SOLUTION: please help me understand how to write in a common fraction in lowest terms 1.6(the 6 reapeating)

Question 92186This question is from textbook
: please help me understand how to write in a common fraction in lowest terms 1.6(the 6 reapeating)
This question is from textbook

Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Write 1.666... as an equivalent fraction in its lowest terms.
Well, the good news is that a repeating decimal (such as 1.666...) is a rational number and can, therefore, be expressed as the ratio of two integers (i.e. a fraction)...but, expressing a repeating decimal as a fraction requires a little more work than does converting a terminating decimal.
Here's how it goes:
First, separate the integer from the decimal so that we can convert just the decimal part (0.666...) to its equaivalent fraction.
Let n = 0.666... Multiply both sides by 10
10n = 6.666... Now subtract n from 10n
10n-n = (6.666...) - (0.666...)
9n = 6 Divide both sides by 9
n = 6/9 ...but n = 0.666..., so
0.666... = 6/9 Reduce this to:
0.666... = 2/3
Finally, add the integer back to get:
1.666... = 1 2/3 or, if you need it as a improper fraction, then:
1.666... = 5/3
You can check this with your calculator by dividing 5 by 3 and the calculator will display 1.666...

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