1.15 as a Simplified Fraction: A Step-by-Step Guide
Converting the decimal 1.15 into a simplified fraction might seem daunting at first, but it's a straightforward process. This guide will walk you through the steps, ensuring you understand the method and can apply it to other decimal-to-fraction conversions.
Understanding Decimals and Fractions
Before we begin, let's quickly review the relationship between decimals and fractions. Decimals represent parts of a whole using a base-ten system, while fractions represent parts of a whole using a numerator (top number) and a denominator (bottom number).
Step 1: Write the Decimal as a Fraction
The decimal 1.15 can be written as the fraction 115/100. We place the digits after the decimal point (15) in the numerator, and since there are two digits after the decimal point, we use 100 as the denominator (102). The whole number (1) is added to the fraction.
Step 2: Simplify the Fraction
Now, we need to simplify the fraction 115/100 to its lowest terms. To do this, we find the greatest common divisor (GCD) of the numerator (115) and the denominator (100). The GCD is the largest number that divides both 115 and 100 without leaving a remainder.
Finding the GCD can be done through prime factorization or by using the Euclidean algorithm. For this example, let's use prime factorization:
- 115 = 5 x 23
- 100 = 2 x 2 x 5 x 5 = 22 x 52
The only common factor is 5.
Step 3: Divide the Numerator and Denominator by the GCD
Divide both the numerator (115) and the denominator (100) by the GCD (5):
- 115 ÷ 5 = 23
- 100 ÷ 5 = 20
This simplifies our fraction to 23/20. Remember that our original decimal had a whole number component which must be added in.
Step 4: Express the Mixed Number (if applicable)
Since 23/20 is an improper fraction (the numerator is larger than the denominator), we convert it to a mixed number:
23 ÷ 20 = 1 with a remainder of 3. Therefore, 23/20 is equal to 1 3/20. Adding back the original whole number from Step 1 (1 + 1 3/20) gives us a final answer of 2 3/20.
Therefore, 1.15 as a simplified fraction is 2 3/20. This comprehensive explanation ensures a clear understanding of the conversion process. You can now confidently convert other decimals to simplified fractions using this step-by-step method.
