 Recurring Decimals are the ones that are non-terminating but have repeating digits next to the decimal point. In this Worksheet on Recurring Decimals as Rational Numbers, we will have different kinds of problems for recurring decimal to rational number conversion.

Practice questions from Converting Recurring Decimals to Rational Numbers Worksheet PDF and improve your problem-solving ability. Answer the Recurring Decimal to Rational Numbers Questions and Answers regularly to build confidence and attempt the exams carefully to score well.

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Converting Recurring Decimals to Rational Numbers Worksheet with Answers

Example 1.
Write the decimal 0.825 as a rational number?

Solution:

Given Decimal Number is 0.825
To write 825 thousandths we use place 825 over 1000
= 825/1000
Simplifying the fraction further we have 33/40

Example 2.
Convert 2.333… into a rational number?

Solution:

Given Recurring Decimal is 2.333…..
Place the repeating digit on the left side of the decimal point. To do so move it by multiplying the original number by 10.
10x = 23.333…..
x= 2.333……
10x-x =23.333….-2.333….
9x=21
x=21/9
Therefore, recurring decimal to a rational number is 21/9

Example 3.
Convert 10.3454545… into a rational number?

Solution:

Given Recurring Decimal x= 10.3454545……..
Place the repeating digit on the left side of the decimal point. To do so move it by multiplying the original number by 1000.
1000x = 10345.454545…..
Shift the repeating digits to the right side of the decimal point. Simply multiply with 10
10x= 103.4545……
1000x-10x =10345.454545…..- 103.4545……
990x=10242
x=10242/990
x=569/55
Therefore, recurring decimal to a rational number is 569/55

Example 4.
Convert the following repeating decimal 0.272727 as a rational number?

Solution:

Given Repeating Decimal x = 0.272727…..
Place the repeating decimal on the left side of the decimal point. Simply multiply the original number by 100
100x = 27.2727….
x = 0.272727……
Subtracting both the equations we have
100x-x=27.272727…….-0.272727…..
99x=27
x =27/99

Example 5.
Convert the following repeating decimal as fraction 0.37777

Solution:

Given repeating decimal = 0.37777…….
Place the repeating digit on the left side of the decimal point. To do so multiply the original number by 10
10x = 3.77777…..
x = 0.37777….
10x-x = 3.777….-0.37777….
9x =3.4
x=3.4/9
x=34/90
x=17/45

Example 6.
Convert 124.45757… into the rational fraction?

Solution:

Given Repeating Decimal x = 124.45757….
Move the repeating digit to the left side of the decimal point at first. To do so multiply with 1000
1000x = 124457.575…..
Now we need to transfer the repeating digits of decimal numbers to the right side of the decimal point. Simply multiply with 10
10x =1244.5757……
Subtracting both the equations we have
1000x-10x = 124457.575….. – 1244.5757……
990x= 123213
x=123213/990
x=41071/330
Therefore, recurring decimal 124.45757… converted to a rational number is 41071/330