We're glad you stopped by Express the repeating decimal as a quotient of integers If possible reduce to lowest terms tex 0 overline 4 tex A tex frac 2 5. This page is here to walk you through essential details with clear and straightforward explanations. Our goal is to make your learning experience easy, enriching, and enjoyable. Start exploring and find the information you need!
Answer :
To express the repeating decimal [tex]\(0.\overline{4}\)[/tex] as a quotient of integers, follow these steps:
1. Identify the repeating portion: The decimal [tex]\(0.\overline{4}\)[/tex] means the digit 4 repeats indefinitely, so it can be written as [tex]\(0.4444...\)[/tex].
2. Set up an equation: Let [tex]\(x = 0.4444...\)[/tex].
3. Eliminate the repeating decimal: Multiply both sides of the equation by 10 to shift the decimal point:
[tex]\[
10x = 4.4444...
\][/tex]
4. Subtract the original equation from this new equation:
[tex]\[
10x - x = 4.4444... - 0.4444...
\][/tex]
This simplifies to:
[tex]\[
9x = 4
\][/tex]
5. Solve for [tex]\(x\)[/tex]: Divide both sides by 9:
[tex]\[
x = \frac{4}{9}
\][/tex]
Therefore, the repeating decimal [tex]\(0.\overline{4}\)[/tex] can be expressed as the quotient [tex]\(\frac{4}{9}\)[/tex].
Checking the given options, the correct answer is:
C. [tex]\(\frac{4}{9}\)[/tex]
1. Identify the repeating portion: The decimal [tex]\(0.\overline{4}\)[/tex] means the digit 4 repeats indefinitely, so it can be written as [tex]\(0.4444...\)[/tex].
2. Set up an equation: Let [tex]\(x = 0.4444...\)[/tex].
3. Eliminate the repeating decimal: Multiply both sides of the equation by 10 to shift the decimal point:
[tex]\[
10x = 4.4444...
\][/tex]
4. Subtract the original equation from this new equation:
[tex]\[
10x - x = 4.4444... - 0.4444...
\][/tex]
This simplifies to:
[tex]\[
9x = 4
\][/tex]
5. Solve for [tex]\(x\)[/tex]: Divide both sides by 9:
[tex]\[
x = \frac{4}{9}
\][/tex]
Therefore, the repeating decimal [tex]\(0.\overline{4}\)[/tex] can be expressed as the quotient [tex]\(\frac{4}{9}\)[/tex].
Checking the given options, the correct answer is:
C. [tex]\(\frac{4}{9}\)[/tex]
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