Write 4.4% as a fraction in simplest form
The Correct Answer and Explanation is :
To convert 4.4% into a fraction in simplest form, we start by understanding what a percentage represents. A percentage is a way of expressing a number as a fraction of 100. Therefore, 4.4% can be expressed as:
[
4.4\% = \frac{4.4}{100}
]
Next, we want to eliminate the decimal in the numerator. We can do this by multiplying both the numerator and the denominator by 10 (since there is one decimal place in 4.4):
[
\frac{4.4 \times 10}{100 \times 10} = \frac{44}{1000}
]
Now we have the fraction (\frac{44}{1000}). The next step is to simplify this fraction. To do so, we need to find the greatest common divisor (GCD) of the numerator and the denominator. The GCD of 44 and 1000 is 4.
Now, we divide both the numerator and the denominator by their GCD:
[
\frac{44 \div 4}{1000 \div 4} = \frac{11}{250}
]
Thus, 4.4% as a fraction in simplest form is (\frac{11}{250}).
To recap the steps:
- Convert the percentage to a fraction: (\frac{4.4}{100}).
- Eliminate the decimal by multiplying the numerator and denominator by 10: (\frac{44}{1000}).
- Simplify the fraction by dividing by the GCD: (\frac{11}{250}).
This process demonstrates how to convert percentages to fractions and simplify them for clearer representation. Understanding how to manipulate fractions and percentages is a valuable skill, especially in fields that involve quantitative data analysis, finance, and statistics.