**INDICES**

CONTENT

- Revision of Standard Form
- Laws Of Indices and Application of Indices
- 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 × 10^{0}

(b) 53.7 = 5.37 × 10^{1}

(c) 537 = 5.37 × 100

= 5.37 × 10 × 10

= 5.37 × 10^{2}

(d) 35.65 = 3.565 × 10

= 3.565 × 10^{1}

(e) 7500 = 7.5 × 1000

= 7.5 × 10^{3}

(f) 1403420 = 1.403420 × 1000000

= 1.403420 × 10^{6}

**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.

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