Convert the decimal into a fraction reduced to lowest terms. 0.54
The Correct Answer and Explanation is:
To convert the decimal 0.540.540.54 into a fraction and reduce it to the lowest terms, follow these steps:
Step 1: Express the Decimal as a Fraction
Start by recognizing that 0.540.540.54 is the same as 54100\frac{54}{100}10054 because there are two decimal places, so the denominator is 100100100. 0.54=541000.54 = \frac{54}{100}0.54=10054
Step 2: Simplify the Fraction
Now, simplify the fraction by finding the greatest common divisor (GCD) of the numerator and the denominator. To do this, we need to find the factors of both 54 and 100 and choose the largest factor they have in common.
- The factors of 545454 are: 1,2,3,6,9,18,27,541, 2, 3, 6, 9, 18, 27, 541,2,3,6,9,18,27,54
- The factors of 100100100 are: 1,2,4,5,10,20,25,50,1001, 2, 4, 5, 10, 20, 25, 50, 1001,2,4,5,10,20,25,50,100
The greatest common divisor (GCD) of 54 and 100 is 2.
Step 3: Divide the Numerator and Denominator by the GCD
Now, divide both the numerator (54) and the denominator (100) by their GCD (which is 2): 54÷2100÷2=2750\frac{54 \div 2}{100 \div 2} = \frac{27}{50}100÷254÷2=5027
Step 4: Conclusion
So, the decimal 0.540.540.54 is equivalent to the fraction 2750\frac{27}{50}5027. This is already in its lowest terms because the numerator and denominator have no common factors other than 1.
Thus, the fraction representation of 0.540.540.54 in its lowest terms is: 0.54=27500.54 = \frac{27}{50}0.54=5027
This method can be applied to any decimal to convert it to a fraction, and simplifying ensures that the fraction is in its simplest form.
