Page 45 - Start Up Mathematics_8 (Non CCE)

 7  − 1 25
11. By what number should   be divided to give the quotient as ?
12. Find x, if:  3  21

− 
− 
 1  − 8  1  − 4  1  − 4x  −  1 −18  −  1 7  −  1 −2x + 1  3 14  3 −3  3 3x + 2
− 
(a)   ×   =   (b)   ÷   =   (c)   ×   =  
 5   5   5   3   3   3   5   5   5 
 2  − 4  3  2
–2
13. If x =   ×   , find the value of (a) (x) (b) (x) –1
 3   2 
1
5
p   −2   2  p  −3
14. If =   ÷   , find the value of   .
5
6
q      q 
2m
7
2
–4
–3
5
15. Find the value of m, if: (a) (6) ÷ (6) = (6) (b) (9) –3m ÷ (9) = (9) (c) (–5) m – 1 ÷ (–5) = (–5) –6
Use of Exponents to Express Small Numbers in Standard Form
You already know how to write large numbers in standard form using exponential notations.
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For example: Speed of light is 300,000,000 m/s = 3 × 10 m/s
8
Solar radius is 69,57,00,000 m (approx.) = 6.957 × 10 m
Similarly, we can write very small numbers in standard form using exponential notations. This can be done
by following the given method:
0
0
1. For numbers greater than 1 and less than 10, write it as a product of the number and 10 . ( 10 = 1)
2. For numbers less than 1,
n
(i) multiply and divide the number by 10 , where n is the number of places the decimal point is to be
shifted to the right, till there is only one non-zero digit to the left of the decimal point.
n
(ii) shift the decimal point to the right and keep 10 as the denominator.
–n
(iii) write the resulting number as the product of the number and 10 .
Example 15: Write in standard form:
(a) 0.5368 (b) 0.00000000000942 (NCERT) (c) 365100000
–6
(d) 16.00007 (e) 0.0035 × 10 (f) 0.002 × 0.006
Solution: (a) To write 0.5368 in standard form:
(i) we have to shift the decimal one place to the right, so that there is only one non-zero
digit to the left of the decimal point.
(ii) multiply and divide by 10 to keep the given number same.
i.e., 0 5368 10. × = 5 368. = 5 368 ( 10) − 1
×
.
10 10 1
So, the standard form of 0.5368 = 5.368 × (10) –1
0 00000000000942. × 10 ( ) 12
(b) 0.00000000000942 = (Shift decimal 12 places to the right)
10 ( ) 12
942.
= = 9.42 × (10) –12
10 ( ) 12

365100000 8
8
(c) 365100000 = × 10 ( ) = 3.651 × (10) (Shift decimal 8 places to the left)
10 ( ) 8

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