 # 6.04 Compare and order

Lesson

We have previously worked with  decimals with digits in the thousandths place  . Let's review.

### Examples

#### Example 1

Write the following in numerals:

Five thousand, six hundred and eighty one tens of thousandths

Worked Solution
Create a strategy

We can use a place value table to help us write the decimal.

Apply the idea

To put it in a place value table, put the 1 in the ten thousands column first as it is the last digit of the number. We then put the remaining numbers in the columns to the left: 8 in the thousands column, 6 in the hundredths column, 5 in the tenths column, and use zeros for place holders:

5681\text{ tens of thousandths}=0.5681

Idea summary

A place value table is helpful in writing a numeral in words as a decimal.

## Compare numbers beyond thousandths

This video demonstrates numbers in the place value columns beyond thousandths, such as tens of thousandths and hundreds of thousandths, and looks at how to compare numbers with this many decimal places.

### Examples

#### Example 2

Write the greater than (\gt) or less than (\lt) symbol, in the box to make this number sentence true:0.6649 \, ⬚ \, 0.6113

Worked Solution
Create a strategy

Use a place value table and compare the numbers.

Apply the idea

Write the decimals in a place value table and use zeros as place holders.

The numbers in the units and tenths columns are the same. In the hundredths column, we can see that 6 is larger than 1. We do not need to compare the remaining columns since we already know which is larger.

We can write the number sentence as:0.6649 \, \gt \, 0.6113

Idea summary

\gt means 'greater than' and \lt means 'less than'.

When using a place value table to compare decimals we can start at the place value column furthest to the left and work to the right, comparing the values in each column to work out the bigger/smaller number.

## Order decimals beyond thousandths

This video looks at how to order 3 numbers that have at least 4 decimal places.

### Examples

#### Example 3

Order these numbers in ascending order: 0.4764, \, 0.2959, \, 0.5385.

Worked Solution
Create a strategy

Use a place value table and compare the numbers. Ascending means smallest to largest.

Apply the idea

Write the decimals in a place value table and use zeros as place holders.

In the tenths column we can see that 2 \lt 4 \lt 5. This means that 0.2959 \lt 0.4764 \lt 0.5385 . So the number in ascending order is: 0.2959, \, 0.4764, \, 0.5385

Idea summary

Ascending order means smallest to largest. Descending order means largest to smallest.

If our numbers are not all expressed as thousandths, starting from the left of our number is one way to compare them. We can rename our numbers so they are all expressed as thousandths, by using 0s as placeholders.

## Compare decimals and fractions

Sometimes, we may need to insert a symbol to make a statement true. This means we need to think about whether one side is less than (\lt), equal to (=), or greater than (\gt) the other side. If one number is expressed as a fraction, and the other a decimal, it can help to look at them both as either fractions or decimals. In this video, we look at how to make a statement true.

### Examples

#### Example 4

Choose the missing symbol to make this a true statement.0.69 \, ⬚ \, \dfrac{23}{100}

A
\lt
B
\gt
Worked Solution
Create a strategy

Convert the fraction into a decimal and use a place value table to compare the numbers.

Apply the idea

\dfrac{23}{100} is the same as 23 hundredths or 0.23.

Now we can write the decimals in a place value table.

In the tenths column, we can see that 6 is larger than 2. We do not need to compare the remaining columns since we already know which is larger.

We can write the number sentence as 0.69 \, \gt \, \dfrac{23}{100}.

So the correct answer is option B.

Idea summary

If we are comparing a fraction and a decimal number, we should convert the fraction into decimals first, before we compare them in a place value table.