15.625 as a fraction

2 min read 01-03-2025

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 15.625 into its fractional equivalent. We'll break it down step-by-step, making it easy to understand and apply to other decimal-to-fraction conversions.

Understanding Decimals and Fractions

Before we begin, let's refresh our understanding of decimals and fractions. A decimal represents a part of a whole number, using a decimal point to separate the whole number from the fractional part. A fraction, on the other hand, represents a part of a whole number as a ratio of two integers: a numerator (top number) and a denominator (bottom number).

Converting 15.625 to a Fraction

The number 15.625 has a whole number part (15) and a decimal part (.625). We'll handle these separately.

Step 1: Address the Decimal Part

The decimal .625 is the part we need to convert into a fraction. To do this, we write it as a fraction with a denominator of 1:

.625/1

Step 2: Eliminate the Decimal Point

To remove the decimal point, we multiply both the numerator and the denominator by a power of 10. The power of 10 we choose depends on the number of digits after the decimal point. Since there are three digits after the decimal point (625), we multiply by 1000:

(0.625 * 1000) / (1 * 1000) = 625/1000

Step 3: Simplify the Fraction

Now we simplify the fraction 625/1000 by finding the greatest common divisor (GCD) of both the numerator and the denominator. The GCD of 625 and 1000 is 625. Dividing both the numerator and the denominator by 625, we get:

625/625 / 1000/625 = 1/8

Step 4: Combine with the Whole Number

Remember, we started with 15.625. We've now converted the .625 to 1/8. To get the final answer, we combine the whole number and the fraction:

15 + 1/8 = 15 1/8

Therefore, 15.625 as a fraction is 15 1/8.

Alternative Method: Using Place Value

Another method involves understanding the place value of each digit after the decimal point. In 0.625:

6 is in the tenths place (6/10)
2 is in the hundredths place (2/100)
5 is in the thousandths place (5/1000)

Adding these together: 6/10 + 2/100 + 5/1000 = 600/1000 + 20/1000 + 5/1000 = 625/1000

This fraction simplifies to 1/8, just as before, leading to the same final answer: 15 1/8.

Conclusion

Converting decimals to fractions might seem daunting at first. However, by following these step-by-step instructions, you can easily convert any decimal, including 15.625, into its fractional equivalent (15 1/8). Remember to always simplify the fraction to its lowest terms for the most accurate representation. This skill is invaluable for various mathematical operations and problem-solving scenarios.