What is 0.5625 as a fraction?
Understand the Problem
The question is asking how to convert the decimal 0.5625 into a fraction. This involves identifying the value in fractional terms, considering its decimal places, and simplifying if possible.
Answer
$\frac{9}{16}$
Answer for screen readers
The fraction representation of 0.5625 is $\frac{9}{16}$.
Steps to Solve
- Write the decimal as a fraction
Start by expressing the decimal 0.5625 as a fraction. Since there are 4 decimal places, we can write it as:
$$ \frac{5625}{10000} $$
- Simplify the fraction
Next, we need to simplify the fraction. We can find the greatest common divisor (GCD) of 5625 and 10000.
- Calculate the GCD
We find the GCD of 5625 and 10000:
The prime factorizations are:
- For 5625: $$ 5625 = 5^4 \times 3^2 $$
- For 10000: $$ 10000 = 10^4 = 2^4 \times 5^4 $$
The GCD is $5^4 = 625$.
- Divide numerator and denominator by the GCD
Now, divide both the numerator and the denominator by their GCD (625):
$$ \frac{5625 \div 625}{10000 \div 625} = \frac{9}{16} $$
So, the simplified fraction of 0.5625 is $\frac{9}{16}$.
The fraction representation of 0.5625 is $\frac{9}{16}$.
More Information
The decimal 0.5625 is equivalent to the fraction $\frac{9}{16}$. This is a common conversion that can be useful in various math applications, especially in contexts where fractions are preferred over decimals, like in measurements.
Tips
- Ignoring to simplify the fraction: When converting decimals to fractions, it's important to simplify the fraction to its lowest terms to provide a more understandable result.
- Forgetting the GCD calculation: Always make sure to calculate the GCD correctly to ensure accurate simplification.