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 ≥ 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   =  10 x 10 x 10 x 10 x 10 x 10  =  1,000,000

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

Power of 10 is less than 1 if the index is a negative number. In this case, the number of zero(s) is after the decimal point  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   = $$\frac{1}{10^6} \scriptsize = 0.000001$$

### Example 1

Convert these powers of 10 to figures:

a. 104

b. 105

c. 10-5

Solution

a. 104 = 10 × 10 × 10 × 10 = 10 000

b. 105 = 10 × 10 × 10 × 10 × 10 =  100  000

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

### Example 2

Express these as powers of 10:

a. 10 × 10 × 10 × 10 × 10
b. 10 × 10 × 10
c. One million
d. One-millionth
e. One billionth
f. One hundred thousand

Solution

a. 10 × 10 × 10 × 10 × 10  =  105

b. 10 × 10 × 10   =  103

c. One million = 1,000,000 =  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   =  100,000  =  105

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