Convert Fractions to Decimals

Converting fractions to decimals is a process of converting a number represented in the form of p/q where q\neq 0 to decimal form. There are two main methods to convert Fractions to decimals are Long division method and the Denominator Adjustment method (for powers of 10).

Example : 1.25 in decimal can be written as 5/4 in fractions.

There are two main methods to convert fractions to decimals:

• Long Division
• Denominator Adjustment (for powers of 10)

Long Division

In this method of Converting Fractions to Decimals, he numerator is divided by the denominator. It treats the fraction as a division problem and where t set up a long division problem with the denominator as the divisor and the numerator as the dividend (add a decimal and a zero to the dividend if needed) works for any fraction. It works for type of fractions.

Perform the division following the usual steps (divide, multiply, subtract, bring down the next digit). We either get a remainder of zero (terminating decimal) or a repeating remainder (repeating decimal).

Steps for the Long division to convert Decimal to Fraction:

• Write the fraction with the denominator (bottom number) as the divisor outside the division bracket.
• Write the numerator (top number) as the dividend inside the bracket.
• Since we're dealing with decimals, add a decimal point and a zero (or more zeros if needed) to the dividend. This makes the division process easier.
• Perform Division like normal ( if at any point the dividend becomes smaller than the divisor you can add as many zeroes as required to the dividend by placing a decimal point to the quotient.

Example: Convert 7/16 to decimal by using Long Division.

Solution: Set up long division:

Performing the division. We get a remainder of 0, so the decimal terminates.

Answer: 7/16 = 0.4375

Denominator Adjustment

This is a shortcut method to Convert Fractions to Decimals in this trick we convert the denominator to power of 10 Ex: 10, 100, 1000. The trick is to multiply both the numerator and denominator by the same number to make the denominator a power of 10. and then place the decimal in the numerator by counting the number of zeroes in the denominator. This makes converting to decimal straightforward because 1/10 = 0.1, 1/100 = 0.01, and so on.

Example: 15/25 = 15/25 \times 4/4 = 60/100 \\60/100 = 6.0

Since 1/10 = 0.1, 1/100 = 0.01, and so on, converting to decimal becomes straightforward.

Example: Let's convert 3/25 to decimal using this method.

3/25 Denominator is not a power of 10
3/25 \times 4/4 = 12/100 (Multiplying both numerator and denominator with 4 to convert to power of 10)
12/100 = 0.12 (Convert into Decimal)

Answer: 3/25 = 0.12

Fraction to Decimal Chart

A fraction-to-decimal chart is a reference for common conversions but it's not a substitute for understanding conversion methods. If you need to convert a fraction not in the chart or want a deeper understanding of the relationship between fractions and decimals, learn the long division or denominator adjustment methods.

There are several ways to categorize fractions, but here are some of the most common types:

By Relationship Between Numerator and Denominator:

• Proper Fraction: The numerator is smaller than the denominator. The fraction represents a part of a whole that is less than the whole itself. (Example: 2/5 of a pie).

• Improper Fraction: The numerator is equal to or larger than the denominator. The fraction can represent a whole or more than a whole. (Example: 5/4 of a pizza, which could be 1 pizza and an extra slice).

• Mixed Fraction: A combination of a whole number and a proper fraction. It represents splitting something into whole units and then further dividing some of those units into parts. (Example: 1 ½ cups of flour).

By Numerator:

• Unit Fraction: A fraction with a numerator of 1. It represents one part out of a certain number of equal parts. (Example: 1/4 cup, which is one out of four equal parts of a cup)

Fraction to Decimal Table

Fraction to decimal table is added below:

Note: If you need to convert a fraction not in the chart, you can use the long division method or the denominator adjustment method explained previously.

Examples on Fraction to Decimal Conversion

Below are the 5 examples showcasing different methods for converting fractions to decimals are as follows :

Example 1: Denominator Adjustment (Power of 10) Convert 3/20 to decimal.

Solution:

Denominator (20) is not a power of 10, but we can multiply by 5 (because 5 x 20 = 100).

So, convert (3 x 5) / (20 x 5) = 15/100.

Now, 15 divided by 100 is 0.15.

Answer: 3/20 = 0.15

Example 2: Long Division (Repeating Decimal). Convert 1/3 to decimal.

Solution:

Set up long division:

We keep dividing and get a remainder of 1 repeatedly. This indicates a repeating decimal.

Answer: 1/3 = 0.3333... (repeating)

Example 3: Denominator Adjustment (Mixed Method). Convert 9/80 to decimal.

Solution:

We can't easily convert the denominator to a power of 10 by multiplying by one number.
But we can see that 9/80 is equivalent to 90/800 (multiply both numerator and denominator by 10).
Now, the denominator is a power of 10 (100), so 90/800 = 0.1125.

Answer: 9/80 = 0.1125

Example 4: Simplifying Before Conversion. Convert 12/24 to decimal.

Solution:

Before converting, we can simplify the fraction by dividing both numerator and denominator by 12 (their greatest common divisor). This gives us 1/2.
Now, converting 1/2 to decimal is easy: 1 divided by 2 is 0.5.

Answer: 12/24 = 0.5 (after simplification)