Convert 76.2 to a fraction.
Understand the Problem
The question requires converting the decimal number 76.2 into its equivalent fractional representation. This involves expressing the decimal as a ratio of two integers.
Answer
$\frac{381}{5}$
Answer for screen readers
$\frac{381}{5}$
Steps to Solve
- Write the decimal as a fraction with a denominator of 1
$76.2 = \frac{76.2}{1}$
- Multiply the numerator and denominator by 10 to remove the decimal point
Since there is one digit after the decimal point, we multiply both the numerator and the denominator by 10
$\frac{76.2 \times 10}{1 \times 10} = \frac{762}{10}$
- Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor (GCD)
The GCD of 762 and 10 is 2. Divide both by 2
$\frac{762 \div 2}{10 \div 2} = \frac{381}{5}$
- The fraction is now in its simplest form
$\frac{381}{5}$
$\frac{381}{5}$
More Information
The fraction $\frac{381}{5}$ can also be expressed as a mixed number: $76\frac{1}{5}$. This is obtained by dividing 381 by 5, which gives a quotient of 76 and a remainder of 1.
Tips
A common mistake is not simplifying the fraction to its lowest terms. For example, stopping at $\frac{762}{10}$ is not the final simplified answer. Always look for common factors in the numerator and denominator to simplify the fraction. Another common mistake is misplacing the decimal when multiplying by powers of 10.
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