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