Page 47 - Start Up Mathematics_8 (Non CCE)

0 000007. × 10 ( ) 6 7
7 (
−
6
Solution: (a) 0.000007 = = =× 10) mm
10 ( ) 6 10 ( ) 6
695000
5
(b) 695000 = × 100000 = 6.95 × (10) km
100000
110 ( )
(c) 1 = 1 =× − 6 m
1000000 10 ( ) 6
0 00001275. × 10 ( ) 5 1 275.
5
−
.
(d) 0.00001275 = = = 1 275×( 10) m
10 ( ) 5 10 ( ) 5
Example 18: Compare the diameter of a wire on a computer chip which is 0.000003 m to that of a plant cell
which is 0.00001275 m.
Solution: Diameter of a wire on computer chip = 0.000003 m

Size of plant cell = 0.00001275 m
–6
Now, 0.000003 mm = 3 × (10) m Try It Out!
–5
and 0.00001275 m = 1.275 × (10) m 1. What is the value of
6 (
Diameter of wire 3×( 10) − 6 3×( 10) −− − 5) –1
So, = = {2 – 3 (2 – 3) }?
.
Size of plant cell 1 275×( 10) − 5 1 275
.
2. What is the value of the
–1
–1
3×( 10) −+ 5 3×( 10) − 1 expression (x + y) (x + y ) when
–1
6
= = it is simplified and expressed
1 275. 1 275.
with negative exponents?
3 = 3 ≈ 3 ≈ 1
1 275 10. × 12 75. 12 4
So, the diameter of wire is approximately one-fourth of the size of the plant cell.
‘≈’ sign denotes the approximate value, e.g., 1.1 ≈ 1

EXERCISE 2.3

1. Write in standard form:
3
(a) 0.000000375 (b) 506.289 (c) 9280000000000 (d)
–5
(e) 4603 × (10) (f) 0.0000478 × (10) 4 100000000
2. Write in usual form:
–8
4
(a) 3.25 × (10) (b) 4.083 × (10) (c) 9.17 × (10) –5 (d) 2.0001 × (10) 9
(e) 8 × (10) –9 (f) 7.9 × (10) 3
7
9
3. Compare the diameter of the sun 1.4 × (10) m to the diameter of the earth 1.2756 × (10) m.

At a Glance

1. If x is a non-zero rational number and n is any positive integer, then
1
n
–n
0
(a) (x) = x × x × x × x × ... n times (b) (x) = (c) (x) = 1
x () n
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