Write the repeating decimal as a fraction. .944944944 ______

Rephrase Problem: Let's first rephrase the ＂How can the repeating decimal 0.944944944... be expressed as a fraction?＂Identify Repeating Part: Identify the repeating part of the decimal. The digits ＂944＂ repeat indefinitely, so we can write the decimal as 0.944944944...Set Equation: Let's set x equal to the repeating decimal: x = 0.944944944...Multiply by 1000: To isolate the repeating part, we can multiply x by 1000, because there are three digits in the repeating sequence. This gives us 1000x = 944.944944944...Subtract Original: Now, subtract the original x from 1000x to get rid of the decimal part: 1000x - x = 944.944944944... - 0.944944944...Perform Subtraction: Perform the subtraction: 999x = 944Solve for x: Now, solve for x by dividing both sides of the equation by 999: x = 944/999Check for Simplification: Check if the fraction can be simplified. The numbers 944 and 999 do not have any common factors other than 1, so the fraction is already in its simplest form.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Write the repeating decimal as a fraction. $\newline$ $.944944944$

View step-by-step help

Home

Math Problems

Algebra 2

Write a repeating decimal as a fraction

Full solution

Q. Write the repeating decimal as a fraction.

\newline

.944944944

Rephrase Problem: Let's first rephrase the ＂How can the repeating decimal $0.944944944\ldots$ be expressed as a fraction?＂
Identify Repeating Part: Identify the repeating part of the decimal. The digits ＂ $944$ ＂ repeat indefinitely, so we can write the decimal as $0.944944944\ldots$
Set Equation: Let's set $x$ equal to the repeating decimal: $x = 0.944944944\ldots$
Multiply by $1000$ : To isolate the repeating part, we can multiply $x$ by $1000$ , because there are three digits in the repeating sequence. This gives us $1000x = 944.944944944\ldots$
Subtract Original: Now, subtract the original $x$ from $1000x$ to get rid of the decimal part: $1000x - x = 944.944944944... - 0.944944944...$
Perform Subtraction: Perform the subtraction: $999x = 944$
Solve for x: Now, solve for x by dividing both sides of the equation by $999$ : $x = \frac{944}{999}$
Check for Simplification: Check if the fraction can be simplified. The numbers $944$ and $999$ do not have any common factors other than $1$ , so the fraction is already in its simplest form.