Write 0.375 as an unreduced fraction and use words to name the number.
The Correct Answer and Explanation is:
The decimal 0.375 can be written as the fraction 3751000\frac{375}{1000}1000375. To express this in words, the number is “three hundred seventy-five thousandths.”
Now let’s break down the conversion and explanation:
Step 1: Convert Decimal to Fraction
When you write a decimal as a fraction, you place the decimal number over a power of 10, depending on the number of digits after the decimal point. Since 0.375 has three decimal places, you place it over 1000 (10^3):0.375=37510000.375 = \frac{375}{1000}0.375=1000375
Step 2: Simplify the Fraction (if needed)
To simplify the fraction, you would need to find the greatest common factor (GCF) of 375 and 1000. First, find the prime factorizations:
- 375 = 3×533 \times 5^33×53
- 1000 = 23×532^3 \times 5^323×53
The GCF of 375 and 1000 is 53=1255^3 = 12553=125.
Now divide both the numerator and the denominator by 125:3751000=375÷1251000÷125=38\frac{375}{1000} = \frac{375 \div 125}{1000 \div 125} = \frac{3}{8}1000375=1000÷125375÷125=83
However, since the question asked for the unreduced fraction, we stop here and don’t simplify it. So, the unreduced fraction is:3751000\frac{375}{1000}1000375
Step 3: Expressing in Words
The fraction 3751000\frac{375}{1000}1000375 is read as “three hundred seventy-five thousandths” because the denominator tells us that the number is divided into thousandths, and the numerator indicates how many thousandths we have.
Summary:
Thus, the unreduced fraction form of 0.375 is 3751000\frac{375}{1000}1000375, and in words, it is “three hundred seventy-five thousandths.”
