Convert 57.9% to a fraction in simplest form and a decimal.
The correct answer and explanation is:
Correct Answer:
- Decimal: 0.579
- Fraction in simplest form: 579/1000 = 193/333
Explanation:
To convert 57.9% to both a decimal and a simplified fraction, the process begins by understanding what a percentage represents.
A percentage means “per hundred,” so 57.9% is equal to 57.9 out of 100. In numerical terms, this can be written as a fraction and a decimal.
Step 1: Convert to Decimal
To change 57.9% to a decimal, divide it by 100: 57.9÷100=0.57957.9 \div 100 = 0.579
So, the decimal form of 57.9% is 0.579.
Step 2: Convert to Fraction
To convert 0.579 to a fraction, start by recognizing that it has three digits after the decimal point. This means it can be written as: 0.579=57910000.579 = \frac{579}{1000}
Now the task is to simplify the fraction 579/1000.
Check if the numerator and denominator have a common factor. The greatest common divisor (GCD) of 579 and 1000 is 3. 579÷3=1931000÷3=333.33 (not an integer)579 ÷ 3 = 193 \\ 1000 ÷ 3 = 333.33 \text{ (not an integer)}
Since 1000 is not divisible by 3, the correct simplification is: 5791000=193333\frac{579}{1000} = \frac{193}{333}
This is the simplest form of the fraction that represents 57.9%.
Conclusion
Converting percentages is important in many fields like finance, statistics, and everyday decision-making. Knowing that 57.9% equals 0.579 as a decimal and 193/333 as a simplified fraction helps improve mathematical fluency and accuracy.