Place value and ordering decimals

Decimal points are used in numbers to separate the whole number from parts of the whole. Like whole numbers, numbers written as decimals can be either positive or negative, for example, 2.6 or -2.6.

Decimals are just one way of expressing numbers that are parts of wholes. These numbers can also be written as fractions or percentages. The number 1.5 (decimal) could also be written as 1 \frac{1}{2} (fraction) or 150% (percentage). They are all exactly the same number.

Knowledge of converting between decimals, fractions and percentages is important.

Place value

Place value gives the value of each digit in a number. For example, in the number 42, the 4 is worth 4 tens, or 40, and the 2 is worth 2 units, or 2. The same process is true for decimals.

In the number 2.78, the 2 is worth two units, the 7 is worth 7 tenths and the 8 is worth 8 hundredths.

HundredsTensUnits.TenthsHundredthsThousandths
2.78

This is the same as 2 and 78 hundredths or 2 \frac{78}{100}.

Ordering decimals

Ordering decimals involves comparing digits in the same columns, starting with the digits in the place value column that is furthest to the left.

Example

Which is greater, 2.5 or 2.15?

Firstly, both numbers have a 2 in the units column, so look at the next digit along. This is the digit in the first decimal place. The first number has a 5 in the tenths column whereas the second number has a 1 in the tenths column. 5 is greater than 1, so that means that 2.5 is greater than 2.15.

To make it easier to compare, make sure all the decimals have the same number of decimal places by adding zeros to the end if you need to.

To compare 2.5 and 2.15, add a zero to 2.5. It’s clear to see now that 2.15 must be smaller than 2.50, just like 215 is smaller than 250.

HundredsTensUnits.TenthsHundredthsThousandths
2.50
2.15
Question

Put these decimals in order, starting with the smallest:

  • 3.72
  • 3.07
  • 3.7
  • 4.3
  • 3.764
HundredsTensUnits.TenthsHundredthsThousandths
3.720
3.070
3.700
4.300
3.764

The answer is: 3.07, 3.7, 3.72, 3.764, 4.3.