1.2 as a fraction

2 min read 16-01-2025

1.2 might seem like a simple decimal, but knowing how to express it as a fraction is a fundamental math skill. This guide will show you how to convert 1.2 into a fraction, and we'll explore different methods to help you understand the process fully. Understanding this conversion is essential for various mathematical operations and problem-solving.

Understanding Decimals and Fractions

Before we dive into the conversion, let's refresh our understanding of decimals and fractions. A decimal is a way of writing 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).

Method 1: Using the Place Value System

The easiest way to convert 1.2 into a fraction is by understanding its place value. The digit "2" is in the tenths place, meaning it represents 2/10. Therefore, 1.2 can be written as:

1 + 2/10 = 1 2/10

This is a mixed number (a whole number and a fraction). We can simplify this fraction further.

Simplifying the Fraction

The fraction 2/10 can be simplified by finding the greatest common divisor (GCD) of the numerator (2) and the denominator (10). The GCD of 2 and 10 is 2. Dividing both the numerator and denominator by 2 gives us:

(2 ÷ 2) / (10 ÷ 2) = 1/5

So, the simplified mixed number is 1 1/5.

Method 2: Converting the Decimal to an Improper Fraction

Another approach involves converting the decimal 1.2 into an improper fraction (where the numerator is greater than or equal to the denominator). First, we remove the decimal point:

Then, we divide this number by 10 (since there is one digit after the decimal point). This gives us:

12/10

Now, we can simplify this fraction, just as we did in Method 1, by dividing both the numerator and denominator by their GCD (2):

(12 ÷ 2) / (10 ÷ 2) = 6/5

This improper fraction, 6/5, is equivalent to 1 1/5.

Converting Improper Fractions to Mixed Numbers

If you end up with an improper fraction like 6/5, you can convert it to a mixed number. Divide the numerator (6) by the denominator (5):

6 ÷ 5 = 1 with a remainder of 1

The quotient (1) becomes the whole number part of the mixed number, and the remainder (1) becomes the numerator of the fraction, keeping the same denominator (5). Therefore, 6/5 = 1 1/5.

1.2 as a Fraction: Summary

We've explored two methods to convert 1.2 into a fraction, both leading to the same simplified result: 1 1/5 or 6/5. Choosing the method that you find easiest and most understandable is key. Remember to always simplify your fractions to their lowest terms for the most accurate representation. Understanding these methods will strengthen your understanding of decimal-to-fraction conversions.