Convert Percent to Fractions and Decimals In the following exercises,

oppvarmet16 2021-11-21 Answered
Convert Percent to Fractions and Decimals In the following exercises, convert each percent to a fraction and simplify all fractions.
37.5%

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Expert Answer

Coon2000
Answered 2021-11-22 Author has 1233 answers

Formula used:
Convert a percent to a fraction:
Step 1: Write the percent as a ratio with the denominator 100.
Step 2: Simplify the fraction if possible.
Calculation:
Consider 37.5%
Let us write the percent as a ratio with the denominator 100.
\(\displaystyle{37.5}\%={\frac{{{37.5}}}{{{100}}}}\)
\(\displaystyle={\frac{{{37.5}}}{{{100}}}}\times{\frac{{{10}}}{{{10}}}}\)
\(\displaystyle{37.5}\%={\frac{{{375}}}{{{1000}}}}\)
Now let us simplify \(\displaystyle{\frac{{{375}}}{{{1000}}}}\) by cancelling out the common factors.
\(\displaystyle{\frac{{{375}}}{{{1000}}}}={\frac{{{5}\cdot{5}\cdot{5}\cdot{3}}}{{{5}\cdot{5}\cdot{5}\cdot{2}\cdot{2}\cdot{2}}}}\)
\(\displaystyle={\frac{{{{{5}}}\cdot{{{5}}}\cdot{{{5}}}\cdot{3}}}{{{{{5}}}\cdot{{{5}}}\cdot{{{5}}}\cdot{2}\cdot{2}\cdot{2}}}}\)
\(\displaystyle{\frac{{{375}}}{{{1000}}}}={\frac{{{3}}}{{{8}}}}\)

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