Write 3/8, 0.38, 37% and 0.4 in order, smallest first.
- Change to decimals: 3/8 = 0.375, 37% = 0.37.
- Write with three decimal places: 0.375, 0.380, 0.370, 0.400.
- In order: 0.370, 0.375, 0.380, 0.400.
Answer: 37%, 3/8, 0.38, 0.4
Ordering
Maths · Number. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
The idea
Ordering means putting numbers in size order and using the symbols =, ≠, >, <, ≥ and ≤ correctly. The open end of > or < always faces the larger number.
Numbers given in different forms cannot be compared by eye. Change them all to the same form, usually decimals with the same number of decimal places, and then compare digit by digit from the left.
On a number line, numbers get larger as you move to the right. This is why −9 is smaller than −7: for negative numbers, the one that looks bigger is the smaller one. Powers and roots of numbers between 0 and 1 also behave in a way that surprises students.
Rules to remember
- a > b means a is greater than b; a < b means a is less than b; ≥ and ≤ include “equal to”.
- Change fractions and percentages to decimals before comparing.
- Write the decimals to the same number of places: 0.7 = 0.700, so 0.7 > 0.69.
- For negative numbers the order reverses: 5 > 3 but −5 < −3.
- For a number between 0 and 1, squaring makes it smaller and the square root makes it larger.
- Dividing by a number between 0 and 1 gives a larger answer.
Common mistake
Judging a decimal by how many digits it has, such as thinking 0.619 is larger than 0.62. Compare 0.619 with 0.620, place by place.
Worked example
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