Page 36 - Maths Skills - 8

34 Maths

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(iv) (6 – 7 ) (v) 3 1 1 (vi) (– 5) × 1 1
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–1
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7 5 5
8. Simplify.

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9 3 12 0 3 1 1 2 2 2 2 1
2 1 1
1

(i) 5 (ii) 2
5 7 9 5 5 4

2

2
9. Find the value of a so that 2 3 6 2 2 a 1 .

5 5 5

10. By which number should 2 3 be divided to get 3 ?

x 2 3 2 9 8

3
11. If , find the value of . 12. Simplify:
y 3
5
z
6
x 2 x y 1 x 8 5 y x (i) 6 xy 1218 z 2 (ii) 4 x 16 2
(i) (ii) (iii)
y
y
y x
13. Simplify:
1

(i) 1 3 (ii) {(5) × (4) } (iii) {(3) ÷ (4) }
–1 3
–1
–1 2
–1
1

3
3 9
1 2 3 3
(iv) {(5) ÷ (3) }–1 × (2) (v) {(1) + (2 )} × (vi) {(4) – (3 )} ×
3
3
–1
2
–1
2
–1
3 4
SCIENTIFIC NOTATION [USE OF EXPONENTS]
We often come across very large numbers as well as very small numbers. For example, the distance of the Sun
from the Earth is 150,000,000 km. It becomes difficult to remember the number of zeros it has. In such case, for
convenience, we write using exponents with base 10, i.e., 150,000,000 can be written as 15 × 10 or 1.5 × 10 .
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Similarly, the number 0.000000022 cm which is the measure of the diameter of the helium atom may be written
as 22 × 10 cm or 2.2 × 10 cm.
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Thus, writing a very large or very small number in the form k × 10 , where k is a terminating decimal such that
n
1 ≤ k < 10 and n is any integer, is called scientific notation or standard form.
Let’s Attempt
Example 1: Express the following numbers in the standard form.
(i) 4134500000 (ii) 0.00000035
Solution: (i) 4134500000 written as 4.1345 × 10 . (ii) 0.00000035 written as 3.5 × 10 .
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Example 2: Express the following numbers in the standard form.
(i) 0.45 (ii) 0.0000000004 (iii) 13500000000
(iv) 39.7 (v) 0.000037 (vi) 160000
Solution: (i) 0.45 = 4.5 × 10 . (ii) 0.0000000004 = 4 × 10 .
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(iii) 13500000000 = 1.35 × 10 . (iv) 39.7 = 3.97 × 10 .
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1
(v) 0.000037 = 3.7 × 10 . (vi) 160000 = 1.6 × 10 .
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