Significant Figures
Suppose we are measuring the length of an object with a meter stick.
Is it 70 cm long?
How about 80 cm long?
Estimate at 74 cm long.
Remember 74 cm  0.74 m
When using a measuring device,
always estimate to the nearest tenth
of the smallest calibration.
What if the meter stick has one hundred calibration marks?
Then the smallest calibration is centimeters and we can therefore estimate to the
nearest tenth of a centimeter. (or thousandth of a meter)
74.0 cm  0.740 m
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)
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.
402 m
3
3. If a decimal point is expressed, all zeroes following
non-zero digits are significant.
42.0 m
42.00 m
420.000 m
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.
420 m
4 200 m
4 200. m
2 
2 
4 
How would you get 3 sig figs?
4.20 103 m
5. Zeroes preceding the first non-zero digit are not
significant, they are placeholders only.
0.042 m
0.0420 m
2 
3
State the number of significant figures in and the precision of each measurement
Example 56.1 m
3 significant figures – Rule 1
This measurement is precise to the nearest tenth of a meter
State the number of significant figures in and the precision of each measurement
1. 44.10 s
4 significant figures – Rules 1, 3
This measurement is precise to the nearest hundredth of a second
State the number of significant figures in and the precision of each measurement
2. 300. g
3 significant figures – Rules 1, 3
This measurement is precise to the nearest one gram
State the number of significant figures in and the precision of each measurement
3. 3.0 x 10-2 m = 0.030 m
2 significant figures – Rules 1, 3
When using significant figures and scientific notation, only the coefficient counts!
This measurement is precise to the nearest thousandth of a meter
State the number of significant figures in and the precision of each measurement
4. 0.0200 cm = 2.00 x 10-2 cm
3 significant figures – Rules 1, 3, 5
This measurement is precise to the nearest ten thousandth of a centimeter
State the number of significant figures in and the precision of each measurement
5. 302.040 kg
6 significant figures – Rules 1, 2, 3
This measurement is precise to the nearest thousandth of a kilogram
State the number of significant figures in and the precision of each measurement
3. 40 020 m = 4.002 x 104 m
4 significant figures – Rules 1, 2, 4
This measurement is precise to the nearest ten meters