How do you convert 0.237 (237 repeating) to a fraction?

Question

Ethan Adkins · Accepted Answer

Use multiplication and a denominator of 100

Multiply the decimal by 100 to convert it to a percentage #0.237xx100=23.7%# 23.7 is the numerator and 100 is the denominator of 0.237 as a fraction. #23.7/100#

Savannah Anderson · Answer

#79/333#

We require to obtain 2 equations with the same repeating part and subtract them to eliminate the repeating part.

#0.bar237# represents 0.237237...

Begin by setting x #=0.bar237........ (A)#

To obtain the same repeating part after the decimal point we require to multiply by 1000.

#rArr1000x=237.bar237........ (B)#

Subtracting (A) from (B) will eliminate the repeated fraction.

(B) - (A) : 999x = 237#rArrx=237/999=79/333" in simplest form"#

Jace Anderson · Answer

undefined To convert 0.237 (237 repeating) to a fraction, you can represent the repeating decimal as $0.\overline{237}$. Let $x = 0.\overline{237}$. Multiply both sides of the equation by 1000 to eliminate the repeating decimal: $1000x = 237.\overline{237}$. Now, subtract the original equation from the multiplied equation: $1000x - x = 237.\overline{237} - 0.\overline{237}$. Simplify to get: $999x = 237$. Solve for $x$: $x = \frac{237}{999}$. Finally, simplify the fraction: $x = \frac{79}{333}$. So, $0.237 (237\text{ repeating}) = \frac{79}{333}$.