How do you express the repeating decimal 0.244 as a fraction?

Question

Lakisha Archer · Accepted Answer

Assuming it is just the 4s

enlacamig · Accepted Answer

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

1000 x = 244.244244 \dots

(2)
Subtract the equation (1) from equation (2)

1000 x = 244.244244 \dots

x = 0.244244 \dots

999 x = 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.

alenahelenash · Accepted Answer

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=2290 Therefore, the fractional form of the decimal 0.87 (7 being repeated) is 2290.

How do you express the repeating decimal 0.244 as a

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