.375 As A Fraction In Simplest Form

.375 as a Fraction in Simplest Form: A Step-by-Step Guide

Understanding how to convert decimals to fractions is a fundamental skill in mathematics. This article will guide you through the process of converting the decimal 0.375 into its simplest fraction form. We'll break down the steps clearly and concisely, ensuring you can easily understand and apply this method to other decimal conversions. This is a crucial skill for students, and anyone working with numbers on a regular basis.

Understanding the Process:

Converting a decimal to a fraction involves understanding place value. The decimal 0.375 represents three tenths (0.3), seven hundredths (0.07), and five thousandths (0.005). We'll use this understanding to build our fraction.

Step 1: Write the Decimal as a Fraction over 1

The first step is to write the decimal as a fraction with a denominator of 1. This looks like this:

0.375/1

Step 2: Multiply the Numerator and Denominator to Eliminate the Decimal

To remove the decimal point, we multiply both the numerator and the denominator by 1000. This is because the decimal extends to the thousandths place (three places after the decimal point). Multiplying by 1000 shifts the decimal point three places to the right, effectively removing it.

(0.375 * 1000) / (1 * 1000) = 375/1000

Step 3: Simplify the Fraction

Now we need to simplify the fraction 375/1000 to its simplest form. This means finding the greatest common divisor (GCD) of both the numerator and the denominator and dividing both by it. The GCD of 375 and 1000 is 125.

375 ÷ 125 = 3
1000 ÷ 125 = 8

Therefore, the simplified fraction is:

3/8

Step 4: Verify the Result

To verify your answer, you can convert the fraction 3/8 back into a decimal by dividing the numerator (3) by the denominator (8). This will give you 0.375, confirming that your conversion was accurate.

Conclusion:

Therefore, the simplest form of the decimal 0.375 is 3/8. This method can be applied to any decimal you want to convert into a fraction. Remember the key steps: write it over 1, eliminate the decimal point by multiplying, and then simplify to its lowest terms. This simple process allows for a clear understanding of decimal-to-fraction conversions, making it an invaluable skill for various mathematical applications. Practice will make you proficient in this valuable skill!