What is 0.76 as a fraction ?
76/100
76/10
76/1000
7/6
The Correct Answer and Explanation is:
The correct answer is: 76/100.
To convert a decimal to a fraction, you need to understand the place value of each digit in the decimal number. For the decimal 0.76, the 7 is in the tenths place, and the 6 is in the hundredths place. This means that 0.76 can be written as “76 hundredths,” which translates directly to the fraction 76/100.
Step-by-Step Explanation
- Identify the Place Value:
- In the decimal 0.76, the 7 is in the tenths place, and the 6 is in the hundredths place. Decimals are typically converted to fractions based on their place values, which help in identifying the denominator.
- Write the Fraction:
- Since 0.76 represents 76 hundredths, you write it as the fraction 76/100. The denominator is 100 because the last digit of the decimal (6) is in the hundredths place.
- Simplify the Fraction (If Possible):
- The fraction 76/100 can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD). Here, the GCD of 76 and 100 is 4.
- Dividing both terms by 4 gives 19/25, so the simplified form of 76/100 is 19/25. However, both 76/100 and 19/25 are correct representations of 0.76.
Why Other Options are Incorrect
- 76/10: This fraction equals 7.6, not 0.76.
- 76/1000: This fraction represents 0.076, which is ten times smaller than 0.76.
- 7/6: This fraction equals approximately 1.17, which is greater than 1 and does not represent 0.76.
Summary
Converting decimals to fractions involves identifying the place value of the decimal and setting up a fraction based on that place. For 0.76, “76 hundredths” corresponds to 76/100. When simplifying, it reduces to 19/25, but 76/100 is a correct and commonly used fraction form for 0.76.