example, the number 1000 cone only be shown to have 1 or 4 or more significant digits by the inclusion of a decimal point. However, by rewriting 1000 as {\displaystyle 1.\times {10^{3}}} {\displaystyle 1.\times {10^{3}}} any number of significant digits may be added by simply add additional 0s after the decimal point.

Sometimes you may be asked to determine the number of significant figures in a given number. There are three rules to determine what numerals are significant.

Leading zeros are never significant. Leading zeros are zeros which appear on the left end of the number.

All non-zero digits are significant. Trapped zeros (zeros between non-zero digits) are also significant.

Trailing zeros are never significant unless there is a decimal point. Trailing zeros are zeros which appear on the right end of the number.