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How do you convert 0.7326 (326 being repeated) to a fraction?

Answer 1

Eva Adamson

#7319/9990#

We first let 0.7326 (326 being repeated) be #x#.

Since #x# is recurring in 3 decimal places, we multiply it by 1000.

#1000x = 732.6326#

Next, we subtract them.

#1000x - x = 732.6326 - 0.7326#

#999x = 731.9#

Lastly, we divide both sides by 999 to get #x# as a fraction.

#x = 731.9/999#

#= 7319/9990#

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Answer 2

Avery Alexander

To convert the decimal 0.7326 (with the 326 sequence repeating) to a fraction, you can follow these steps:

Let x be the repeating decimal: x = 0.7326326326...
Multiply x by 1000 to move the decimal point three places to the right: 1000x = 732.6326326...
Subtract x from 1000x to eliminate the repeating part: 1000x - x = 732.6326326... - 0.7326326326... 999x = 732
Solve for x: x = 732/999

So, the fraction representation of 0.7326 (with the 326 sequence repeating) is 732/999.

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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.