# How do you express the repeating decimal 0.244 as a

Donald Johnson 2022-01-17 Answered
How do you express the repeating decimal 0.244 as a fraction?
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Lakisha Archer
enlacamig
First, create an equation that represents the repeating decimal that you want to convert to a fraction
$x=0.244244\dots .$ (1)
There are 3 repeating decimals, multiply both sides of the equation by $103=1000$ so that both equations have the same repeating digits to the right of the decimal point
$1000x=244.244244\dots$ (2)
Subtract the equation (1) from equation (2)
$1000x=244.244244\dots$
$x=0.244244\dots$
$999x=244$
Solve for the x in the equation to determine the equivalent fraction.
$x=\frac{244}{999}$
Therefore, 244/999 is simplified fraction of 0.244 repeating.
###### Not exactly what you’re looking for?
alenahelenash
Hint: In this problem, we have to find the fraction for the given decimal. We can first assume x to the given decimal. We can then multiply the both to 10 and 100, we will get two equations. We can then subtract the both equations to get the value of x, that is the exact fraction of the given decimal number. Complete step by step answer: We know that the given decimal number to be converted into its fraction is 0.244, where 4 is repeated, so we can write as 0.2444…. We can assume the decimal number to x, we get $⇒x=0.2444...$ (1) Now we can multiply the number 10 on both sides were in right-hand side the decimal point moves one point to the right, we get $⇒10x=2.444...$ (2) Now we can multiply 100 on both side of equation (1), we get $⇒100x=24.444...$ (3) We can now subtract the equation (2) and (3), we get $⇒90x=22.00$ We can now divide the number 90 on both the sides, we get $⇒x=\frac{22}{90}$ Therefore, the fractional form of the decimal 0.87 (7 being repeated) is $\frac{22}{90}$.