INDICES

CONTENT

1. Revision of Standard Form
2. Laws Of Indices and Application of Indices
3. Simple Indicial Equations

Revision of Standard Form

Example 1: Express the following in standard form.

(a) 5.37 (b)  53.7 (c) 537 (d) 35.65  (e) 7500  (f) 1403420

Solution:

(a) 5.37 = 5.37 × 1

= 5.37 × 10⁰

(b) 53.7 = 5.37 × 10¹

(c) 537 = 5.37 × 100

= 5.37 × 10 × 10

= 5.37 × 10²

(d) 35.65 = 3.565 × 10

=  3.565 × 10¹

(e) 7500 = 7.5 × 1000

= 7.5 × 10³

(f) 1403420 = 1.403420 × 1000000

=  1.403420 × 10⁶

Example 2:  Express the following in standard form.

(a) 0.037 (b)  0.00065   (c)  0.0058   (d)  0.61

Method 1:

(a) 0.037 = 3.7 × 0.01

= 3.7 × 10⁻²

(b) 0.00065 = 6.5 × 0.0001

= 6.5 × 10⁻⁴

(c) 0.0058 = 5.8 × 0.001

= 5.8 × 10⁻³

(d) 0.61 = 6.1 × 0.1

= 6.1 × 10⁻¹

Method 2:

(a) \(\mathsf {0.037} = \frac{0.037}{1} \\ = \frac{3.7}{100} \\ = \frac{3.7}{10^2} \\ = 3.7 \times 10^{-2}\)

(b) \(0.00065 = \frac{0.00065}{1} \\ = \frac{6.5}{10000} \\ = \frac{6.5}{10^4} \\ = 6.5 \times 10^{-4}\)

(c) \(0.0058 = \frac{0.0058}{1} \\ = \frac{5.8}{1000} \\ = \frac{5.8}{10^3} \\ = 5.8 \times 10^{-3}\)

(d) \(0.061 = \frac{0.61}{1} \\ = \frac{6.1}{10} \\ = 6.1 \times 10^{-1}\)

Class Activity:

Express the following in standard form.