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Decimal to fraction

Here you will learn strategies on how to convert decimals to fractions.

Students will first learn about converting decimals to fractions in 4th grade math as part of their work in number and operations with fractions.

What is decimals to fractions?

Converting decimals to fractions is when you represent a decimal as a fraction without changing its value.

Here is a visual model representing $0.43.$ The hundredths grid is made up of $100$ equal parts. $43$ pieces are shaded out of $100$ equal parts which is $\cfrac{43}{100}.$

You can also use a place value chart to convert decimals to fractions.

Decimals as fractions $\hspace{1cm}$


Decimal $\to 0.43$ Read as forty-three hundredths. $43$ is the numerator of the fraction and $100$ is the denominator because the last digit of the decimal is in the hundredths column of the place value chart, $\bf{0.43 = \cfrac {43}{100}}$	Decimal $\to 0.009$ Read as nine thousandths. $9$ is the numerator of the fraction and $1000$ is the denominator because the $9$ is in the thousandths column of the place value chart, $\bf{0.009 = \cfrac {9}{1000}}$

Decimal $\to 0.43$

Read as forty-three hundredths.

$43$ is the numerator of the fraction and $100$
is the denominator because the last digit of
the decimal is in the hundredths column of
the place value chart,

$\bf{0.43 = \cfrac {43}{100}}$

Decimal $\to 0.009$

Read as nine thousandths.

$9$ is the numerator of the fraction and $1000$
is the denominator because the $9$ is in the
thousandths column of the place value
chart,

$\bf{0.009 = \cfrac {9}{1000}}$

Decimals as fractions with simplifying
Decimal $\to 0.25$ Read as twenty-five hundredths. $25$ is the numerator of the fraction and $100$ is the denominator because the last digit of the decimal is in the hundredths place. $\cfrac{25}{100} \,$ can be simplified. The common factor between $25$ and $100$ is $25.$ $\cfrac{25\div 25}{100\div 25} \, =\cfrac{1}{4}$ $\bf{\cfrac{25}{100} \, =\cfrac{1}{4}}$

Decimals as fractions with simplifying

Decimal $\to 0.25$

Read as twenty-five hundredths.

$25$ is the numerator of the fraction and $100$ is the denominator because
the last digit of the decimal is in the hundredths place.

$\cfrac{25}{100} \,$ can be simplified. The common factor between $25$ and $100$ is $25.$

$\cfrac{25\div 25}{100\div 25} \, =\cfrac{1}{4}$

$\bf{\cfrac{25}{100} \, =\cfrac{1}{4}}$

Decimals bigger than $\bf{1}$ to a mixed number
Decimal $\to 1.4$ Read as one and four tenths. $1$ is a whole number, $4$ is the numerator of the fraction and $10$ is the denominator. $1\cfrac{4}{10}$ $\cfrac{4}{10} \,$ can be simplified. The common factor between $4$ and $10$ is $2.$ $\cfrac{4\div 2}{10\div 2} \, =\cfrac{2}{5}$ $\bf{1\cfrac{4}{10}} \,$ in its simplest form is $\bf{1\cfrac{2}{5}} \,$

Decimals bigger than $\bf{1}$ to a mixed number

Decimal $\to 1.4$

Read as one and four tenths.

$1$ is a whole number, $4$ is the numerator of the fraction and $10$ is the
denominator.

$1\cfrac{4}{10}$

$\cfrac{4}{10} \,$ can be simplified. The common factor between $4$ and $10$ is $2.$

$\cfrac{4\div 2}{10\div 2} \, =\cfrac{2}{5}$

$\bf{1\cfrac{4}{10}} \,$ in its simplest form is $\bf{1\cfrac{2}{5}} \,$

What is decimals to fractions?

$What is decimals to fractions?$

Common Core State Standards

How does this apply to 4th grade math and 5th grade math?

Grade 4 – Number and Operations – Fractions (4.NF.C.5)
Express a fraction with denominator $10$ as an equivalent fraction with denominator $100,$ and use this technique to add two fractions with respective denominators $10$ and $100.$ For example, express $\frac{3}{10}$ as $\frac{30}{100},$ and add $\frac{3}{10} + \frac{4}{100} = \frac{34}{100}.$

Grade 5 – Number and Operations in Base 10 (5.NBT.A.3)
Read, write, and compare decimals to thousandths.

How to convert decimals to fractions

In order to write a decimal as a fraction with a hundredths chart model:

Represent the decimal on the hundredths chart.
The shaded part is the numerator, and the total amount of equal parts is the denominator.
Write the fraction and simplify if possible.

In order to write a decimal as a fraction:

Write the decimal in words.
The numerator is the digits of the decimal, and the denominator is the column of the last digit on the place value chart.
Write the fraction and simplify if possible.

In order to write a decimal bigger than $1$ as a mixed number:

Write the decimal in words.
Keep the whole number.
The numerator is the digits to the right of the decimal point, and the denominator is the column of the last digit in the place value chart.
Write the mixed number and simplify if possible.

