Converting a decimal fraction to a mixed number

🏆Practice transition from a decimal fraction to a mixed fraction

Converting a decimal to a mixed number

To convert a decimal fraction to a mixed fraction,
we ask ourselves how to read the decimal fraction or in other words, what the last digit represents –
if we use the word tenths – we place 10 in the denominator
if we use the word hundredths – we place 100 in the denominator
if we use the word thousandths – we place 1000 in the denominator

The number itself – everything that appears after the decimal point, we place in the numerator.
The whole number in the decimal fraction, we add to the mixed fraction as the whole number in the mixed fraction.

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Test yourself on transition from a decimal fraction to a mixed fraction!

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Write the following fraction as a decimal:

\( \frac{5}{100}= \)

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Converting a decimal fraction to a mixed number

The transition from a decimal fraction to a mixed number is simple and easy if you just know the right way.
To do it correctly without making mistakes, we recommend that you make sure you know how to read decimal fractions properly.
If you know how to read decimal fractions correctly – the path to success in transitioning from a decimal fraction to a simple fraction is completely paved for you.

How do you read a decimal fraction?

A decimal fraction represents a fraction or a non-whole number using a decimal point.
The decimal point divides the fraction as follows:
*Notations in a Word file*

Explanation:

The entire part to the left of the decimal point is called whole numbers.
The entire part to the right of the decimal point is divided as follows:
The first digit after the point represents tenths
The second digit after the point represents hundredths
The third digit after the point represents thousandths

Remember! There is no unity – the counting starts from tenths.

How do we know the denominator of the mixed fraction?
As we saw above, decimal fractions consist of whole numbers that are before the decimal point and parts that are after the decimal point, where the parts are made up of tenths, hundredths, and thousandths.
If we convert the tenths, hundredths, and thousandths to a denominator in a simple fraction, we get:

*Symbols in Word file*

Remember:
Thousandths – 1000 in the denominator
Hundredths – 100 in the denominator
Tenths – 10 in the denominator

How will you remember this?
It is very easy and simple.
Tenths come from the word 10, so the denominator that should appear is 10.
Hundredths come from the word 100, so the denominator that should appear is 100.
Thousandths come from the word 1000, so the denominator that should appear is 1000.

The key to success lies here:
To read a decimal fraction correctly, we need to ask ourselves what the last digit in the decimal fraction represents.


For example:
How do we read the decimal 9.569.56?
6 is the last digit and it represents hundredths, so we read the decimal as 99 whole and 5656 hundredths.
How wonderful! We just learned the notation for hundredths - *Notation in a Word file*

All that remains for us is to put 5656 in the numerator, 99 in the whole number part and get the simple fraction of the decimal 9.569.56:
9561009 \frac{56}{100}

Let's practice more:
Convert the decimal 4.24.2 to a mixed number

Solution:
Let's ask ourselves – how do we read the fraction? 
44 wholes and 22 tenths.
Therefore, we will use the tenths notation (denominator 1010) and place 22 in the numerator and 44 in the wholes:
42104 \frac{2}{10}

Convert the fraction 7.2007.200 to a simple fraction

Solution:
Let's ask ourselves – how do we read the fraction?
77 wholes and 200200 thousandths.
Therefore, we will use the thousandths notation (denominator 10001000), place 200200 in the numerator and 77 as the whole number: 720010007 \frac{200}{1000}
Note – if the fraction can be simplified, you can simplify it without changing its value:

7210=720010007 \frac{2}{10} = 7 \frac{200}{1000}
And indeed we already know that: 7.200=7.27.200 = 7.2

Convert the fraction 1.651.65 to a simple fraction
Solution:
Let's ask ourselves – how do we read the fraction? 
11 whole and 6565 hundredths
Therefore, we will use the hundredths notation – denominator 100100, place 6565 in the numerator and 11 as the whole number.
We get:

1651001 \frac{65}{100}
We can simplify by dividing by 55 and get: 113201 \frac{13}{20}

Another example
Convert the decimal 6.226.22 to a mixed number

Solution:
Let's ask ourselves – how do we read the fraction? 
66 wholes and 2222 hundredths 
Therefore, we will use the hundredths notation - denominator 100100 and place 2222 in the numerator. Let's not forget to add 66 wholes on the side and we get:

6221006 \frac{22}{100}

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