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Answer :
To write [tex]\(97.5\%\)[/tex] as a fraction in simplest form, follow these steps:
1. Understand the Percentage:
- [tex]\(97.5\%\)[/tex] means [tex]\(97.5\)[/tex] out of [tex]\(100\)[/tex].
2. Convert to a Fraction:
- Start by writing it as a fraction: [tex]\(\frac{97.5}{100}\)[/tex].
3. Eliminate the Decimal:
- To eliminate the decimal, multiply both the numerator and the denominator by [tex]\(10\)[/tex] to make the numerator a whole number:
[tex]\[
\frac{97.5 \times 10}{100 \times 10} = \frac{975}{1000}
\][/tex]
4. Simplify the Fraction:
- To simplify [tex]\(\frac{975}{1000}\)[/tex], find the greatest common divisor (GCD) of [tex]\(975\)[/tex] and [tex]\(1000\)[/tex]. The GCD here is [tex]\(25\)[/tex].
5. Divide by the GCD:
- Divide both the numerator and denominator by [tex]\(25\)[/tex]:
[tex]\[
\frac{975 \div 25}{1000 \div 25} = \frac{39}{40}
\][/tex]
6. Final Result:
- Therefore, [tex]\(97.5\%\)[/tex] as a fraction in simplest form is [tex]\(\frac{39}{40}\)[/tex].
1. Understand the Percentage:
- [tex]\(97.5\%\)[/tex] means [tex]\(97.5\)[/tex] out of [tex]\(100\)[/tex].
2. Convert to a Fraction:
- Start by writing it as a fraction: [tex]\(\frac{97.5}{100}\)[/tex].
3. Eliminate the Decimal:
- To eliminate the decimal, multiply both the numerator and the denominator by [tex]\(10\)[/tex] to make the numerator a whole number:
[tex]\[
\frac{97.5 \times 10}{100 \times 10} = \frac{975}{1000}
\][/tex]
4. Simplify the Fraction:
- To simplify [tex]\(\frac{975}{1000}\)[/tex], find the greatest common divisor (GCD) of [tex]\(975\)[/tex] and [tex]\(1000\)[/tex]. The GCD here is [tex]\(25\)[/tex].
5. Divide by the GCD:
- Divide both the numerator and denominator by [tex]\(25\)[/tex]:
[tex]\[
\frac{975 \div 25}{1000 \div 25} = \frac{39}{40}
\][/tex]
6. Final Result:
- Therefore, [tex]\(97.5\%\)[/tex] as a fraction in simplest form is [tex]\(\frac{39}{40}\)[/tex].
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