Write 0.375 as both a percentage and as a fraction in lowest terms. 1. Show and explain your work in converting 0.375 to a percentage. 2. Show and explain your work in converting 0.375 to a fraction in lowest terms. 3. Write a sentence that puts your answers into the context of the problem.
The Correct Answer and Explanation is:
1. Converting 0.375 to a Percentage
To convert a decimal to a percentage, you simply multiply the decimal by 100 and add the percentage sign. Here’s the process for 0.375:0.375×100=37.50.375 \times 100 = 37.50.375×100=37.5
Thus, 0.375 as a percentage is 37.5%.
Explanation:
Multiplying a decimal by 100 shifts the decimal point two places to the right. The percentage sign is added to indicate that the result represents a portion of 100.
2. Converting 0.375 to a Fraction in Lowest Terms
To convert a decimal like 0.375 into a fraction, follow these steps:
- Step 1: Write the decimal as a fraction with the decimal part as the numerator and 1 as the denominator.
0.375=37510000.375 = \frac{375}{1000}0.375=1000375
- Step 2: Simplify the fraction by finding the greatest common divisor (GCD) of 375 and 1000. The GCD of 375 and 1000 is 125.
- Step 3: Divide both the numerator and the denominator by the GCD (125):
375÷1251000÷125=38\frac{375 \div 125}{1000 \div 125} = \frac{3}{8}1000÷125375÷125=83
Thus, 0.375 as a fraction in its lowest terms is 3/8.
Explanation:
To convert the decimal to a fraction, we wrote it as 375/1000, and then simplified the fraction by dividing both the numerator and denominator by their GCD.
3. Contextual Sentence
In this problem, we have converted the decimal 0.375 to a percentage, resulting in 37.5%, and to a fraction, resulting in 3/8, which allows us to express the same value in two different formats: as a part of 100 and as a ratio of two integers.
