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Hello Can you teach me how to convert a decimal into a fraction please!

User Hnin
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1 Answer

18 votes
18 votes

Repeating decimals to fractions

Case: one repeating digit

Example: 0.11111...

Let's define:

x: repeating decimal

x = 0.11111...

Multiplying by 10 at both sides:

10x = 10*0.11111...

10x = 1.1111...

Subtracting x to 10x

10x - x = 1.1111... - 0.11111...

9x = 1

x = 1/9

example: 2.999....

Similarly than before:

x = 2.999....

Multiplying by 10 at both sides:

10x = 29.999...

Subtracting x to 10x:

10x - x = 29.999... - 2.999...

9x = 27

x = 27/9

x = 3

example: 1.2565656...

x = 1.2565656...

Multiplying by 100 at both sides:

100x = 100*1.2565656...

100x = 125.65656...

Subtracting x to 100x:

100x - x = 125.65656... - 1.2565656...

99x = 124.4

x = 124.4/99 = 1244/990 = 622/495

User Afsar Ahamad
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