1.375 as a fraction

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15-01-2025

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Understanding how to convert decimals to fractions is a fundamental math skill. This guide will walk you through converting the decimal 1.375 into its fractional equivalent. We'll break it down step-by-step, making it easy to understand and replicate for other decimal-to-fraction conversions.

Understanding Decimals and Fractions

Before we begin, let's refresh our understanding of decimals and fractions. Decimals represent parts of a whole number using a decimal point, while fractions represent parts of a whole using a numerator (top number) and a denominator (bottom number).

Converting 1.375 to a Fraction: Step-by-Step

Here's how to convert the decimal 1.375 into a fraction:

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

This is our starting point:

1.375/1

Step 2: Multiply the numerator and denominator by 1000.

We multiply by 1000 because there are three digits after the decimal point. This removes the decimal point from the numerator.

(1.375 * 1000) / (1 * 1000) = 1375/1000

Step 3: Simplify the fraction.

Now, we need to simplify the fraction 1375/1000 to its lowest terms. This means finding the greatest common divisor (GCD) of both the numerator and the denominator and dividing both by it.

The GCD of 1375 and 1000 is 125.

1375 ÷ 125 = 11 1000 ÷ 125 = 8

Therefore, the simplified fraction is:

11/8

Step 4: Convert to a mixed number (optional).

The fraction 11/8 is an improper fraction (the numerator is larger than the denominator). We can convert this to a mixed number, which includes a whole number and a proper fraction.

Dividing 11 by 8, we get 1 with a remainder of 3. This means:

11/8 = 1 3/8

Therefore, 1.375 as a fraction is 11/8 or 1 3/8.

Alternative Method: Using Place Value

Another way to approach this is to consider the place value of each digit after the decimal point.

• .3 represents 3 tenths or 3/10
• .07 represents 7 hundredths or 7/100
• .005 represents 5 thousandths or 5/1000

Adding these together, we get:

3/10 + 7/100 + 5/1000

To add these fractions, we need a common denominator (1000):

300/1000 + 70/1000 + 5/1000 = 375/1000

This fraction simplifies to 11/8 (as shown above). Then, add the whole number 1 to get 1 3/8.

Practice Makes Perfect

Try converting other decimals to fractions using these methods. The more you practice, the easier it will become! Remember to always simplify your fractions to their lowest terms.