Question

Write the decimal 0.262 as a fraction in simplest form

Answer 1

To convert the decimal 0.262 into a fraction, we can follow these steps:

1. Recognize that 0.262 can be expressed as:
\[
\frac{262}{1000}
\]
since there are three digits after the decimal point.

2. Next, we simplify the fraction \(\frac{262}{1000}\). To do this, we need to find the greatest common divisor (GCD) of 262 and 1000.

3. The prime factorization of 262 is:
- \(262 = 2 \times 131\)
- (131 is a prime number)

The prime factorization of 1000 is:
- \(1000 = 10^3 = 2^3 \times 5^3\)

4. The only common factor between 262 and 1000 is 2. Therefore, the GCD of 262 and 1000 is 2.

5. Now, divide both the numerator and the denominator by their GCD (2):
\[
\frac{262 \div 2}{1000 \div 2} = \frac{131}{500}
\]

So, the decimal 0.262 in simplest fractional form is:
\[
\frac{131}{500}
\]