How is 1 2/5 expressed as a percent
The Correct Answer and Explanation is :
To convert the mixed fraction ( 1 \frac{2}{5} ) into a percentage, follow these steps:
Step 1: Convert the mixed fraction to an improper fraction.
A mixed fraction consists of a whole number and a fraction. To convert ( 1 \frac{2}{5} ) to an improper fraction, we multiply the whole number (1) by the denominator (5), and then add the numerator (2). Here’s the calculation:
[
1 \frac{2}{5} = \frac{1 \times 5 + 2}{5} = \frac{5 + 2}{5} = \frac{7}{5}
]
Step 2: Convert the improper fraction to a decimal.
To convert ( \frac{7}{5} ) into a decimal, divide the numerator (7) by the denominator (5):
[
\frac{7}{5} = 1.4
]
Step 3: Convert the decimal to a percentage.
To convert a decimal to a percentage, multiply it by 100 and add the percent sign (%). In this case:
[
1.4 \times 100 = 140
]
Thus, ( 1 \frac{2}{5} ) as a percentage is ( 140\% ).
Explanation:
Understanding how to convert fractions and decimals into percentages is a key skill in both basic arithmetic and many real-world applications, such as budgeting, data analysis, and statistical reporting. The process of converting a mixed number to an improper fraction simplifies calculations, allowing for consistent and accurate conversions. By multiplying the decimal by 100, we convert it to a percentage, which is simply a way of expressing a number as a fraction of 100.
This process illustrates the close relationship between fractions, decimals, and percentages. They are all different representations of the same underlying value, and understanding how to switch between them is essential in a variety of mathematical and practical contexts. Whether you’re working in finance, science, or even everyday life, knowing how to convert between these forms is crucial for problem-solving.