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Writing fractions as repeating decimals review

Review converting fractions to repeating decimals, and then try some practice problems.

Writing fractions as decimals

To convert a fraction to a decimal, we divide the numerator by the denominator.
Example:$\frac{2}{5}$
$\frac{2}{5}=2÷5$
$\frac{2}{5}=0.4$

Writing fractions as repeating decimals

However, it does not always work out that nicely.
Sometimes, when we divide the numerator by the denominator, it becomes clear that the digits will keep repeating. In this case, we write the answer as a repeating decimal.
In our answer, we write a bar over the repeating digits to show that they repeat.
Example:$\frac{4}{9}$
$\frac{4}{9}=4÷9$
No matter how long we divide, the $4$ will continue to repeat in our quotient.
$\frac{4}{9}=0.\stackrel{―}{4}$

Practice

Problem 1
Select the decimal that is equivalent to $\frac{2}{3}$.

Want to try more problems like this? Check out this exercise.

Want to join the conversation?

• why does math have to be hard like life is hard already
• ong bro
• "Want to try more problems like this?" Absolutively not
• fr bro, like who wants to keep doin' this? i dont
(1 vote)
• UH I am still a bit confused like how would we solve 0.36 but only the 6 is repeating
• Let x = 0.3666....

Only 1 digit (the 6) repeats, so multiply both sides by 10^1=10 to get

10x = 3.6666...

Subtract the first equation from the second equation to cancel out repeating parts, to get

9x = 3.3

Divide both sides by 9 to get

x = 3.3/9 .

We can simplify 3.3/9 by first multiplying top and bottom by 10 (getting rid of the decimal) to get 33/90, then dividing top and bottom by 3 to get 11/30.

Have a blessed, wonderful day!
• why does the math have to be so hard
• Math makes life hard.
• Thanks to Corona Virus, My teacher posted 402 assignments on here
• its over for bro