Change 8.08 to a fraction, reduced to the lowest terms.
A.
8 2/5
B.
8 8/100
C.
8 2/25
D.
8 8/1000
The correct answer and Explanation is :
To convert 8.08 into a fraction and reduce it to its lowest terms, let’s break it down step by step:
Step 1: Separate the whole number from the decimal part.
- The number 8.08 consists of the whole number 8 and the decimal 0.08.
Step 2: Convert the decimal to a fraction.
- The decimal part, 0.08, can be written as a fraction. Since there are two digits after the decimal point, place 0.08 over 100, so it becomes:
[
0.08 = \frac{8}{100}
]
Step 3: Simplify the fraction.
- Now, simplify (\frac{8}{100}) by dividing both the numerator and the denominator by their greatest common divisor, which is 4:
[
\frac{8}{100} = \frac{8 \div 4}{100 \div 4} = \frac{2}{25}
]
Step 4: Combine the whole number with the fraction.
- Now, put together the whole number 8 and the simplified fraction (\frac{2}{25}). This gives:
[
8.08 = 8 \frac{2}{25}
]
Step 5: Conclusion.
Thus, the correct fractional representation of 8.08, reduced to the lowest terms, is:
Answer: 8 (\frac{2}{25})
Explanation:
- Conversion of decimals to fractions: Decimals can be converted to fractions by writing them as the numerator over a power of 10. For example, 0.08 becomes (\frac{8}{100}) since it has two decimal places.
- Simplification of fractions: Once in fraction form, you can simplify it by dividing both the numerator and the denominator by their greatest common divisor.
- Mixed numbers: If the original number is a mixed decimal (like 8.08), the whole number part stays the same, and only the decimal part gets converted to a fraction.
Thus, the correct answer is C: 8 (\frac{2}{25}).