Download Rules for Significant Figures

Name: ___________________________
Date: ____________________________
Flynt - ___ Period
___th Grade Science
Significant Figures
Any measurement is inaccurate to some degree. The inaccuracy stems from several factors—the precision
of the measuring device used, errors by the person doing the measurement, a faulty experimental
technique, etc. In scientific investigations, communicating our uncertainty in a measurement is equally
important as the measurement itself. We convey our uncertainty in measured quantities by abiding by
the rules of significant figures.
Rules for Significant Figures
1. Significant figures in a measurement made by you, the scientist, include all of the digits that
are known precisely plus one last digit that is estimated.
2. Non-zero digits (numbers 1-9) in measurements are always significant.
103.230002
3. Final zeros after the decimal point in measurements are always significant.
0.0420
4. Zeros located between other significant digits are always significant.
6.000
12.740 ;
10.0 ; 2004 ;
5. Zeros used only for spacing the decimal point are NOT significant.
a) Zeros to the left of non-zero digits serve only to locate the decimal point; they are NOT
significant.
.00000233 ; 0.05
b) Any zero printed to the right of a non-zero digit may or may not be significant if there is no
decimal point indicated.
100
o
For example, if someone tells you that a mountain is 3600 m high, he or she is probably
certain of the 3, and estimated or rounded the 6. In other words, there are likely 2
significant digits in the measurement (the tens and ones were not measured). 3600
o
However, 3600 m could also have 3 significant digits (if the measurement was taken to
the nearest 10 meters, but not to the nearest meter) or even 4 significant digits (if the
measurement was taken to the nearest 1 m). But we have no way of knowing based on
the info provided.
o
UNLESS… the number is written in scientific notation OR unless a decimal is added
to indicate the level of significance! 3.60 x 103 ; 3600.

In fact, one reason for writing a number in scientific notation is to clearly indicate
the number of significant digits!
6. If you add or subtract two numbers, the answer is rounded to the same number of decimal
places as the measurement with the least number of decimal places.
7. If you multiply or divide two numbers, the answer is rounded off to the number of significant
figures in the least precise term used in the calculation (i.e. the measurement with the fewest
significant figures).
8. All mathematical constants and any number that is counted instead of measured has an infinite
number of significant digits. There are 3 test tubes (assumed to be 3.000000000… to ∞ b/c you
wouldn’t count a fraction of a test tube) ; When multiplying by 100 to calculate a percent
(100.00000000… to ∞)
Practice Identifying Significant Figures:
1. Identify the number of significant digits in each of the following.
2. Then write the # for each of the RULES that supports your answer choice!!!
1) 705 kg
2) 0.00056 dL
3) 40280. cm
4) 2.003 mg
6) 23.7 x 10-5 m
7) 1.4 x 107 kL
8) 4.000 x 104 dkg 9) 43,000.08 hm
5) 600.0 g
10) 0.020 L
RULE #6 Practice: When adding or subtracting your answer can only show as many decimal places
as the measurement having the fewest number of decimal places.
Perform the following calculations and round according to the rule above.
1)
4)
4.60 m + 3 m =
200 dkg - 87.3 dkg =
2)
0.008 cg + 0.05 cg =
3)
5)
67.5 km - 0.009 km =
6)
22.4420 mL + 56.981 mL =
71.86 L - 13.1 L =
RULE #7 Practice: When multiplying or dividing, your answer may only show as many significant
digits as the multiplied or divided measurement showing the least number of significant digits.
Perform the following calculations and round according to the rule above.
1)
4)
13.7 m x 2.5 m =
5003 m / 3.781 sec =
2)
200 cm x 3.58 cm =
3)
5)
89 g / 9.0 cm3 =
6)
0.00003 km x 727 km =
5000 mg / 55 mL =