Write 40% as a decimal and as a simplified fraction

Write 40% as a decimal and as a simplified fraction

The correct Answer and Explanation is:

To convert 40% into a decimal and a simplified fraction, we can follow two straightforward steps.

Conversion of 40% to Decimal

1. Understanding Percentages: The term “percent” means “per hundred.” Therefore, 40% can be expressed as:40%=4010040\% = \frac{40}{100}40%=10040​
2. Converting to Decimal: To convert a percentage to a decimal, you divide by 100. Thus, we perform the following calculation:40100=0.40\frac{40}{100} = 0.4010040​=0.40So, 40% as a decimal is 0.40.

Conversion of 40% to Simplified Fraction

1. Starting with the Fraction: As noted, 40% can be expressed as the fraction 40100\frac{40}{100}10040​.
2. Simplifying the Fraction: To simplify a fraction, we divide both the numerator (40) and the denominator (100) by their greatest common divisor (GCD). The GCD of 40 and 100 is 20. We can find it by listing the factors:
   • Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
   • Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100
   The largest common factor is 20. Now, we divide both the numerator and the denominator by 20:40÷20100÷20=25\frac{40 \div 20}{100 \div 20} = \frac{2}{5}100÷2040÷20​=52​Therefore, 40% as a simplified fraction is 25\frac{2}{5}52​.

Summary

In conclusion, the percentage 40% can be converted to a decimal as 0.40 and to a simplified fraction as 25\frac{2}{5}52​. Understanding how to convert percentages into decimals and fractions is an essential skill in mathematics. It helps in various applications, including financial calculations, statistical analyses, and everyday situations like calculating discounts or determining proportions. Being proficient in these conversions enhances numerical literacy, which is crucial in both academic settings and real-world scenarios.