Home > Algebra > Conversion of Decimals, Fractions, and Percent

How do you convert 0.2 (2 repeating) as a fraction?

Answer 1

Eli Assouline

#0.22222222...........=2/9#

Let #x=0.22222222...........# ..................................(1)

then #10x=2.22222222...........# ..................................(2)

After deducting (1) from (2), we obtain

#9x=2#

and hence #x=2/9# or

#0.22222222...........=2/9#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Nathan Axel

To convert 0.2 (2 repeating) to a fraction, you can use the following steps:

Step 1: Let x = 0.2 (2 repeating) Step 2: Multiply both sides of the equation by 10 to shift the decimal point: 10x = 2.2 (2 repeating) Step 3: Subtract the original equation from the shifted equation to eliminate the repeating decimal: 10x - x = 2.2 (2 repeating) - 0.2 (2 repeating) Step 4: Solve for x: 9x = 2 Step 5: Divide both sides by 9: x = 2/9

So, 0.2 (2 repeating) as a fraction is 2/9.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.