MathematicsExam code: 0580

Number Toolkit

Number

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

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

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
The further from zero, the smaller the 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

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