What is .275 in a fraction in simplest form?
The Correct Answer and Explanation is :
The correct answer is: (\frac{275}{1000})
To convert the decimal 0.275 into a fraction, we can follow a systematic approach. Here’s how to do it step-by-step:
- Write the Decimal as a Fraction: The decimal 0.275 can be expressed as (\frac{275}{1000}) because there are three digits after the decimal point. This means that 0.275 is equivalent to 275 thousandths.
- Simplify the Fraction: The next step is to simplify (\frac{275}{1000}) by finding the greatest common divisor (GCD) of the numerator (275) and the denominator (1000).
- Finding the GCD:
- The prime factorization of 275 is (5 \times 5 \times 11) or (5^2 \times 11).
- The prime factorization of 1000 is (10 \times 10 \times 10) or (2^3 \times 5^3).
- The common prime factor here is 5.
- Calculating the GCD: The GCD of 275 and 1000 is 5.
- Dividing by the GCD: To simplify (\frac{275}{1000}), we divide both the numerator and the denominator by their GCD (5):
[
\frac{275 \div 5}{1000 \div 5} = \frac{55}{200}
] - Further Simplification: Next, we check if (\frac{55}{200}) can be simplified further. The prime factorization of 55 is (5 \times 11) and for 200, it’s (2^3 \times 5^2). The common factor again is 5.
- Dividing both by 5 gives:
[
\frac{55 \div 5}{200 \div 5} = \frac{11}{40}
]
- Final Result: The simplest form of the fraction equivalent to the decimal 0.275 is (\frac{11}{40}).
Summary
The decimal 0.275 can be expressed as the fraction (\frac{275}{1000}). By simplifying this fraction through finding the GCD and reducing, we arrive at (\frac{11}{40}) as the simplest form. This process illustrates the conversion from decimal to fraction and the importance of simplifying for clarity and ease of use.