# Convert 0.667 to a fraction [Solved] .

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Source(s): https://en.wikipedia.org/wiki/Overline#Math_and_sc
http://www.icoachmath.com/math_dictionary/bar_nota

Your text is apparently being a little sloppy when it says that 0.667 = 66.67/100. We know that in order to consider this to be true, we must interpret each side of the equal sign as a representation of 2/3. (Usually, we want to be more rigorous than that in our interpretation of what = means.)
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Suppose you have a repeating decimal that has a 6-digit repeat. (For example, 1/7 = 0.142857_142857. Call this value n. Now you can multiply n by 10^6, where the exponent 6 is the number of repeating digits. Then you have
.. n = 0.142857142857_142857
.. 10^6*n = 142857.142857142857_142857
Subtracting n from 10^6*n, we get
999999n = 142857 exactly. The repeating decimal fraction cancels in the subtraction. (You will note there are 6 nines, the number of repeating digits.)
Now, you can find n as a common fraction.
.. n = 142857/999999
Reducing this, we have
.. n = 1/7

Yes, 0.667 = 667/1000, but note that
667/1000 = 66.7/100 = 6.67/10 = 66.7/1, etc.

Source(s): https://en.wikipedia.org/wiki/Overline#Math_and_sc
http://www.icoachmath.com/math_dictionary/bar_nota

Source(s): https://en.wikipedia.org/wiki/Overline#Math_and_sc
http://www.icoachmath.com/math_dictionary/bar_nota

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We got that number, .667 by diving 2/3. Though the answer is a repeating .6666666 we round it to .667. Divide it out and youll see.

Some common fractions and there decimal equivalents:

1/2 = 0.5
1/4 = 0.25
1/8 = 0.125
3/4 = 0.75
3/8 = 0.375
5/8 = 0.625
7/8 = 0.875
1/3 = 0.33333. where the 3s repeat forever
2/3 = 0.66666. where the 6s repeat forever
1/5 = 0.2
2/5 = 0.4
3/5 = 0.6
4/5 = 0.8

667/1000.

We got that number, .667 by diving 2/3. Though the answer is a repeating .6666666 we round it to .667. Divide it out and youll see.

667/1000.

2/3 = 0.6666666. where the 6s continue forever

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Yes, 0.667 = 667/1000, but note that
667/1000 = 66.7/100 = 6.67/10 = 66.7/1, etc.

Yes, 0.667 = 667/1000, but note that
667/1000 = 66.7/100 = 6.67/10 = 66.7/1, etc.

This post is last updated on hrtanswers.com at Date : 1st of September – 2022