Page 75 - ICSE Math 7

8. Simplify and answer each of the following in exponential form.

– 3 5 – 3 4 – 3 8 1 – 2 7 – 2 3 – 2 2
2 3
(a) c m × c m ÷ c m (b) {(–3) } × (c) c ( m ÷ c m 2 × c m
31 31 31 {(–3) } 5 5 5
3 2
9. Simplify each of the following and express each as a rational number.
 2  4  3  2  2  3  3  4  7  3
(a)   ×   (b)   ×   ×  
 3   4   3   5   2 
– 1 5  3  2 – 3 3 – 5 3
3
(c) c m × 3 ×   (d) c ( m ÷ c m 2 ÷ 2 3
3  4  4 2

3 11 3 7 3 8 3 10
10. Simplify c ( m × c m 2 ÷ c ( m × c m 2 and express the result as power of 10.
17 17 17 17
11. Determine the value of x in each of the following:

11
7x
3 7
9
(a) {(3) } = 3 (b) (–2) ÷ (–2) = (–2) 2x
2 
21
x
(c) (47) ÷ (47) = (47) 45 (d)  2  26 ÷    22 =  2  x
 
 
3 
3 



3 
12. Simplify.
  1 2  −2  −1 – 9 – 2 3 2 - 1 – 5 - 1 - 1
–1
–1 –1
(a)      −    (b) c 2 m ÷ c m (c) ( c m ÷ c m 2 (d) (3 – 5 )
 
    3     3 3 3 2


 p   2 9  2 8  p  2
− 
− 
=
13. If     ÷   , find the value of   .
 q   3   3   q 
3
p   18   16  p  2
3
14. If =   ÷   , find the value of   .
4
q      q 
4
Scientific Notation of Numbers
At times it becomes difficult to express very large or very small
numbers in their full form. We know that the mass of the earth Maths Info
is roughly 6,000,000,000,000,000,000,000,000 kg. In fact simply
looking at these figures, we can’t even get their exact magnitudes. The scientific notation of number
is also known as standard form of
It is cumbersome to remember and count the number of zeros in the number.
such numbers. Therefore, to overcome this, we use the scientific
notation of a number.
n
We write very large or very small numbers in the form p × 10 , where p is a terminating decimal such
that 1 ≤ p < 10 and n is an integer. The number written in this form is said to be in scientific notation.
Example 13: Write the following numbers in expanded form.
2,89,704; 48,06,196; 3,10,005
2
1
4
3
5
Solution: 2,89,704 = 2 × 10 + 8 × 10 + 9 × 10 + 7 × 10 + 0 × 10 + 4 × 10 0
1
3
2
6
4
5
48,06,196 = 4 × 10 + 8 × 10 + 0 × 10 + 6 × 10 + 1 × 10 + 9 × 10 + 6 × 10 0
3
5
2
4
1
3,10,005 = 3 × 10 + 1 × 10 + 0 × 10 + 0 × 10 + 0 × 10 + 5 × 10 0
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