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Convert decimals to fractions examples

Example 1: write a decimal as a fraction using a model

Represent $0.21$ as a fraction using a model.

Represent the decimal on the hundredths chart.

There are $21$ parts shaded out of the $100$ equal parts.

2The shaded part is the numerator, and the total amount of equal parts is the denominator.

Since there are $21$ shaded parts and $100$ equal parts. $21$ will be the numerator of the fraction, and $100$ is the denominator of the fraction.

3Write the fraction and simplify if possible.

0.21 → \cfrac{21}{100}

$\cfrac{21}{100} \,$ is in lowest terms.

Example 2: convert a simple decimal to a fraction (without simplifying)

Change $0.3$ to a fraction.

Write the decimal in words.

$0.3$ in words is three-tenths.

The numerator is the digits of the decimal, and the denominator is the column of the last digit on the place value chart.

$0$ is in the ones column, $3$ is in the tenths column.

$3$ will be the numerator and $10$ will be the denominator.

Write the fraction and simplify if possible.

0.3 → \cfrac{3}{10}

$\cfrac{3}{10} \,$ is in lowest terms.

Example 3: convert a decimal to a fraction (with simplifying)

Convert $0.22$ to a fraction.

Write the decimal in words.

$0.22$ in words is twenty-two hundredths.

The numerator is the digits of the decimal, and the denominator is the column of the last digit on the place value chart.

$0$ is in the ones column, $2$ is in the tenths column, and $2$ is in the hundredths column.

$22$ will be the numerator and $100$ will be the denominator.

Write the fraction and simplify if possible.

0.22 → \cfrac{22}{100}

$\cfrac{22}{100} \,$ can be simplified. The common factor between $22$ and $100$ is $2.$

$\cfrac{22}{100}=\cfrac{22\div2}{100\div 2}=\cfrac{11}{50}$

$\cfrac{22}{100} \,$ in lowest terms is $\cfrac{11}{50}.$

Example 4: convert a decimal to a fraction involving thousandths

Convert $0.387$ to a fraction.

Write the decimal in words.

$0.387$ in words is three hundred eighty-seven hundredths.

The numerator is the digits of the decimal, and the denominator is the column of the last digit on the place value chart.

$0$ is in the ones column, $3$ is in the tenths column, $8$ is in the hundredths column, and $7$ is in the thousandths column.

$387$ will be the numerator and $1000$ will be the denominator.

Write the fraction and simplify if possible.

0.387 → \cfrac{387}{1000}

$\cfrac{387}{1000} \,$ is in lowest terms.

Example 5: convert a decimal bigger than 1 to a mixed number

Convert $1.7$ to a mixed number.

Write the decimal in words.

$1.7$ in words is one and seven tenths.

Keep the whole number.

The whole number will stay at $1.$

The numerator is the digits to the right of the decimal point, and the denominator is the column of the last digit in the place value chart.

$1$ is in the ones column, and $7$ is in the tenths column.

$7$ will be the numerator and $10$ will be the denominator of the fraction part of the mixed fraction.

Write the mixed number and simplify if possible.

1.7 → 1\cfrac{7}{10}

$1\cfrac{7}{10} \,$ is in lowest terms.

Example 6: convert a decimal bigger than 1 to a mixed number (with simplifying)

Convert $2.04$ to a fraction.

Write the decimal in words.

$2.04$ in words is two and four hundredths.

Keep the whole number.

$2$ will be the whole number.

The numerator is the digits to the right of the decimal point, and the denominator is the column of the last digit in the place value chart.

$2$ is in the ones column, $0$ is in the tenths column, and $4$ is in the hundredths column.

$4$ will be the numerator and $100$ will be the denominator of the fraction part of the mixed fraction.

Write the mixed number and simplify if possible.

$2.04$ as mixed number is $\, 2\cfrac{4}{100}.$

$2\cfrac{4}{100} \,$ can be simplified because $4$ is the common factor between $4$ and $100.$

$\cfrac{4 \, \div \, 4}{100 \, \div 4}=\cfrac{1}{25}$

$2\cfrac{4}{100} \,$ in lowest terms is $2\cfrac{1}{25}.$

Teaching tips for converting decimals to fractions

Use a visual model to introduce the topic since students should be familiar with how to create a fraction from a model.

Use a number line to help students formulate number sense with decimal and fraction numbers.

Reinforcing the decimal value will help students be able to write it in fraction form.

When teaching the math lessons on converting fractions to decimals, have students change improper fractions to mixed numbers first before making the conversion.

Easy mistakes to make

Placing the decimal number in the wrong columns on a place value chart
For example, placing the $3$ in the decimal number $0.03$ in the tenths column instead of the hundredths column.

Forgetting to write the fraction in lowest terms
Always look to see if there is a common factor between the numerator and the denominator of the fraction.

Confusing the numerator and the denominator
The numerator is the top number, and the denominator is the bottom number.
When converting a decimal to a fraction, the digits of the decimal will be the numerator (top number) and a power of ten will be the denominator (bottom number).

