SIGNIFICANT FIGURES

Are they significant, or “insignificant”?

SIGNIFICANT…

…means “important”

There is no such a thing as an “insignificant figure”.

Digits that are not significant are called “non-significant digits”

RULES for determining which figures are significant

1. Non-zero digits are always significant.Ex: 0.0509 and 203,400.0

2. Trailing zeros to the right of the decimal point are significant.

Ex: 0.0509 and 203,400.0

3. Zeros between non-zero digits are significant.Ex: 0.0509 and 203,400.0

RULES (cont’d)

4. Zeros between non-zero digits and a decimal point are significant.

Ex: 0.0509 and 203,400.0

5. Zeros used solely to place the decimal point are not significant.

Ex: 0.0509 and 203,400.0

Answer: 0.0509 has 3 and 203,400.0 has 7 sig. figs.

OPERATIONS with SIG. FIGS

There are two categories of operations with sig. figs we will consider. Each has its own set of rules.

ADDITION/SUBTRACTION

MULTIPLICATION/DIVISION

Note: they are a simplification of the more general rules to all operations, which are beyond the scope of this course.

Addition/Subtraction Rule• The final answer has the same number of digits

to the right of the decimal point as the number with the smallest number of digits to the right of the decimal point.

• Example: 97.3 + 5.85 = 103.1597.3 has one digit after the decimal5.85 has two digits after the decimal

answer = 103.2 (one digit after the decimal)

Note that both numbers have 3 sig. figs!

Multiplication/Division Rule

• The final answer must have the same number of significant figures as the least precise measurement – the one with the least number of sig. figs.

• Example: 6.78 * 34 = 230.526.78 has 3 sig. figs34 has 2 sig. figs

answer = 230 (2 sig. figs)

THE END

Lilian Wehner ©