What is 0.375 as a fraction?

Step 1: Understand the Decimal

The decimal 0.375 can be read as "three hundred seventy-five thousandths." This tells us that it’s 375 parts out of 1,000.

Step 2: Write as a Fraction

To start, write the decimal as a fraction with the decimal number as the numerator and a power of 10 as the denominator. Since 0.375 has three decimal places, we can express it as:

\[ \frac{375}{1000} \]

Step 3: Simplify the Fraction

To simplify the fraction, we need to find the greatest common divisor (GCD) of 375 and 1000. Let’s find the GCD:

1. Find the prime factors:

- 375:
- 375 is divisible by 5: \( 375 ÷ 5 = 75 \)
- 75 is divisible by 5: \( 75 ÷ 5 = 15 \)
- 15 is divisible by 5: \( 15 ÷ 5 = 3 \)
- 3 is a prime number.
- Prime factorization of 375: \( 375 = 5^3 \times 3 \)

- 1000:
- 1000 is divisible by 2: \( 1000 ÷ 2 = 500 \)
- 500 is divisible by 2: \( 500 ÷ 2 = 250 \)
- 250 is divisible by 2: \( 250 ÷ 2 = 125 \)
- 125 is divisible by 5: \( 125 ÷ 5 = 25 \)
- 25 is divisible by 5: \( 25 ÷ 5 = 5 \)
- 5 is a prime number.
- Prime factorization of 1000: \( 1000 = 2^3 \times 5^3 \)

2. Find the GCD:

- Common factors between 375 and 1000 are \( 5^3 \)
- GCD of 375 and 1000 is \( 125 \)

3. Divide both the numerator and denominator by their GCD:

\[
\frac{375 \div 125}{1000 \div 125} = \frac{3}{8}
\]

Step 4: Conclusion

So, the fraction 0.375 simplified is:

\[
\frac{3}{8}
\]