Practice converting decimals to fractions questions

\cfrac{33}{1000}

\cfrac{33}{100}

\cfrac{3}{10}

\cfrac{30}{100}

$33$ shaded parts out of $100$ equal parts as a fraction is $\, \cfrac{33}{100}.$

\cfrac{10}{100}

\cfrac{1}{10}

\cfrac{0.1}{1}

\cfrac{0.01}{100}

$0.1$ in words is one tenth. Put it on a place value chart.

Decimals to Fractions practice question 2

$0$ is in the ones column and $1$ is in the tenths column.

$1$ will be the numerator, and $10$ will be the denominator.

$0.1$ as a fraction is $\, \cfrac{1}{10}.$

$\cfrac{1}{10} \,$ is in lowest terms.

\cfrac{40}{100}

\cfrac{4}{10}

\cfrac{2}{5}

\cfrac{0.4}{1}

$0.4$ in words is four tenths. Put it on the place value chart.

Decimals to Fractions practice question 3

$0$ is in the ones column and $4$ is in the tenths column.

$4$ will be the numerator, and $10$ will be the denominator.

$0.4$ as a fraction is $\, \cfrac{4}{10}.$

$\cfrac{4}{10} \,$ can be simplified because the common factor of $4$ and $10$ is $2.$

\cfrac{4 \, \div \, 2}{10 \, \div \, 2}=\cfrac{2}{5}

$\cfrac{4}{10} \,$ in lowest terms is $\, \cfrac{2}{5}.$

\cfrac{16}{100}

\cfrac{4}{25}

\cfrac{16}{1000}

\cfrac{2}{125}

$0.016$ in words is sixteen thousandths. Put it on the place value chart.

Decimals to Fractions practice question 4

$0$ is in the ones column, $0$ is in the tenths column, $1$ is in the hundredths column, and $6$ is in the thousandths column.

$16$ will be the numerator, and $1000$ will be the denominator.

$0.16$ written as fraction is $\, \cfrac{16}{1000}.$

$8$ is the common factor between $16$ and $1000.$

\cfrac{16 \, \div \, 8}{1000 \, \div \, 8}=\cfrac{2}{125}

$\cfrac{16}{1000} \,$ in lowest terms is $\, \cfrac{2}{125}.$

1\cfrac{23}{100}

\cfrac{23}{100}

1\cfrac{23}{1000}

1\cfrac{23}{10}

$1.23$ in words is one and twenty-three hundredths. Put it on the place value chart.

Decimals to Fractions practice question 5

$1$ is in the ones column, $2$ is in the tenths column, and $3$ is in the hundredths column.

$1$ is the whole number part of the mixed number. $23$ is the numerator, and $100$ is the denominator of the fractional part of the mixed number.

$1.23$ as a fraction is $\, 1\cfrac{23}{100}.$

$1\cfrac{23}{100} \,$ is in lowest terms.

2\cfrac{5}{10}

2\cfrac{1}{2}

2\cfrac{5}{100}

2\cfrac{1}{20}

$2.05$ in words is two and five hundredths. Put it on the place value chart.

Decimals to Fractions practice question 6

$2$ is in the ones column, $0$ is in the tenths column, and $5$ is in the hundredths column.

$2$ is the whole number part of the mixed number. $5$ is the numerator, and $100$ is the denominator of the fractional part of the mixed number.

$2.05$ written as a fraction is $\, 2\cfrac{5}{100}.$

$5$ is the common factor between $5$ and $100.$

\cfrac{5\div 5}{100\div 5}=\cfrac{1}{20}

$2\cfrac{5}{100} \,$ in lowest terms is $\, 2\cfrac{1}{20}.$

Converting decimals to fractions FAQs

Are the denominators always going to be a power of ten?

Yes, when converting a decimal to a fraction the denominator of the fraction will always be a power of ten. This is because our decimal system breaks apart the decimal number into tenths $(\cfrac{1}{10}),$ hundredths $(\cfrac{1}{100}),$ thousandths $(\cfrac{1}{1000}),$ etc.

Do you always have to simplify the fraction?

It’s a good practice to always write a fraction in lowest terms, but refer to your state standards for specific guidance.

Can you convert a fraction back into a decimal?

Yes, you can go from decimal representation to fraction representation and vice versa. For example, to convert $\cfrac{9}{10} \,$ to a decimal, you can put it on the place value chart.

Decimals to Fractions FAQS
$9$ will go in the tenths column, so the decimal representation of $\cfrac{9}{10} \,$ is $0.9.$

Do you have to use a place value chart to convert a decimal to a fraction?

No, there are other ways to convert decimals to fractions. You can use the fraction calculator converter.

What are decimal fractions?

A decimal fraction is when the denominator of the fraction is a power of $10.$ For example, $\cfrac{3}{100} \,$ is a decimal fraction because $100$ is $10^2.$

Can you convert a repeating decimal to a fraction?

Yes, repeating decimals are rational numbers. Rational numbers can be written as fractions. So, repeating decimals can be written as fractions. You will learn how to do this fraction conversion in 8th grade math.

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