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:
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 9.56?
6 is the last digit and it represents hundredths, so we read the decimal as 9 whole and 56 hundredths.
How wonderful! We just learned the notation for hundredths - *Notation in a Word file*
All that remains for us is to put 56 in the numerator, 9 in the whole number part and get the simple fraction of the decimal 9.56:
910056
Let's practice more:
Convert the decimal 4.2 to a mixed number
Solution:
Let's ask ourselves – how do we read the fraction?
4 wholes and 2 tenths.
Therefore, we will use the tenths notation (denominator 10) and place 2 in the numerator and 4 in the wholes:
4102
Convert the fraction 7.200 to a simple fraction
Solution:
Let's ask ourselves – how do we read the fraction?
7 wholes and 200 thousandths.
Therefore, we will use the thousandths notation (denominator 1000), place 200 in the numerator and 7 as the whole number: 71000200
Note – if the fraction can be simplified, you can simplify it without changing its value:
7102=71000200
And indeed we already know that: 7.200=7.2
Convert the fraction 1.65 to a simple fraction
Solution:
Let's ask ourselves – how do we read the fraction?
1 whole and 65 hundredths
Therefore, we will use the hundredths notation – denominator 100, place 65 in the numerator and 1 as the whole number.
We get:
110065
We can simplify by dividing by 5 and get: 12013
Another example
Convert the decimal 6.22 to a mixed number
Solution:
Let's ask ourselves – how do we read the fraction?
6 wholes and 22 hundredths
Therefore, we will use the hundredths notation - denominator 100 and place 22 in the numerator. Let's not forget to add 6 wholes on the side and we get:
610022
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examples with solutions for converting a decimal fraction to a mixed number
Exercise #1
Write the following fraction as a decimal:
107=
Video Solution
Step-by-Step Solution
Write the simple fraction in decimal form
7.0
Since the fraction is divisible by 10, move the decimal point one place to the left and get:
.7
Let's add the zero to the left of the decimal point and get:
0.7
Answer
Exercise #2
Write the following fraction as a decimal:
105=
Video Solution
Step-by-Step Solution
Write the simple fraction in decimal form
5.0
Since the fraction is divided by 10, move the decimal point one place to the left and get:
.5
Complete the zero to the left of the decimal point and get:
0.5
Answer
Exercise #3
Video Solution
Step-by-Step Solution
Let's pay attention to where the decimal point is located in the number.
Remember:
One number after the decimal point represents tenths
Two numbers after the decimal point represent hundredths
Three numbers after the decimal point represent thousandths
And so on
In this case there are three numbers after the decimal point so the number is divided by 1000
Write the fraction in the following way:
10000171
We will remove the extra zeros and get:
1000171
Answer
1000171
Exercise #4
Write the following fraction as a decimal:
1001=
Video Solution
Answer
Exercise #5
Write the following fraction as a decimal:
10020=
Video Solution
Answer