Converting Decimal Fractions

less than a minute read 09-11-2024

Converting decimal fractions is a fundamental skill in mathematics, essential for various applications in daily life, academics, and professional settings. This article will provide a clear explanation of how to convert decimal fractions into different forms, such as fractions and percentages.

What is a Decimal Fraction?

A decimal fraction is a fraction where the denominator is a power of ten, typically expressed using a decimal point. For example, the decimal fraction 0.75 represents 75/100.

Converting Decimal Fractions to Common Fractions

Step 1: Identify the Decimal

Take the decimal fraction you want to convert. For example, consider the decimal 0.6.

Step 2: Write it as a Fraction

Write the decimal as a fraction with a denominator of 1.

For example: [ 0.6 = \frac{0.6}{1} ]

Step 3: Eliminate the Decimal Point

Multiply both the numerator and the denominator by 10 for every digit after the decimal point. Since there is one digit after the decimal point in 0.6, we multiply by 10:

[ 0.6 = \frac{0.6 \times 10}{1 \times 10} = \frac{6}{10} ]

Step 4: Simplify the Fraction

Now simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD).

In this case, the GCD of 6 and 10 is 2:

[ \frac{6 ÷ 2}{10 ÷ 2} = \frac{3}{5} ]

So, 0.6 as a fraction is ( \frac{3}{5} ).

Converting Decimal Fractions to Percentages

To convert a decimal fraction into a percentage, follow these simple steps:

Step 1: Multiply by 100

Take your decimal fraction and multiply it by 100.

For example, to convert 0.75 to a percentage: [ 0.75 \times 100 = 75 ]

Step 2: Add the Percentage Sign

Don’t forget to add the percentage sign (%) to the result:

So, 0.75 as a percentage is 75%.

Summary

In conclusion, converting decimal fractions is a straightforward process:

To convert to a common fraction: Identify the decimal, write it over 1, eliminate the decimal point, and simplify.
To convert to a percentage: Multiply the decimal by 100 and add the percentage sign.

Understanding these conversions can greatly assist in numerical problem-solving and real-life applications.