Fractions

To convert a decimal into a fraction, we need to first write the given decimal in the form of a fraction by adding a denominator 1. Then, we multiply both the numerator and denominator with multiples of 10 to remove the decimal point. For example, 1.9 is a decimal number, and its equivalent fraction is 19/10, which cannot be simplified further.

Decimal: In terms of a computer, decimal numbers have a base 10. In mathematics, a decimal number has a dot (.) or decimal point between the digits. Decimals are essentially fractions with denominators as 10 or multiples of 10. Examples include 3.2, 10.9, 55.1, 1.28, and 9.234.

Fractions: A fraction represents a part of a whole number. It is denoted as a ratio of two numbers a/b, where a and b are integers, and b ≠ 0. The two numbers are called the numerator and denominator. For example, 1/2 is a part of 1, and 3/5 is a part of 3. Fractions can be proper, improper, or mixed.

Follow these steps to convert a decimal into a fraction:

• Write the given decimal as a ratio (p/q), where the denominator is 1.
• Multiply the numerator and denominator by multiples of 10 for every decimal point, so that the decimal in the numerator becomes a whole number. (For example, if there are two numbers after the decimal point, multiply by 100/100).
• Simplify the resulting fraction.

These steps make decimal-to-fraction conversion simple and accurate.

Here are some examples of decimal-to-fraction conversions to help you understand the concept better.

Example 1: Find the fraction form of the decimal 0.7.

Solution: Given the decimal number 0.7, we need to find its fraction form.
0.7 = 7/10
Now, multiply 7/10 by 2 in both the numerator and denominator:
(7 × 2) / (10 × 2) = 14/20
To find more equivalent fractions, multiply 7/10 by 5 and 10:
(7 × 5) / (10 × 5) = 35/50
(7 × 10) / (10 × 10) = 70/100
Therefore, the fractions of 0.7 are 7/10, 35/50, and 70/100.

Example 2: Convert 7.15 into a fraction.

Solution: Given the decimal number 7.15, multiply and divide by 100:
7.15 × 100 / 100 = 715/100
Simplify the fraction:
715/100 = 143/20
To find equivalent fractions, multiply the numerator and denominator by 2:
(143 × 2) / (20 × 2) = 286/40
Therefore, the fractions of 7.15 are 715/100, 143/20, and 286/40.

Explanation:
To convert 0.375 into a fraction, follow these steps:

Step 1: Write 0.375 as the numerator and place 1 in the denominator, followed by the number of zeros equal to the decimal places. Since 0.375 has three decimal places, the denominator becomes 1000.
0.375 = 375/1000

Step 2: Simplify the fraction 375/1000.
375/1000 = 3/8

Therefore, 0.375 as a fraction is 3/8.