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

  1. Identify the Decimal Place Value

The decimal number $0.046875$ has five decimal places. This can be expressed as:

$$ 0.046875 = \frac{46875}{1000000} $$

  1. 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 $125$.

  1. Divide Both the Numerator and the Denominator by the GCD

Now we divide both the numerator and the denominator by $125$:

$$ \frac{46875 \div 125}{1000000 \div 125} = \frac{375}{8000} $$

  1. 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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