Find 0.038 as a fraction in its lowest terms
The Correct Answer and Explanation is:
To express 0.038 as a fraction in its lowest terms, follow these steps:
Correct Answer:
0.038=195000.038 = \frac{19}{500}0.038=50019
Explanation:
The decimal number 0.038 is a terminating decimal, which means it can be easily converted into a fraction.
Step 1: Write the decimal as a fraction
Start by writing 0.038 over 1:0.038=0.03810.038 = \frac{0.038}{1}0.038=10.038
Now eliminate the decimal by multiplying both numerator and denominator by 1000. This is because there are three decimal places in 0.038:0.038×10001×1000=381000\frac{0.038 \times 1000}{1 \times 1000} = \frac{38}{1000}1×10000.038×1000=100038
Step 2: Simplify the fraction
Next, reduce the fraction 381000\frac{38}{1000}100038 to its lowest terms. To do this, find the greatest common divisor (GCD) of 38 and 1000.
Factors of 38: 1, 2, 19, 38
Factors of 1000: 1, 2, 4, 5, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000
The common factor is 2.
Now divide both the numerator and the denominator by 2:38÷21000÷2=19500\frac{38 \div 2}{1000 \div 2} = \frac{19}{500}1000÷238÷2=50019
Step 3: Final Result
So, 0.038 as a simplified fraction is:19500\boxed{\frac{19}{500}}50019
This fraction is in its lowest terms because 19 is a prime number and does not share any other factor with 500.
Why This Matters
Converting decimals to fractions helps with exact representation in mathematics, particularly in algebra, measurements, and applications that require precision. Using the lowest terms simplifies calculations and comparisons with other fractions.
