Write 4.135 as a fraction
The Correct Answer and Explanation is :
To convert the decimal 4.135 into a fraction, we can follow a systematic process:
- Identify the Whole Number and Decimal Part: The number 4.135 consists of a whole number part, which is 4, and a decimal part, which is 0.135.
- Convert the Decimal to a Fraction: The decimal 0.135 can be expressed as a fraction. Since there are three digits after the decimal point, we can write 0.135 as (\frac{135}{1000}). This is because the decimal place indicates the power of ten that corresponds to the fraction’s denominator.
- Simplify the Fraction: Next, we need to simplify (\frac{135}{1000}). To do this, we find the greatest common divisor (GCD) of the numerator (135) and the denominator (1000).
- The prime factorization of 135 is (3^3 \times 5) (since (135 = 3 \times 45 = 3 \times 3 \times 15 = 3^2 \times 3 \times 5)).
- The prime factorization of 1000 is (10^3 = 2^3 \times 5^3). The common factor is (5), so we divide both the numerator and the denominator by (5): [
\frac{135 \div 5}{1000 \div 5} = \frac{27}{200}.
]
- Combine Whole Number and Fraction: Now, we can express the original number 4.135 as a mixed number. Since 4 is the whole number and (\frac{27}{200}) is the fractional part, we write it as: [
4.135 = 4 + \frac{27}{200} = \frac{4 \times 200 + 27}{200} = \frac{800 + 27}{200} = \frac{827}{200}.
]
Thus, the decimal 4.135 can be expressed as the fraction (\frac{827}{200}).
In conclusion, converting decimals to fractions involves isolating the decimal part, converting it to a fraction, simplifying, and then combining it with any whole number. The final result is that (4.135) equals (\frac{827}{200}).