Convert 0.16667 as a fraction
Understand the Problem
The question is asking how to convert the decimal 0.16667 into a fraction. This involves determining the equivalent fraction that represents this decimal accurately.
Answer
The equivalent fraction is $$ \frac{16667}{100000} $$.
Answer for screen readers
The equivalent fraction for the decimal 0.16667 is $$ \frac{16667}{100000} $$.
Steps to Solve
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Identify the Decimal Place Value First, recognize the decimal 0.16667 has five decimal places. This means we can express it as a fraction with a denominator of $10^5 = 100000$.
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Write the Fraction Convert the decimal into a fraction:
$$ \frac{0.16667}{1} = \frac{16667}{100000} $$ -
Simplify the Fraction Now, we need to simplify the fraction if possible. To do this, find the greatest common divisor (GCD) of 16667 and 100000. You can do this using a method like the Euclidean algorithm or by trial division.
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Divide by the GCD Let's assume the GCD of 16667 and 100000 is 1 (you can check, but for many decimals, this will be the case). Thus, the fraction does not simplify further: $$ \frac{16667 \div 1}{100000 \div 1} = \frac{16667}{100000} $$
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Final Fraction Representation The final step is to write down the equivalent fraction: $$ \frac{16667}{100000} $$
The equivalent fraction for the decimal 0.16667 is $$ \frac{16667}{100000} $$.
More Information
This fraction represents a very close approximation of the decimal, and its simplicity remains intact since both numbers involved share no common divisors other than 1. Understanding how to convert decimals to fractions can be very useful in various mathematical applications.
Tips
- Not Identifying Proper Decimal Place: Sometimes students might not realize they need to convert the decimal based on its place value.
- Forgetting to Simplify: After conversion, it's easy to forget to check if the fraction can be simplified.
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