To convert the decimal number 2.85 into an improper fraction, follow these detailed steps:
1. Identify the Components:
- The integer part of 2.85 is 2.
- The decimal part of 2.85 is 0.85.
2. Convert the Decimal Part to a Fraction:
- The decimal 0.85 can be expressed as a fraction. 0.85 is equivalent to [tex]\( \frac{85}{100} \)[/tex].
3. Express the Decimal as an Improper Fraction:
- Combine the integer part with the fraction part. The fraction part is derived from the 0.85, which makes it 85/100, when you multiply the integer part (2) by the denominator (100) and add the numerator of the fraction part (85):
[tex]\[
2 + \frac{85}{100} = \frac{2 \times 100 + 85}{100} = \frac{200 + 85}{100} = \frac{285}{100}
\][/tex]
The numerator of the improper fraction is 285.
Thus, none of the provided options (A. 33, B. 57, C. 77, D. 81) is correct, since the correct numerator should be 285.
