1.2 Standard Form (Part 1)

1.2 Standard Form (Part 1)
1. Standard form is a way of writing very large numbers or very small numbers in the form of A × 10n, where  1 A < 10  and n is a positive or a negative integer.

Example 1:
Express each of the following numbers in standard form.
(a) 7244
(b) 32567
(c) 750000
(d) 0.65
(e) 0.0428
(f) 0.000369

Solution:
(a) 7244 = 7.244 × 1000 = 7.244 × 103

(b) 32567 = 3.2567 × 10000 = 3.2567 × 104

(c) 750000 = 7.5 × 100000 = 7.5 × 105

(d) 0.65
= 6.5 × 1 10
= 6.5 × 10-1

(e) 0.0428
= 4.28 × 1 100
= 4.28 × 10-2

(f) 0.000369
= 3.69 × 1 10000
= 3.69 × 10-4


Example 2:
Express each of the following numbers in standard form.
(a) 63.4
(b) 2738
(c) 23000
(d) 428000000
(e) 0.0063
(f) 0.000000038

Solution
:

(a) 63.4 = 6.34 × 10

(b) 2738 = 2.738 × 1000 = 2.738 × 10³

(c) 23000 = 2.3 × 10000 = 2.3 × 104

(d) 42800000 = 4.28 × 10000000 = 4.28 × 107

(e) 0.0063
= 6.3 × 1 1000
= 6.3 × 10-3
 
(f) 0.000000038
= 3.8 × 1 100000000
= 3.8 × 10-8
 

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