/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 55 Express each repeating decimal a... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

Express each repeating decimal as a quotient of integers. If possible, reduce to lowest terms. \(0 . \overline{257}\)

Short Answer

Expert verified
The repeating decimal \(0 . \overline{257}\) can be expressed as a quotient of integers as \(\frac{257}{999}\)

Step by step solution

01

Create an equation

Let \(x = 0 . \overline{257}\)
02

Multiply by 1000

Multiply the equation by 1000, \(1000x = 257 . \overline{257}\)
03

Subtract the two equations

Subtract the first equation from the second to eliminate the repeating decimal: \(1000x - x = 257 . \overline{257} - 0 . \overline{257}; 999x = 257\)
04

Solve for x

Divide both sides by 999 to solve for x: \(x= \frac{257}{999}\)

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