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How do you convert 7.12 (12 being repeated) to a fraction?

Answer 1

Eli Assouline

#235/33#

We first let 7.12 be #x#.

Since #x# is recurring in 2 decimal places, we multiply it by 100.

#100x = 712.12#

Next, we subtract them.

#100x - x = 712.12 - 7.12#

#99x = 705#

Lastly, we divide both sides by 99 to get #x# as a fraction.

#x = 705/99#

#= 235/33#

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Answer 2

Isaiah Anthony

To convert the repeating decimal 7.12 (12 repeating) to a fraction, you can follow these steps:

Step 1: Let x = 7.121212...

Step 2: Multiply x by 100 to move the decimal point two places to the right: 100x = 712.121212...

Step 3: Subtract x from 100x to eliminate the repeating decimal: 100x - x = 712.121212... - 7.121212... 99x = 705

Step 4: Solve for x: x = 705 / 99

Therefore, 7.12 (12 repeating) can be expressed as the fraction 705/99.

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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.