Express the given percentage as a reduced fraction and a decimal.
175%
The correct answer and explanation is :
Step 1: Converting the Percentage to a Fraction
To convert a percentage to a fraction, you divide the percentage value by 100.
Given:
175%
The formula to convert a percentage to a fraction is:
[
\text{Fraction} = \frac{\text{Percentage}}{100}
]
So,
[
175\% = \frac{175}{100}
]
Now, we need to simplify this fraction.
Step 2: Simplifying the Fraction
We simplify the fraction (\frac{175}{100}) by finding the greatest common divisor (GCD) of 175 and 100.
- The factors of 175 are: 1, 5, 7, 25, 35, 175.
- The factors of 100 are: 1, 2, 4, 5, 10, 20, 25, 50, 100.
- The greatest common divisor of 175 and 100 is 25.
Now, divide both the numerator and denominator by 25:
[
\frac{175}{100} = \frac{175 \div 25}{100 \div 25} = \frac{7}{4}
]
Thus, the reduced fraction form of 175% is (\frac{7}{4}).
Step 3: Converting the Fraction to a Decimal
To convert the fraction (\frac{7}{4}) to a decimal, divide 7 by 4:
[
\frac{7}{4} = 1.75
]
Thus, 175% as a decimal is 1.75.
Summary
- Fraction form: (\frac{7}{4})
- Decimal form: 1.75
Explanation
Percentages are essentially fractions out of 100. When we are given a percentage like 175%, we express it as (\frac{175}{100}) to show the relationship of the percentage to the whole (100%). After simplifying the fraction (\frac{175}{100}) by dividing both the numerator and denominator by the greatest common divisor (25), we get the reduced fraction (\frac{7}{4}). Additionally, to express the fraction as a decimal, we divide 7 by 4, resulting in 1.75.
This approach highlights the mathematical process of simplifying and converting between different forms of numbers (percentage, fraction, and decimal), which is an important skill in both mathematics and daily life calculations.