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Approximations and Estimations

  • To round off a number means to find an approximate value. To approximate means to round off.
  • When rounding off numbers, we round up or round down, depending on the digit to the right of the digit being rounded.
    • If the digit to the right is 0, 1, 2, 3, 4, round down.
    • If the digit to the right is 5, 6, 7, 8, 9, round up.
  • Significant figures (s.f.) begin from the first non-zero digit at the left of a number. For example:
    • 18329 to 2 s.f. = 18000
    • 0.0092752 to 3 s.f. = 0.00928
  • Decimal places (d.p.) are counted from the decimal point. Zeros after the point are taken into consideration. For example:
    • 2.0816 to 1 d.p. = 2.1
    • 2.0816 to 2 d.p. = 2.08
    • 2.0816 to 3 d.p. = 2.082
Examples
  1. A football match is watched by 56742 persons. Write this number correct to the nearest,
    1. ten thousand
      • 56742 to the nearest ten thousand = 60000
    2. thousand
      • 56742 to the nearest thousand = 57000
    3. 10
      • 56742 to the nearest ten = 56740
  2. Write the following numbers correct to 3 sf:
    1. 47396
      • 47396 to 3 sf = 47400
    2. 313179
      • 313179 to 3 sf = 313000
    3. 20.294
      • 20.294 to 3 sf = 20.3
    4. 0.0004678
      • 0.0004678 to 3 sf = 0.000468
  3. Write each of the following numbers correct to the number of decimal places specified.
    1. 0.2348 to 2 dp
      • 0.2348 to 2 dp = 0.23
    2. 5.3989 to 3 dp
      • 5.3989 to 3 dp = 5.399
    3. 124.5489 to 1 dp
      • 124.5489 to 1 dp = 124.5
    4. 0.0008764 to 4 dp
      • 0.0007764 to 4 dp = 0.0008
  4. Approximate 79.75 to the nearest
    1. hundred
      • 79.75 to the nearest hundred = 100
    2. ten
      • 79.75 to the nearest ten = 80
    3. whole number
      • 79.75 to the nearest whole number = 80.
      • NOTE: The fraction 0.75 is nearer to 1 than 0; thus 79 is rounded up to the nearest whole number, 80)
    4. tenth
      • 79.75 to the nearest tenth = 79.8
      • NOTE: The last digit of 79.75 is 5; round up
Minimum 4 characters