The Correct Answer and Explanation is:
80.45
To write the mixed number 80 9/20 as a decimal, we need to address both the whole number part and the fractional part separately and then combine them.
The given number is 80 9/20. This can be understood as the sum of the whole number 80 and the fraction 9/20. The whole number, 80, will form the part of the decimal that is to the left of the decimal point. Our main task is to convert the fraction 9/20 into its decimal form.
There are two primary methods to convert a fraction to a decimal.
The first method involves finding an equivalent fraction with a denominator that is a power of 10 (like 10, 100, 1000, etc.). This is often the simplest approach if the denominator can be easily converted. For the fraction 9/20, we can see that the denominator, 20, can be multiplied by 5 to get 100. To ensure the value of the fraction remains the same, we must also multiply the numerator, 9, by the same factor of 5.
So, the calculation for the equivalent fraction is:
(9 × 5) / (20 × 5) = 45/100
The fraction 45/100 is read as “forty-five hundredths,” which directly translates to the decimal 0.45.
The second method is to perform division. A fraction represents a division problem where the numerator is divided by the denominator. In this case, we would divide 9 by 20.
9 ÷ 20 = 0.45
Both methods yield the same result: the fractional part 9/20 is equal to 0.45.
Finally, we combine the whole number part with the decimal part. We add the whole number 80 to the decimal 0.45:
80 + 0.45 = 80.45
Therefore, the mixed number 80 9/20 is equivalent to the decimal number 80.45.
