This document provides information about significant figures and how they are used in scientific measurements and calculations. It defines significant figures as the reliable digits in a measurement that are known with certainty, indicating the accuracy of the measurement. Rules are presented for determining the number of significant figures in given measurements, as well as rules for performing calculations while preserving the correct number of significant figures based on the least accurate measurement in the calculation. Examples are provided to demonstrate applying the significant figures rules when adding, subtracting, multiplying and dividing measurements.

1. OPHS Chemistry
Unit 1
Scientific Inquiry & Measurement
Section 4: Significant Figures & Scientific Notation

2. Significant Figures
• There are 2 kinds of numbers:
– Exact: the amount of money in your account. Known
with certainty.
– Approximate (MEASURED): weight, height—no
measurement is perfect.
• Significant figures are the reliable digits in a
measurement which are known with certainty. They
show the accuracy in measurements.
– A measurement that contains more number of
significant figures is more accurate than a
measurement that contains less number of
significant figures.
2

3. Significant Figures
• When a measurement is recorded only those digits
that are dependable are written down.
• If you measured the width of a paper with your ruler
you might record 21.7cm.
– To a mathematician 21.70, or 21.700 is the same.
– But to a scientist…
• 21.700cm to a scientist means the measurement
is accurate to within one thousandth of a cm.
• If you used an ordinary ruler, the smallest
marking is the mm, so your measurement has to
be recorded as 21.7cm. 3

4. Significant Figure Rules
• Non-zeros are always significant, ex: 1, 2, 3, 4, …9
• Zeros between non-zeros are significant, ex: 109
• Zeros at the end of significant digits following a
decimal point are significant (they show
precision in measurement), ex: 139.00
• Place keeper zeros are NOT significant
– Zeros preceding significant digits, ex: 0.1
– Zeros following significant digits without a
decimal point, ex: 10
4
X
X

5. Practice
5
Measurement
1.2
4.00
0.0792
7,083,000,00
0.5
56.76
2100
2100.
7 x 105
# of Significant Figures
2
3
3
4
1
4
2
4
1

6. Adding/Subtracting
Significant Figures
Rule: When adding or subtracting measured
numbers, the answer can have no more places after
the decimal than the LEAST of the measured
numbers.
• 2.45 cm + 1.2 cm = 3.65cm
Round to = 3.7cm (answer has 1 decimal place)
• 7.432 cm + 2 cm = 9.432
Round to = 9cm (answer has 0 decimal places)
6
2 1
03

7. Multiplying/Dividing
Significant Figures
Rule: When multiplying or dividing measured
numbers, the answer can have no more significant
figures (SF) than the LEAST reliable measurement
(i.e., the least number of significant figures)
• 56.78 cm + 2.45 cm = 139.111 cm2
Round to = 139 cm2 (answer has 3 SF)
• 75.8 cm + 9.6 cm = 727.68 cm2
Round to = 7.2 x 102 cm2 (answer has 2 SF)
7
4 SF 3 SF
2 SF3 SF