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10. If 6 2x + 1 ÷ 36 = 216, find the value of x.
11. Find the value of x if
x
 5 − 5  5 − 11  5 8x  2 − 3  2 8  2 2 + 1
(a)   ×   =   (b)   ×   =  

3

3
7 

7 

3

7 

12. Write the following decimals in expanded form using exponents of 10.
(a) 2.368 (b) 45.2394 (c) 0.359898
Use of Exponents to Express Small Numbers and Large
Numbers in Standard Form/Scientific Notation
In previous class, we have learnt how to write large numbers such as mass of the Sun, speed of
light, diameter of the Earth, etc., in scientific notation. Let us recall it with an example.
The mass of the Earth is 5,970,000,000,000,000,
000,000,000 kg. It is represented in standard form A number is said to be in the scientific
n
(scientific notation) as 5.97 × 10 kg. Note: notation if it is in the form k × 10 , where
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1 ≤ k < 10 and n is any integral power.
We can also represent very small numbers using
power notation. It can be done by use of exponents which are negative integers.
The average diameter of a Red Blood cell is 0.000007 m. We can write it in standard form as
–6
7.0 × 10 m Conversion to Scientific Notation
This notation expresses a number
as the product of a decimal number 2.7,600,000,000. 0.00007.3
and a power of 10. The number has 10 9 8 7 6 5 4 3 2 1 1 2 3 4 5
one digit to the left of the decimal
point, and the exponent of 10 10 Places to the Left! 5 Places to the Right!
indicates how many places the Moving to left Positive Exponent Moving to Right Negative Exponent
decimal point has to move. 2.76 × 10 10 7.3 × 10 –5

• If the decimal point has moved
to the left, then we multiply by a positive power of 10.
• If the decimal point has moved to the right, then we multiply by a negative power of 10.

Example 8: Write scientific notation for the following numbers:
(a) 14960000000 (b) 0.0000078 (c) 0.0000002465

Solution: (a) 14960000000 = 1.496 × 10000000000 = 1.496 × 10 10
.
78 78 78 10
×
78 × 10 10
78 10
(b) 0.0000078 = = = = . × − 7 = . × − 6
10000000 10 7 10 7
.
2465 2465 2 465 1000
×
×
2 465 10 ×
(c) 0.0000002465 = = = = . × 3 10 − 10 = 2.4465 10 − 7
10000000000 10 10 10 10
Example 9: Express the numbers used in the following facts in the scientific notation.
(a) The speed of the light is 300000000 m/s.
(b) The distance from the Earth to the Moon is 384400000 m.
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Solution: (a) The speed of light = 300000000 m/s = 3 × 10 m/s.
8
(b) The distance from the Earth to the Moon = 384400000 m = 3.844 × 10 m.
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