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# Place value and ordering decimals

## Decimal place values

We use a decimal point to separate units from parts of a whole (like tenths, hundredths, thousandths, etc).

• 0.1 is a tenth, 1/10 of a unit
• 0.01 is a hundredth, 1/100 of a unit
• 0.001 is a thousandth. 1/1000 of a unit

In 52.13, the value of the figure 1 is 1/10 , and the value of the figure 3 is 3/100.

## Ordering decimals

When ordering numbers, always compare the left digits first.

Eg Which is greater, 2.301 or 2.32?

Units   Tenths Hundredths Thousandths
2 . 3 0 1
2 . 3 2

Both numbers have two units and three tenths, but 2.301 has no hundredths, whereas 2.32 has two hundredths. Therefore, 2.32 is greater than 2.301.

Another way to look at it is to add a zero to the end of 2.32 (this doesn't change its value as it's after the decimal point).

The two numbers are now 2.320 and 2.301 and it is quite easy to see that 2.320 is bigger (just as 2 320 is bigger than 2 301).

Question

Q1. In the number 3.546, what is the value of the figure 4?

Q2. Place the following numbers in order, smallest first: 3.2, 3.197, 3.02, 3.19

A1. The value of the figure 4 is 4/100.

A2. Did you get 3.02, 3.19, 3.197, 3.2?

All the numbers have three units, so start by comparing the tenths. 3.02 has no tenths, 3.197 and 3.19 have one tenth, and 3.2 has two tenths. Therefore, 3.02 is the smallest and 3.2 is the largest.

You could also write the numbers as 3.020, 3.190, 3.197 and 3.200 and compare them.

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