Topics
5. Decimals
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Level 5

5.02 Beyond thousandths

Lesson
Practice
Lesson

Are you ready?

In the previous lesson we learned about  thousandths and how to convert between decimal and fraction forms  . Let's try an example.

Examples

Example 1

Write the fraction \dfrac{81}{1000} as a decimal.

Worked Solution
Create a strategy

Use a place value table to convert it to a decimal.

Apply the idea

The fraction is 81 thousandths. To put it in a place value table the last digit should be in the thousandths column. We use zeros for place holders.

Units.TenthsHundredthsThousandths
0.081

\dfrac{81}{1000}=0.081

Idea summary

To write a fraction out of 10, \, 100, or 1000 as a decimal, we can use a place value table.

Smaller than thousandths

This video looks at converting decimals smaller than thousandths between fraction and decimal forms.

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Examples

Example 2

Given the number 36\,917 hundred thousandths, write this as a:

a

Fraction

Worked Solution
Create a strategy

Write the number as the numerator and 100\,000 as the denominator.

Apply the idea

36\,917 hundred thousandths is the same as 36\,917 out of 100\,000. So 36\,917 would be the numerator and 100\,000 would be the denominator. 36\,917 \text{ hundred thousandths} = \dfrac{36\,917}{100\,000}

b

Decimal

Worked Solution
Create a strategy

Use a place value table to convert it to decimal. The last digit should be in the "hundred thousandths" column.

Apply the idea
Units.TenthsHundredthsThousandthsTen thousandthsHundred thousandths
0.36917

36\,917 \text{ hundred thousandths} = 0.369\,17

Idea summary

1 hundred thousandth can be written as \dfrac{1}{100\,000}=0.000\,01

Read and write beyond thousandths

This video shows us how to read and write numbers that are smaller than thousandths.

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Examples

Example 3

Choose the word form of the following numeral: 0.068\,81.

A
six thousand, eight hundred and eighty one tens of thousandths
B
six thousand, eight hundred and eighty one hundreds of thousandths
C
six thousand, nine hundred and eighty one hundreds of thousandths
Worked Solution
Create a strategy

Use a place value table.

Apply the idea
Units.TenthsHundredthsThousandthsTen thousandthsHundred thousandths
0.06881

From the table we can see that there are 6 hundredths, 8 thousandths, 8 ten thousandths and 1 hundred thousandth.

Altogether it is six thousand, eight hundred and eighty one hundreds of thousandths. So the correct answer is option B.

Idea summary

The pattern in the naming of the place value column for whole numbers has the same pattern when we go the other way for decimals. Instead of tens, hundreds, thousands, ten thousands; we have tenths, hundredths, thousandths and ten thousandths.

We can use a place value table to write a decimal in words.

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