Lesson 6, Topic 1
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Power of 10

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The power of ten is ten multiplied by itself a certain number of times. It is a way of writing very large and very small sizes compactly.

By the power of 10, we mean 10 multiplying itself several times.

1. Examples of Power of 10, greater than or equal to 1 ( 100 â‰¥ 1)

10o   =  1

101  =  10

102  =  10 x 10  =  100

103  = 10 x 10 x 10  =  1000

104  =   10 x 10 x 10 x 10  =   10,000

105   =  10 x 10 x 10 x 10 x 10   =  100,000

106 Â  =Â  10 x 10 x 10 x 10 x 10 x 10Â  =Â  1,000,000

2. Example of Power of 10 less than 1Â  (10 < 1)

Power ofÂ 10 is less than 1 if the index is a negative number. In this case, the number of zero is after the decimal pointÂ  e.g

10-1  = $$\frac{1}{10} \scriptsize = 0.1$$

10-2  = $$\frac{1}{10^2} \scriptsize = 0.01$$

10-3  = $$\frac{1}{10^3} \scriptsize = 0.001$$

10-4  = $$\frac{1}{10^4} \scriptsize = 0.0001$$

10-5  = $$\frac{1}{10^5} \scriptsize = 0.00001$$

10-6 Â  = $$\frac{1}{10^6} \scriptsize = 0.00001$$

Example 1

Convert theseÂ powers of 10 to figures

a. 104

b. 105

c. 10-5

Solution

a. 104 = 10×10 x 10 x 10 = 10 000

b. 105 = 10 x 10 x 10 x 10 x 10 =  100  000

c. 10-5 Â = $$\frac{1}{10^5} \scriptsize = 0.00001$$

Example 2

Express these as powers of 10

a. 10 x 10 x 10 x 10 x 10

b. 10 x 10 x 10

c. One million

d. One-millionth

e. One billionth

f. One hundred thousand

Solution

a. 10 x 10 x 10 x 10 x 10Â  =Â  105

b. 10 x 10 x 10 Â  =Â  103

c. One million = 1,000,000 =Â  106

d. One millionth= $$\frac{1}{1000000} \\ = \frac{1}{10^6} \\ = \scriptsize 10^{-6}$$

e. One billionth= $$\frac{1}{1000000000} \\= \frac{1}{10^9}\\ = \scriptsize 10^{-9}$$

f. One hundred thousand Â  =Â  100,000Â  =Â  105

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