0580

Number Toolkit

Number

Putting numbers in order

  • Ascending order runs from smallest to largest; descending order runs from largest to smallest
  • To compare whole numbers, compare the highest place value first, then work rightwards until the digits differ
  • To compare decimals, give every number the same number of decimal places by padding with zeros
    • 3.6, 3.58 and 3.605 become 3.600, 3.580 and 3.605, so the order is 3.58, 3.6, 3.605
  • Length of a decimal is not a guide to its size: 0.9 is larger than 0.4999

Ordering negative numbers

  • On a number line, values increase from left to right, so any negative number is smaller than any positive number
  • Among negatives, the larger the digits, the smaller the value
    • −11 is smaller than −4
  • With a mixed list, order the negatives and the positives separately, then place all the negatives first
Exam tip

Put every number into the same form before comparing any of them: same number of decimal places, or all converted to one unit. Mark schemes award the method mark for that conversion, not for the final ordering.

Worked example

Ordering a mixed list of decimals

Write these numbers in ascending order: 0.62, −1.4, 0.7, −0.35, 1.08, −1.09

Solution:

  • Separate the signs: negatives are −1.4, −0.35, −1.09; positives are 0.62, 0.7, 1.08
  • Pad the negatives to the same number of decimal places: −1.40, −0.35, −1.09
  • Larger digits mean a smaller value, so the negatives run −1.40, −1.09, −0.35
  • Pad the positives: 0.62, 0.70, 1.08, which are already in order
  • Ascending order: −1.4, −1.09, −0.35, 0.62, 0.7, 1.08