How do you find the repeating decimal 0.246 with 246 repeated as a fraction?

Answer 1

Set the decimal as a variable to be multiplied by a power of ten (such that the repeating decimal part remains the same), then subtract the original from the multiplied number, and simplify as needed to get:
#0.246246246... = 82/333#

Set this repeating decimal to a variable, say, #N#.
#N = 0.246246246...#
Now, multiply this by a power of #10#, one that keeps the decimal part of the number the same:
#1000N = 246.246246246...#
Here, the whole number changes, but what is repeating is still #246#. We can then subtract the original from the multiplied number:
#1000N - N = (246.246246246...) - (0.246246246...)#

The repeated decimals ought to be eliminated:

#999N = 246#
We can finally divide by #999# to get our answer:
#(999N)/999 = 246/999#
#N = 246/999#

And make it simple:

#N = 82/333#
Therefore, #0.246246246... = 82/333#
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Answer 2

To find the repeating decimal 0.246 with 246 repeated as a fraction:

Step 1: Let x = 0.246246...

Step 2: Multiply x by 1000 (because there are three decimal places):

0.246246... * 1000 = 246.246246...

Step 3: Subtract x from 1000x:

1000x - x = 246.246246... - 0.246246... 999x = 246

Step 4: Solve for x:

x = 246 / 999

Step 5: Simplify the fraction:

x = 82 / 333

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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.

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.

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.

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.

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