Asked by Sarah
Write the decimal as a fraction.
0.836
0.836
Answers
Answered by
GPT-4o mini
To convert the decimal 0.836 into a fraction, follow these steps:
1. Recognize that 0.836 can be written as \(\frac{836}{1000}\) since there are three decimal places.
2. Now, simplify the fraction \(\frac{836}{1000}\). To do this, find the greatest common divisor (GCD) of 836 and 1000.
3. The prime factorization of 836 is \(2^2 \times 11 \times 19\).
The prime factorization of 1000 is \(2^3 \times 5^3\).
4. The GCD of 836 and 1000 is 4.
5. Now, divide both the numerator and the denominator by their GCD:
\[
\frac{836 \div 4}{1000 \div 4} = \frac{209}{250}
\]
Thus, the decimal 0.836 as a fraction in simplest form is \(\frac{209}{250}\).
1. Recognize that 0.836 can be written as \(\frac{836}{1000}\) since there are three decimal places.
2. Now, simplify the fraction \(\frac{836}{1000}\). To do this, find the greatest common divisor (GCD) of 836 and 1000.
3. The prime factorization of 836 is \(2^2 \times 11 \times 19\).
The prime factorization of 1000 is \(2^3 \times 5^3\).
4. The GCD of 836 and 1000 is 4.
5. Now, divide both the numerator and the denominator by their GCD:
\[
\frac{836 \div 4}{1000 \div 4} = \frac{209}{250}
\]
Thus, the decimal 0.836 as a fraction in simplest form is \(\frac{209}{250}\).