Write 24% as a decimal and as a simplified fraction.
The Correct Answer and Explanation is :
The correct answer is:: 24% as a decimal is 0.24.
Fraction Representation: 24% as a simplified fraction is (\frac{6}{25})
To convert 24% into a decimal and a simplified fraction, we can follow these steps:
Conversion to Decimal
- Understanding Percentage: The term “percent” means “per hundred.” Therefore, 24% can be interpreted as 24 out of 100.
- Decimal Conversion: To convert a percentage to a decimal, divide the percentage by 100. Thus:
[
24\% = \frac{24}{100} = 0.24
]
Conversion to Fraction
- Starting with the Percentage: Again, we start with 24%, which we can express as a fraction:
[
24\% = \frac{24}{100}
] - Simplifying the Fraction: To simplify the fraction, we need to find the greatest common divisor (GCD) of the numerator (24) and the denominator (100). The GCD of 24 and 100 is 4.
- Dividing Both Numerator and Denominator: We can now simplify the fraction by dividing both the numerator and the denominator by their GCD:
[
\frac{24 \div 4}{100 \div 4} = \frac{6}{25}
]
Final Results
- Decimal Representation: 24% as a decimal is 0.24.
- Fraction Representation: 24% as a simplified fraction is (\frac{6}{25}).
Explanation of Steps
Understanding percentages and their conversions is fundamental in mathematics. Percentages express a ratio out of 100, which makes it straightforward to translate them into decimals and fractions. Dividing by 100 when converting to a decimal directly indicates the portion of a whole, while simplifying fractions ensures that the numbers are presented in their simplest form, making them easier to work with in various mathematical contexts. Recognizing and performing these conversions can be crucial in various fields, including finance, statistics, and everyday life situations. Whether you are calculating discounts, interest rates, or data analysis, mastering these conversions enhances numerical fluency and comprehension.