What Is 7.2 As A Fraction

What is 7.2 as a Fraction? A Simple Guide

This article will guide you through the process of converting the decimal number 7.2 into its fractional equivalent. Understanding this process is crucial for various mathematical applications and helps solidify your grasp of decimal-fraction conversion. We'll break down the steps clearly and concisely, making it easy to understand, even for beginners.

Understanding Decimals and Fractions

Before we begin, let's briefly refresh our understanding of decimals and fractions. Decimals represent parts of a whole number using a base-ten system, separated by a decimal point. Fractions, on the other hand, represent parts of a whole number as a ratio of two integers – a numerator (top number) and a denominator (bottom number).

Converting 7.2 to a Fraction: Step-by-Step

1. Identify the Place Value: The digit '2' in 7.2 is in the tenths place. This means it represents two-tenths.

2. Write as a Fraction: We can express two-tenths as the fraction 2/10. Therefore, 7.2 can be initially written as 7 and 2/10.

3. Convert to an Improper Fraction (Optional but Recommended): To simplify further, we can convert the mixed number (7 and 2/10) into an improper fraction. We do this by multiplying the whole number (7) by the denominator (10), adding the numerator (2), and keeping the same denominator:

   (7 * 10) + 2 = 72

   This gives us the improper fraction 72/10.

4. Simplify the Fraction: Finally, we simplify the fraction by finding the greatest common divisor (GCD) of the numerator and denominator. The GCD of 72 and 10 is 2. Dividing both the numerator and denominator by 2, we get:

   72 ÷ 2 = 36 10 ÷ 2 = 5

Therefore, 7.2 as a fraction is 36/5.

Further Applications and Considerations

This process is applicable to converting any decimal number into a fraction. Remember the key steps: identify the place value of the decimal digits, write it as a fraction, and then simplify if possible. Understanding this fundamental conversion is beneficial for various mathematical problems involving fractions, decimals, and percentages.

This method of conversion also provides a solid foundation for more complex decimal to fraction conversions involving recurring decimals or decimals with more digits after the decimal point. Practice with different decimal numbers will further solidify your understanding.