10.8 as a fraction

2025

2 min read 30-03-2025

Understanding how to convert decimals to fractions is a fundamental skill in mathematics. This guide will show you exactly how to convert the decimal 10.8 into its fractional equivalent. We'll break it down step-by-step, making it easy to understand, even for beginners.

Understanding Decimals and Fractions

Before we begin, let's quickly review the basics. A decimal is a way of expressing a number that is not a whole number, using a decimal point to separate the whole number part from the fractional part. A fraction, on the other hand, represents a part of a whole, expressed as a ratio of two numbers (numerator and denominator).

Converting 10.8 to a Fraction: The Steps

Here's how to convert the decimal 10.8 into a fraction:

Step 1: Write the decimal as a fraction over 1.

This is the first step in the conversion process. We write 10.8 as a fraction by placing it over 1:

10.8/1

Step 2: Eliminate the decimal point.

To eliminate the decimal point, we multiply both the numerator and the denominator by 10 (since there's one digit after the decimal point). If there were two digits after the decimal point, we'd multiply by 100, and so on.

(10.8 * 10) / (1 * 10) = 108/10

Step 3: Simplify the fraction.

Now we simplify the fraction by finding the greatest common divisor (GCD) of the numerator (108) and the denominator (10). The GCD of 108 and 10 is 2. We divide both the numerator and the denominator by 2:

108/2 = 54 10/2 = 5

Therefore, the simplified fraction is 54/5.

10.8 as a Mixed Number

We can also express 10.8 as a mixed number. A mixed number combines a whole number and a fraction. Since 54 divided by 5 is 10 with a remainder of 4, we can write it as:

10 4/5

This means 10 and four-fifths.

Why This Method Works

This method works because multiplying both the numerator and the denominator of a fraction by the same number doesn't change its value. It's simply a way to represent the decimal in a different form while maintaining its numerical equivalence.

Practice Problems

Try converting these decimals into fractions:

2.5
3.75
15.2

Remember the steps: write it over 1, multiply to eliminate the decimal, and then simplify. The solutions are provided below, but try them yourself first!

Solutions to Practice Problems

2.5 = 5/2
3.75 = 15/4
15.2 = 76/5

Conclusion

Converting decimals to fractions is a straightforward process. By following these steps, you can confidently convert any decimal, including 10.8, into its fractional equivalent, whether as an improper fraction (54/5) or a mixed number (10 4/5). Remember to practice to solidify your understanding. Understanding this conversion is crucial for various mathematical applications.