 4 Ijesha Close, Ilupeju, Lagos
+2347 086 296 002

#### Large and Small Numbers

• To avoid confusion, when writing large numbers or small decimal fractions, group the digits in threes from the decimal point. E.g. 49 560 216 and 0.003 48.
• A number in standard form is written as a × 10n, where a is a number between 1 and 11 and n is a positive or negative integer.
• The laws of indices are:
• ya × yb = ya+b
• xa ÷ xb = xa-b
• x0 = 1
• x-a = 1/xa
• (xa)b = xab
###### Examples
1. Express the following numbers in standard form:
1. 60 000
• = 6 × 10 000
• = 6 × 104
2. 480 000 000
• = 4.8 × 100 000 000
• = 4.8 × 108
2. Express the following in ordinary form:
1. 4.3 × 104
• = 4.3 × 10 000
• = 43 000
2. 7.8 × 107
• = 7.8 × 10 000 000
• = 78 000 000
3. Write the following as decimal fractions:
1. 350 millionths
• = 1 millionth × 350
• = 0.000 001 × 350
• = 0.000 350
• = 0.000 35
• NOTE: In a decimal fraction, it is not necessary to write any zeros after the last non-zero digit.
2. 865/100 000
• = 0.008 65
• NOTE: There are five zeros in the denominator. The decimal fraction is obtained by moving the digits in the numerator five places to the right.
4. Simplify the following:
1. 104 × 102
• = (10 × 10 × 10 × 10) × (10 × 10)
• = 10 × 10 × 10 × 10 × 10 × 10
• = 106
• OR more quickly, by adding indices: 104 × 102 = 104+2 = 106
2. 4c³ × 7c²
• = 4 × c × c × c × 7 × c × c
• = 4 × 7 × c × c × c × c × c
• = 28c5
• OR more quickly, by adding indices: 4c³ × 7c² = 4 × 7 × c3+2 = 28c5
5. Simplify the following:
1. 104 ÷ 102
• Using one of the laws of indices:
• = 104 – 2
• ∴ 104 ÷ 102 = 102
2. 4c³ ÷ 7c²
• 4/7 × c3-2
• ∴ 4c³ ÷ 7c² = 4/7C
Minimum 4 characters