0.575 as a fraction
Understand the Problem
The question is asking how to convert the decimal number 0.575 into a fraction. This involves determining the appropriate numerator and denominator that represent this decimal value as a fraction.
Answer
The fraction representation of 0.575 is $\frac{23}{40}$.
Answer for screen readers
The decimal 0.575 can be expressed as the fraction $\frac{23}{40}$.
Steps to Solve
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Identify the Decimal Place Value The decimal number 0.575 has three digits after the decimal point. This means we can represent it as a fraction with a denominator of 1000 (since $10^3 = 1000$).
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Write as a Fraction We can write the decimal as a fraction: $$ \frac{575}{1000} $$
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Simplify the Fraction Next, we need to simplify the fraction by finding the greatest common divisor (GCD) of the numerator (575) and the denominator (1000).
To find the GCD, we can use the prime factorization method:
- The prime factorization of 575 is $5 \times 5 \times 23 = 5^2 \times 23$.
- The prime factorization of 1000 is $10^3 = (2 \times 5)^3 = 2^3 \times 5^3$.
The GCD is the product of the lowest power of the common factors:
- The common factor here is 5, and the minimum power is $5^2$.
Thus, GCD(575, 1000) = 25.
Now divide both the numerator and the denominator by their GCD: $$ \frac{575 \div 25}{1000 \div 25} = \frac{23}{40} $$
- Final Fraction Representation Now, we can express the decimal 0.575 as the simplified fraction: $$ \frac{23}{40} $$
The decimal 0.575 can be expressed as the fraction $\frac{23}{40}$.
More Information
Converting decimals to fractions can help to understand rational numbers better. In this case, 0.575 is exactly represented by the fraction $\frac{23}{40}$, showing that it can be expressed in a relationship of parts to whole.
Tips
- Forgetting to simplify the fraction after writing it as a fraction of 1000. Always check if both numerator and denominator can be divided by a common factor.
- Misidentifying the place value or incorrectly determining the denominator. Remember the number of decimal places will always dictate the appropriate power of 10 for the denominator.
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