1.40 in fraction

Breiz Heurope

2 min read

·

11-03-2025

12

0

Share

1.40, or 1.4, might seem simple, but converting decimals to fractions requires understanding place value. This article will guide you through converting 1.40 into its simplest fractional form. We'll cover the process step-by-step and explore different methods to solidify your understanding.

Understanding Decimals and Fractions

Before we begin, let's quickly refresh our understanding of decimals and fractions. Decimals represent parts of a whole using a base-ten system (tenths, hundredths, thousandths, etc.). Fractions, on the other hand, represent parts of a whole using a numerator (top number) and a denominator (bottom number). The denominator shows how many equal parts the whole is divided into, and the numerator shows how many of those parts we have.

Converting 1.40 to a Fraction: The Method

Here's how to convert 1.40 into a fraction:

Step 1: Write the decimal as a fraction with a denominator of 1.

1.40 can be written as 1.40/1

Step 2: Multiply the numerator and denominator by a power of 10 to remove the decimal point.

Since there are two decimal places (hundredths), we multiply both the numerator and the denominator by 100:

(1.40/1) * (100/100) = 140/100

Step 3: Simplify the fraction.

Find the greatest common divisor (GCD) of 140 and 100. The GCD of 140 and 100 is 20. Divide both the numerator and the denominator by 20:

140 ÷ 20 = 7 100 ÷ 20 = 5

Therefore, the simplified fraction is 7/5.

Step 4: Express as a Mixed Number (Optional)

Since 7/5 is an improper fraction (the numerator is larger than the denominator), we can convert it to a mixed number. Divide the numerator (7) by the denominator (5):

7 ÷ 5 = 1 with a remainder of 2

This means 7/5 is equal to 1 2/5.

Alternative Method: Using Place Value Directly

You can also use the place value of the decimal directly to write the fraction. The digit 4 is in the tenths place, and the 0 in the hundredths doesn't change the value. This gives us 4/10 immediately. We can then add the whole number 1 and simplify 1 4/10 to 1 2/5 (as shown above).

Why Simplify Fractions?

Simplifying fractions is crucial for a couple of reasons:

• Clarity: A simplified fraction is easier to understand and work with.
• Accuracy: In many mathematical operations, working with simplified fractions leads to more accurate results.

Conclusion: 1.40 as a Fraction

Therefore, 1.40 can be expressed as the improper fraction 7/5 or the mixed number 1 2/5. Both are correct, but the choice depends on the context of the problem. Understanding the steps involved in converting decimals to fractions is fundamental to various mathematical concepts and applications. Remember to always simplify your fractions to their simplest form for clarity and accuracy.