Turn the decimal .375 into a fraction
The correct answer and explanation is:
The decimal 0.375 can be converted into a fraction by following a straightforward process. Here’s the step-by-step method:
Step 1: Write the decimal as a fraction over a power of 10
Since 0.375 has three decimal places, you can write it as: 0.375=37510000.375 = \frac{375}{1000}
This is because 0.375 means 375 thousandths.
Step 2: Simplify the fraction
Now, we simplify 3751000\frac{375}{1000} by finding the greatest common divisor (GCD) of 375 and 1000.
- Factors of 375: 1, 3, 5, 15, 25, 75, 125, 375
- Factors of 1000: 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000
The largest common factor is 125.
Divide numerator and denominator by 125: 375÷1251000÷125=38\frac{375 \div 125}{1000 \div 125} = \frac{3}{8}
Step 3: Result
So, the decimal 0.375 as a simplified fraction is: 38\boxed{\frac{3}{8}}
Explanation
Decimals are another way to represent fractions, especially those with denominators that are powers of 10 (like 10, 100, 1000, etc.). Here, 0.375 means 375 parts out of 1000 (thousandths).
To convert decimals to fractions:
- Count the number of digits after the decimal point.
- Use that many zeros in the denominator (for 3 digits, use 1000).
- Write the decimal number without the decimal point as the numerator.
- Simplify the fraction by dividing numerator and denominator by their greatest common divisor (GCD).
This process ensures the fraction is in its simplest form, which is important for clarity and further calculations.
0.375 is a common decimal that converts cleanly into 38\frac{3}{8}, a fraction often used in measurements (like inches in the U.S. customary system).