Convert 75 percent to decimal fraction and also to fraction in the simplest form
The Correct Answer and Explanation is :
To convert 75 percent to a decimal fraction and a fraction in simplest form, we can follow these steps:
Conversion to Decimal Fraction
- Understanding Percentage: A percentage represents a part per hundred. Thus, 75 percent means 75 out of 100.
- Decimal Conversion: To convert a percentage to a decimal, you divide the percentage by 100. So:
[
75\% = \frac{75}{100} = 0.75
]
Conversion to Fraction in Simplest Form
- Setting up the Fraction: As established, 75 percent can be written as a fraction:
[
\frac{75}{100}
] - Simplifying the Fraction: To simplify the fraction, we need to find the greatest common divisor (GCD) of the numerator (75) and the denominator (100).
- The factors of 75 are: 1, 3, 5, 15, 25, 75.
- The factors of 100 are: 1, 2, 4, 5, 10, 20, 25, 50, 100.
- The GCD of 75 and 100 is 25.
- Dividing by the GCD: Now, we divide both the numerator and the denominator by their GCD (25):
[
\frac{75 \div 25}{100 \div 25} = \frac{3}{4}
]
Summary of Results
- Decimal Fraction: (0.75)
- Fraction in Simplest Form: (\frac{3}{4})
Explanation
Understanding percentages is crucial in many areas, including finance, statistics, and everyday calculations. When we convert percentages to decimals, we make them easier to work with, especially in mathematical operations. The conversion from percentage to fraction involves expressing the percentage over 100 and then simplifying it to its lowest terms. This helps clarify the relationship between different values, making comparisons and calculations more straightforward. In this case, 75 percent indicates a significant portion—three-quarters of a whole—which is represented as (0.75) in decimal form and (\frac{3}{4}) in fractional form. These conversions are useful for visualizing data, making decisions, or performing calculations in various contexts.