The Correct Answer and Explanation is:
The correct answer is 95.175.
To convert the mixed number 95 7/40 into a decimal, you can follow a two-step process. A mixed number consists of a whole number part and a fractional part. In this case, the whole number is 95, and the fraction is 7/40. The decimal representation will be the sum of the whole number and the decimal equivalent of the fraction.
First, let’s focus on converting the fraction 7/40 into a decimal. This is done by dividing the numerator (7) by the denominator (40).
We perform the division: 7 ÷ 40.
- Since 7 is smaller than 40, the result will be less than 1. We start by placing a decimal point and adding a zero to 7, making it 70.
- Now we divide 70 by 40. 40 goes into 70 one time (1 × 40 = 40), with a remainder of 30 (70 – 40 = 30). So, the first digit after the decimal point is 1.
- We bring down another zero and attach it to the remainder, making it 300. Now we divide 300 by 40. 40 goes into 300 seven times (7 × 40 = 280), with a remainder of 20 (300 – 280 = 20). The next digit in our decimal is 7.
- We bring down one more zero and attach it to the new remainder, making it 200. We divide 200 by 40. 40 goes into 200 exactly five times (5 × 40 = 200), with a remainder of 0. The final digit of our decimal is 5.
So, the fraction 7/40 is equal to the decimal 0.175.
Now for the second step, we add this decimal value to the whole number part, which is 95.
Whole Number + Decimal Fraction = Final Decimal
95 + 0.175 = 95.175
Thus, the mixed number 95 7/40 written as a decimal number is 95.175.
