Significant Figures

Suppose we are measuring the length of an object with a meter stick.

long? it Is cm70 long? aboutHow cm80

long. at Estimate cm74

When using a measuring device, always estimate to the nearest tenth

of the smallest calibration.

mcm Remember 74.074

What if the meter stick has one hundred calibration marks?

cm 0.74 mcm 740.00.74

In this case we know that the 0 is the estimated digit because we made the measurement.

Significant Figures – All of the digits in a measurement that represent marked calibrations plus the one estimated digit (tenths of the smallest calibration)

Then the smallest calibration is centimeters and we can therefore estimate to the nearest tenth of a centimeter. (or thousandth of a meter)

Rules for counting Significant Figures

1. All non-zero digits in a measurement are significant.

2. Zeroes are significant if bounded by non-zero digits. m 402 3

3. If a decimal point is expressed, all zeroes following non-zero digits are significant.

m 0.42m 00.42

m 000.420

3 4 6

4. If a decimal point is not explicitly expressed, zeroes following the last non-zero digit are not significant, they are placeholders only.

m 420

m 2004m .2004

2 2

4

How would you get 3 sig figs?

m 31020.4

5. Zeroes preceding the first non-zero digit are not significant, they are placeholders only.

m 042.0

m 0420.0 3

2

Example 56.1 m

State the number of significant figures in and the precision of each measurement

This measurement is precise to the nearest tenth of a meter

3 significant figures – Rule 1

1. 44.10 s

This measurement is precise to the nearest hundredth of a second

4 significant figures – Rules 1, 3

State the number of significant figures in and the precision of each measurement

2. 300. g

This measurement is precise to the nearest one gram

3 significant figures – Rules 1, 3

State the number of significant figures in and the precision of each measurement

3. 3.0 x 10-2 m

This measurement is precise to the nearest thousandth of a meter

2 significant figures – Rules 1, 3

When using significant figures and scientific notation, only the coefficient counts!

State the number of significant figures in and the precision of each measurement

3. 3.0 x 10-2 m = 0.030 m

4. 0.0200 cm

This measurement is precise to the nearest ten thousandth of a centimeter

3 significant figures – Rules 1, 3, 5

State the number of significant figures in and the precision of each measurement

4. 0.0200 cm = 2.00 x 10-2 cm

5. 302.040 kg

This measurement is precise to the nearest thousandth of a kilogram

6 significant figures – Rules 1, 2, 3

State the number of significant figures in and the precision of each measurement

3. 40 020 m

This measurement is precise to the nearest ten meters

4 significant figures – Rules 1, 2, 4

State the number of significant figures in and the precision of each measurement

3. 40 020 m = 4.002 x 104 m