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Chapter 37: Chapter 37

Problem 1143

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Find \(0.2525\) as a quotient of integers.

Short Answer

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The decimal \(0.2525\) can be expressed as the quotient of integers \(\frac{25}{99}\).
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TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: Identify the repeating block

Let's work with the decimal number \(0.2525\). We can see that the repeating block is "25", so our number can be represented as \(0.\overline{25}\).

Step 2: Convert the repeating decimal to a fraction

Let's represent the repeating decimal as \(x\). So our goal is to find a fraction equivalent to the repeating decimal: \[x=0.\overline{25}\] To convert this repeating decimal to a fraction, we'll first multiply it by 100 (because there are 2 decimal places in the repeating block, we need two zeroes): \[100x = 25.\overline{25}\] Now, subtract the original equation from the new equation: \[100x - x = 25.\overline{25} - 0.\overline{25}\] \[99x = 25\]

Step 3: Simplify the fraction

To find the fraction, we now just need to solve for \(x\): \[x = \frac{25}{99}\] So, we can express the decimal \(0.2525\) as the quotient of integers \(\frac{25}{99}\).

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