What is 15.52 as a Fraction?

Understanding 15.52 as a Fraction in 6 Simple Steps

1. Separate the whole number and the decimal

The original number we're dealing with is 15.52. This number is not just a decimal, it's a combination of a whole number and a decimal. In other words, it's a mixed number - a number that includes both a whole number and a fraction.

In 15.52, the number to the left of the decimal point is the whole number part, and the number to the right is the decimal part. So in this case:

• The whole number part is "15"
• The decimal part is "52"

This is significant because in our next steps we're going to treat these two parts separately.

2. Determine the Decimal Place Value

The place value of a decimal is determined by the number of digits to the right of the decimal point. In the case of turning 15.52 into a fraction, we find its place value is in the hundredths place because are two digits after the decimal point.

Here is the breakdown of the digits after the decimal point (see image for better understanding):

• 5 is at the tenths place
• 2 is at the hundredths place

3. Write the decimal part as a fraction

Given the decimal 15.52, you'd write it over the place value. This means 52 (the numbers to the right of the decimal point) over 100 (denoting its place value).

This gives 52/100 as the initial fraction.

4. Simplify the fraction

To simplify the fraction, you need to find the greatest common divisor (GCD), also known as the greatest common factor (GCF), for both the numerator and the denominator.

Let's use the fraction from Step 3, which is 52/100.

How do you find the GCD of 52 and 100? There are several methods to find the GCD of two numbers, including the division method, prime factorization, or using Euclid's algorithm. However, we'll use the prime factorization method as it's often the simplest:

• Factorize both numbers into their prime factor. Tip - use our prime factors calculator for quick results:
  • The prime factors of 52 are 2, 2, 13
  • The prime factors of 100 are 2, 2, 5, 5
• Identify the common factors of both numbers from the prime factors above:
  • The common factors between 52 and 100 are 2, 2
• Calculate the GCD: To find the GCD, multiply the common prime factors together:
  • 2 * 2 = 4

Hence, the GCD of 52 and 100 is 4.

Now, divide both the numerator and the denominator of the fraction by their GCD (4) to simplify the fraction.

• 52 ÷ 4 = 13
• 100 ÷ 4 = 25

Therefore, the fraction 52/100 simplifies to 13/25.

5. Combine the whole number and the fraction

Now, just combine the whole number and the fraction. In this case, combine 15 and 13/25 to make the mixed number 1513/25.

6. Convert to improper fraction

Lastly, we want to convert this mixed number into a fraction. The numerator of this fraction will be calculated by (Whole Number * Denominator of the fraction) + Numerator of the fraction:

(15 * 25) + 13 = 388

The denominator of our improper fraction is the same as the denominator of the fraction in step 5. So, the denominator is 25.

Put it together: The improper fraction is 388/25.

So, the decimal 15.52 is equivalent to the mixed number 1513/25 which can be represensted as an improper fraction 388/25.