In the previous two posts, we discussed the meaning of significant figures, counting them in a number, and the rules of using them in addition, subtraction, multiplication, and division. These are the main ideas you need to remember when working on problems involving significant figures. When counting them, remember that significant figures apply to measured numbers such as length, volume speed and etc. because of the uncertainty in those measurements. Any standard number given by a definition is considered to have an infinite number of significant figures.

Now, when identifying them in a number, remember that all nonzero digits are significant. Whether a zero is significant or not, is determined based on its position. Read the article about significant figures for more information.

For the mathematical operations, you need to remember that in multiplication and subtraction, the answer is rounded off the same number of significant figures as the initial one with the fewest.

For addition and subtraction, you need to go based on the number of decimal places. In any calculation though, you want to keep in mind that the idea is to drop any numbers that are not significant. Read the article on significant figures in calculations for more details.

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1.
How many significant figures are in each number?

a) 632

b) 45.0

c) 4706.0

d) 0.0075

e) 0.006840

f) 0.15000

g) 2.30 x 10^{4}

h) 5,000

i) 1.234 x 10^{-3}

j) 340.010

k) 0.004050

a)
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b)
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c)
answer

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d)
answer

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e)
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f)
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g)
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h)
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i)
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Solution

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2.
Round off the following numbers as indicated.

a) 125.64 to 3 significant figures

b) 26547 to 4 significant figures in scientific notation

c) 9849 to 2 significant figures in scientific notation

d) 748965 to 5 significant figures in scientific notation

a)
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b)
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c)
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d)
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3.
Which numbers are exact indicating they have an unlimited number of significant figures?

a) MPG of the car showing as 28 miles per gallon

b) 1 km = 1000 m

c) A bag of potatoes labeled as 3 lb

d) A class with 26 students

e) 1 ft = 12 in

a)
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b)
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c)
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d)
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e)
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4.
Perform the following calculations and report the answers in the correct number of significant figures.

a)
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b)
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c)
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d)
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e)
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f)
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g)
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h)
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i)
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j)
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k)
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l)
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m)
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n)
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o)
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p)
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q)
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r)
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