The Correct Answer and Explanation is:
The correct answer is 238/5 or 47 3/5.
Here is a detailed explanation of how to convert the decimal 47.6 into a fraction:
To convert a decimal number into a fraction, you can follow a straightforward two-step process. First, you write the decimal as a fraction with a denominator that is a power of 10. Second, you simplify this fraction to its lowest terms.
Step 1: Write the decimal over a power of 10.
The number 47.6 has one digit after the decimal point. This single digit, the ‘6’, is in the tenths place. This tells us that the denominator for our initial fraction should be 10. We can remove the decimal point from 47.6 to get the numerator, which is 476. So, the initial fraction is 476/10. This is an improper fraction because the numerator (476) is larger than the denominator (10), but it is a mathematically correct representation of the original decimal.
Step 2: Simplify the fraction.
The next step is to simplify the fraction 476/10 to its lowest terms. To do this, we find the greatest common divisor (GCD) for both the numerator and the denominator. In this case, both 476 and 10 are even numbers, so we know they are both divisible by 2.
- Divide the numerator by 2: 476 ÷ 2 = 238
- Divide the denominator by 2: 10 ÷ 2 = 5
This gives us the simplified improper fraction 238/5. Since 5 is a prime number and 238 is not divisible by 5 (it does not end in a 0 or 5), this fraction is now in its simplest form.
Converting to a Mixed Number
For additional clarity, this improper fraction can be converted into a mixed number, which consists of a whole number and a proper fraction. To do this, we divide the numerator (238) by the denominator (5).
- 238 divided by 5 is 47, with a remainder of 3.
The result of the division, 47, becomes the whole number. The remainder, 3, becomes the new numerator, and the denominator stays as 5. This gives us the mixed number 47 3/5.
