Converting Decimals to Fractions: A Guide to 0.75 in Simplest Form

Conversion of decimal numbers to fractions is an essential skill in mathematics. This guide will walk you through the process of converting 0.75 to its simplest fractional form. Understanding this concept can be crucial for various applications ranging from basic arithmetic to more complex mathematical and scientific calculations.

Step-by-Step Conversion: 0.75 to 3/4

Let's begin by converting the decimal 0.75 into a fraction. The first step is to write the decimal as a fraction, recognizing that 0.75 is in the hundredths place.

Step 1: Write the decimal as a fraction.

Since 0.75 can be thought of as 75 hundredths, we can express it as:

0.75 75/100

Step 2: Simplify the fraction.

To simplify the fraction 75/100, we need to find the greatest common divisor (GCD) of 75 and 100. The GCD is 25. By dividing both the numerator and the denominator by 25:

75 ÷ 25 3 and 100 ÷ 25 4

Therefore, the simplified fraction is:

75/100 3/4

Hence, 0.75 as a fraction in its simplest form is 3/4.

Understanding the Conversion Process

The process of converting decimals to fractions is straightforward, but it involves a series of logical steps. Here's a step-by-step breakdown of the process:

Step 1: Express the Decimal as a Fraction

The decimal 0.75 can be expressed as a fraction by writing it over 100, since 0.75 is in the hundredths place:

0.75 75/100

Step 2: Simplify the Fraction

The next step is to simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 75 and 100 is 25:

75 ÷ 25 3 and 100 ÷ 25 4

Therefore, the simplified fraction is:

75/100 3/4

Additional Examples and Calculations

Let's explore a few more examples to solidify your understanding of converting decimals to fractions:

Example 1: 0.95 to Fraction

Express 0.95 as a fraction:

Step 1: Write the decimal as a fraction.

0.95 95/100

Step 2: Simplify the fraction.

The GCD of 95 and 100 is 5:

95 ÷ 5 19

100 ÷ 5 20

Therefore, the simplified fraction is:

95/100 19/20

Example 2: 0.8 to Fraction

Express 0.8 as a fraction:

Step 1: Write the decimal as a fraction.

0.8 8/10

Step 2: Simplify the fraction.

The GCD of 8 and 10 is 2:

8 ÷ 2 4

10 ÷ 2 5

Therefore, the simplified fraction is:

8/10 4/5

Conclusion

Converting decimals to fractions is a fundamental mathematical skill that can be applied in various scenarios. By following the steps outlined in this guide, you can easily convert 0.75 to the fraction 3/4. Practice with additional examples will help you master this technique and ensure accuracy in your calculations.

FAQ

Q: What is the simplified form of 0.75 as a fraction?

A: The simplified form of 0.75 as a fraction is 3/4.

Q: How do you convert decimals to fractions?

A: To convert a decimal to a fraction, write the decimal over 100 (or 1000, 10000, etc., depending on the number of decimal places). Then, simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD).

Q: What is the GCD used for in simplifying fractions?

A: The GCD (greatest common divisor) is the largest number that divides both the numerator and the denominator of a fraction. Dividing both by their GCD simplifies the fraction to its lowest terms.