What time is it?

• Someone might say “1:30” or “1:28” or “1:27:55”

• Each is appropriate for a different situation

• In science we describe a value as having a certain number of “significant digits”

• The # of significant digits in a value includes all digits that are certain and one that is uncertain

• “1:30” likely has 2, 1:28 has 3, 1:27:55 has 5

• There are rules that dictate the # of significant digits in a value

Rules for Determining Significant Zeros

Rule Examples

1) Zeros appearing between nonzero digits are significant

a) 40.7 has 3 sig. figs.

b) 87009 kL has five sig. figs

2) Zeros appearing in front of all nonzero digits are not significant

a) 0.095897 m has 5 sig. figs.

b) 0.0009 kg has 1 sig. fig.

3) Zeros at the end of a number and to the right of a decimal point are significant

a) 85.00 m has 4 sig. figs.

b) 9.0000000 g has 8 sig. figs.

4) Zeros at the end of a number but to the left of a decimal point may or may not be significant

a) 2000 m has 1 sig. fig.

b) 2000. m has 4 sig. figs

12.6172 has 6 significant figures1.7 has 2 significant figures

Student Challenge. Identify the number of significant digits shown in each of the following examples.

A) 259

B) 3500

C) 0.050090

D) 4.50 x 108

E) 0.004

F) 3500.

Rule for Multiplication and Division

For multiplication and division, your answer must show the same number of significant digits as the measurement in the calculation with the least number of significant digits.

Rule for Addition and Subtraction

For addition and subtraction, your answer must show the same number of decimal places as the number in the calculation with the least number of decimal places.

Rule for Addition and Subtraction

For example,

25.1 g + 2.03 g = 27.13 g

27.13 suggests that we can measure

with certainty to the hundreths place.

But the measurement of 25.1 says

we don’t know that value with

certainty to the hundredths place.

So we must round down to 27.1 g.

Rule for Multiplication and Division

For example,

3.40 cm x 12.61 cm x 18.25 cm = 782.4505 cm3 before rounding

We, can’t report an answer with seven significant digits if the measurement with the least number of significant digits in our calculation, 3.40 cm, shows only three significant digits. We must round our answer to three significant digits, giving us a rounded answer of 782 cm3.