Wize University Statics Textbook (Master) > Introduction

Significant Figures 

Significant figures indicate the precision of a measurement and determine how precisely a calculated number can be represented.

Rules for identifying significant figures:
All non-zero numbers are significant.
Place holder zeros and leading zeros (zeros on the left of the number) are not significant.
Extra zeros after a decimal point are significant.
Zeros between two other significant figures are significant.
All digits in scientific notation are significant.

Watch Out!
Counting numbers are exact, and have no uncertainty. If I have 4 goats, I am absolutely sure that I have 4 goats. Unless I'm very bad at counting things.
This means we don't assign significant figures to these values.


Examples: 

 0.00450.00450.0045 has two
 significant figures 
 234000234000234000 has three
 significant figures 
 234000.0234000.0234000.0 has seven
 significant figures 
 3.400×1053.400 \times 10^53.400×105 has four
 significant figures  

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Significant Figures in Calculations

If sig figs tell us how precise a number is, what happens when we do calculations with them? How many sig figs will be in our final answer?

Wize Concept
A number should not get more precise just because we are doing a mathematical operation to it. Always make sure you are looking at the least reliable digit, or the least reliable number. 

Addition and subtraction
Write your answer to the decimal point of the last s.f. of the least reliable value.

Examples:

1200.0cm+ 12.24cm= 1212.24cm→1212.2cm1200.0cm +\ 12.24cm =\ 1212.24cm \rightarrow 1212.2cm1200.0cm+ 12.24cm= 1212.24cm→1212.2cm

57.23oC−273.2oC+69oC=−146.97oC→−147oC57.23^oC - 273.2^oC +  69^oC = -146.97^oC \rightarrow -147^oC57.23oC−273.2oC+69oC=−146.97oC→−147oC

Multiplication and division
Write your answer to the same number of s.f. as the value with the least number of s.f.

Examples:

1200.0cm×12.24cm= 14688cm→14690cm1200.0cm \times 12.24cm =\ 14688cm \rightarrow 14690cm1200.0cm×12.24cm= 14688cm→14690cm

57.23oC×273.2oC÷69oC=226.5976...oC→230oC57.23^oC \times 273.2^oC \div   69^oC = 226.5976...^oC \rightarrow 230^oC57.23oC×273.2oC÷69oC=226.5976...oC→230oC

Wize Tip
Try to keep as many s.f. as you can until the final answer. Then round them off to the correct number of s.f.

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Examples: Significant Figures

Here are some examples to clarify significant figures.

How many significant figures are in the below numbers
1128.01001km1128.01001km1128.01001km
002.54min002.54min002.54min
23.5m/s23.5m/s23.5m/s
1990K1990K1990K

a. 9 s.f.
b. 3 s.f.
c. 3 s.f.
d. 3 s.f.

2.  How many significant figures are in the final answer?

(2.3+23)×210.3(2.3 + 23) \times 210.3(2.3+23)×210.3

2 s.f.

The addition portion will leave us with 2 s.f., since the least reliable digit is in 232323 , which is precise to the ones place.

Multiplying with 210.3210.3210.3, we will keep our answer to 2 s.f., since that is the lowest number of s.f. between the two values.

3. How many significant figures are in the final answer?

$21.02+$1.313 shirts\dfrac{\$21.02 + \$1.31}{3\text{ shirts}}3 shirts$21.02+$1.31​

4 s.f.

Remembering order of operations, we will do the addition first. This will leave us with 4 s.f., since both $21.02\$ 21.02$21.02 and $1.31\$1.31$1.31are both equally reliable to the hundreths place.

Then dividing by 3 shirts. Remember that counting numbers are exactly precise, so we cannot give it any s.f. The lowest number of s.f. is 4, from $22.33\$22.33$22.33 which is what our final answer will have.

Write your answer to the following with the correct significant figures.
0.125+1.22200.0×32.4\frac{0.125 + 1.22}{200.0 \times 32.4}200.0×32.40.125+1.22​

Answer

I don't know