Place value and ordering decimals

Decimal place values

We use a decimal point to separate units from parts of a whole, such as tenths, hundredths, thousandths, etc.

• is a tenth, , of a unit
• is a hundredth, , of a unit
• is a thousandth, , of a unit

In , the value of the is one tenth or , and the value of the digit is three hundredths or .

Ordering decimals

When ordering numbers, always compare the left digits first.

For example, which is greater or ?

Both numbers have two units and three tenths, but has no hundredths, whereas has two hundredths. Therefore, is greater than .

Another way to look at it is to add a zero to the end of . This doesn't change the value as it is after the decimal point. This means that both numbers will have the same number of digits after the decimal point.

The two numbers are now and . It is easier to see that is bigger - just as is bigger than .

Question

Q1. In the number , what is the value of the digit ?

Q2. Place the following numbers in order, smallest first: , , ,

A1. The value of the digit is four hundredths, or .

A2. Did you get , , , ?

All the numbers have three units, so start by comparing the tenths. has no tenths, and have one tenth, and has two tenths. Therefore, is the smallest and is the largest.

When comparing and , both have hundredths. has no further digits, but also has thousandths, meaning that is smaller than .

You can add zeros to the ends of the numbers and so write the numbers as , , and and compare them.