Year 7AC9M7N04

Decimal Place Value and Ordering

Find equivalent representations of rational numbers and represent rational numbers on a number line.

Longer does not mean larger. That one idea causes more decimal mistakes than anything else, and the fix is to line up the decimal points and compare column by column.

Method

Each column is ten times smaller

\text{tenths} \ \rightarrow\ \text{hundredths} \ \rightarrow\ \text{thousandths}

Moving right divides by 10 every time.

More digits does not mean bigger

0{,}5 > 0{,}45

Five tenths beats four tenths, whatever comes after.

Zeros on the end change nothing

0{,}5 = 0{,}50 = 0{,}500

Use this to give every number the same number of places before comparing.

Compare from the left

Start at the biggest column. The first column that differs decides it.

Worked example

e.g.

\text{Order } 0{,}4,\ 0{,}38,\ 0{,}409 \text{ and } 0{,}5 \text{ from smallest to largest.}

Give every number the same number of decimal places by adding zeros. $0{,}400 \quad 0{,}380 \quad 0{,}409 \quad 0{,}500$
Compare the tenths column first. $3 < 4 = 4 < 5$
Two numbers tie on tenths, so move to the hundredths column. $0{,}400 \quad \text{vs} \quad 0{,}409 \ \rightarrow\ 0 = 0$
Still tied, so move to the thousandths column. $0 < 9$
Write the order using the original numbers. $0{,}38,\ 0{,}4,\ 0{,}409,\ 0{,}5$

Practice

Add zeros so every number has the same number of places.

\text{Which is larger: } 0{,}7 \text{ or } 0{,}68?

Answer

0{,}7 \text{ — seven tenths beats six tenths}

\text{Order smallest first: } 1{,}2,\ 1{,}09,\ 1{,}25

Answer

1{,}09,\ 1{,}2,\ 1{,}25

\text{What is the value of the 6 in } 3{,}461?

Answer

6 \text{ hundredths} = 0{,}06

\text{Round } 4{,}678 \text{ to two decimal places.}

Answer

4{,}68

\text{Round } 12{,}349 \text{ to one decimal place.}

Answer

12{,}3

\text{Write a decimal between } 0{,}3 \text{ and } 0{,}31

Answer

0{,}305 \text{ (any value between works)}