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Decimal equivalents: Tenths and hundredths

Decimal equivalents: Tenths and hundredths

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Summary

Decimal equivalents: Tenths and hundredths

​​In a nutshell

Tenths, hundredths and even thousandths can be easily converted to decimals using place value columns.


Simple conversions

Tenths, hundredths and thousandths are examples of simple fractions that, along with a few others, can easily be converted to decimals. It's worth learning these off by heart.


NAME

FRACTION

DECIMAL

One quarter

​​14\dfrac{1}{4}​​

0.250.25​​

One half

12\dfrac{1}{2}​​

0.50.5​​

Three quarters

34\dfrac{3}{4}​​

0.750.75​​

One tenth

110\dfrac{1}{10}​​

0.10.1​​

One hundredth

1100\dfrac{1}{100}​​

0.010.01​​

One thousandth

11000\dfrac{1}{1000}​​

0.0010.001​​


Converting using place value

Using the denominator can help you decide which place value columns the numerator's digits should be placed in the decimal form.


From fractions to decimals

Where the denominator is 1010:​

Place the ones digit of the numerator in the tenths column and place every other digit to the left.

Where the denominator is 100100:

Place the ones digit of the numerator in the hundredths column and place every other digit to the left.

Where the denominator is 10001000:

Place the ones digit of the numerator in the thousandths column and place every other digit to the left.


Example 1

Convert 510\dfrac{5}{10} to a decimal.


The numerator is 55 - place 55​ in the tenths column.

O.TthHthThth.5\begin{array}{cccc}&\text{O} & \text{.} & \text{Tth} & \text{Hth} &\text{Thth} \\&& . & 5 & \\ \end{array}


Fill in the ones column with zero as is necessary.

510=0.5\dfrac{5}{10}=\underline{0.5}


Example 2

Convert 189100\dfrac{189}{100} to a decimal.


The numerator is 189189.


Place the 99 in the hundredths column and place the other digits to the left.

O.TthHthThth1.89\begin{array}{cccc}&\text{O} & \text{.} & \text{Tth} & \text{Hth} &\text{Thth} \\&1& . & 8 & 9 \\ \end{array}

189100=1.89\dfrac{189}{100}=\underline{1.89}

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Note: Sometimes you might need to use equivalent fractions to get the denominator of a fraction to be 10,10010,100 or 10001000!

From decimals to fractions

Converting from decimals to fractions is very similar.


Procedure

​​1.

Identify the place value of the last digit.

2. 

Write all the digits of the decimal as the numerator.

3.

Choose the denominator based on the place value column of that last digit:

  • For tenths: use 1010.​
  • For hundredths: use 100100.​
  • For thousandths: use 10001000.


Example 3

Convert 0.280.28 to a fraction.


Identify the place value column of the 88.

O.TthHth0.28\begin{array}{cccc}&\text{O} & \text{.} & \text{Tth} &\underline{\text{Hth}} \\&0& . & 2&8 \\ \end{array}​​


Write as a fraction with 2828 in the numerator and 100100 in the denominator.

0.28=281000.28=\underline{\dfrac{28}{100}}


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FAQs - Frequently Asked Questions

How do I convert decimals to fractions out of ten and one hundred?

How do I convert tenths and hundredths to decimals?

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