What is 62.5% as a fraction in simplest form?
The Correct Answer and Explanation is:
To convert 62.5% to a fraction in its simplest form, follow these steps:
- Convert the percentage to a fraction:
Since 62.5% means 62.5 out of 100, the initial fraction is:
[
\frac{62.5}{100}
] - Eliminate the decimal:
To remove the decimal, multiply both the numerator and denominator by 10:
[
\frac{62.5 \times 10}{100 \times 10} = \frac{625}{1000}
] - Simplify the fraction:
Now, simplify the fraction by finding the greatest common divisor (GCD) of 625 and 1000. The GCD is 125. Divide both the numerator and the denominator by 125:
[
\frac{625 \div 125}{1000 \div 125} = \frac{5}{8}
]
Thus, 62.5% as a fraction in its simplest form is 5/8.
Explanation:
Percentages represent parts out of 100. When converting a percentage to a fraction, you place the percentage number over 100. For example, 62.5% is equivalent to 62.5 over 100, written as ( \frac{62.5}{100} ).
Decimals in fractions complicate calculations, so the next step is to eliminate the decimal. By multiplying both the numerator and denominator by 10, you shift the decimal place to the right, converting 62.5 into 625 and 100 into 1000.
Next, to simplify the fraction, we find the greatest common divisor (GCD). The GCD is the largest number that can divide both the numerator and the denominator evenly. For 625 and 1000, the GCD is 125, meaning that both numbers can be divided by 125. When you do this, you are left with the fraction ( \frac{5}{8} ), which cannot be simplified further.
In conclusion, 62.5% simplifies to the fraction 5/8, showing that fractions and percentages are different ways to express parts of a whole.