0.046875 as a fraction
Understand the Problem
The question is asking to convert the decimal number 0.046875 into a fractional representation. This involves expressing the decimal as a fraction with a numerator and a denominator.
Answer
$\frac{3}{64}$
Answer for screen readers
The fractional representation of $0.046875$ is $\frac{3}{64}$.
Steps to Solve
- Identify the Decimal Place Value
The decimal number $0.046875$ has five decimal places. This can be expressed as:
$$ 0.046875 = \frac{46875}{1000000} $$
- Simplify the Fraction
Next, we need to simplify the fraction. We can find the greatest common divisor (GCD) of the numerator and the denominator. For $46875$ and $1000000$, the GCD is $125$.
- Divide Both the Numerator and the Denominator by the GCD
Now we divide both the numerator and the denominator by $125$:
$$ \frac{46875 \div 125}{1000000 \div 125} = \frac{375}{8000} $$
- Further Simplification
We must check if $375$ and $8000$ can be simplified further. The GCD of $375$ and $8000$ is $125$, so we divide again:
$$ \frac{375 \div 125}{8000 \div 125} = \frac{3}{64} $$
Thus, the simplified fractional representation of $0.046875$ is $\frac{3}{64}$.
The fractional representation of $0.046875$ is $\frac{3}{64}$.
More Information
The decimal $0.046875$ is a terminating decimal, which means it can be exactly represented as a fraction. In this case, it is equal to $\frac{3}{64}$, where both $3$ and $64$ share no common factors other than $1$.
Tips
- Forgetting to simplify the fraction completely can lead to an incorrect answer. Always check for a GCD greater than $1$ and simplify as much as possible.
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