If 2.85 is written as an improper fraction, what is the numerator?
The Correct Answer and Explanation is:
To express the decimal 2.85 as an improper fraction, follow these steps:
Step 1: Separate the whole number and the decimal part
The decimal 2.85 can be split into two parts:
- The whole number is 2.
- The decimal part is 0.85.
So, we have:
2.85=2+0.852.85 = 2 + 0.852.85=2+0.85
Step 2: Convert the decimal part to a fraction
To convert 0.85 to a fraction:
- Write 0.85 as 85100\frac{85}{100}10085, because there are two decimal places.
- Simplify the fraction by finding the greatest common divisor (GCD) of 85 and 100, which is 5.
85100=85÷5100÷5=1720\frac{85}{100} = \frac{85 \div 5}{100 \div 5} = \frac{17}{20}10085=100÷585÷5=2017
So, 0.85 is equivalent to 1720\frac{17}{20}2017.
Step 3: Combine the whole number and the fractional part
Now, combine the whole number 2 and the fraction 1720\frac{17}{20}2017:
2+17202 + \frac{17}{20}2+2017
To add these, express the whole number 2 as a fraction with a denominator of 20:
2=2×2020=40202 = \frac{2 \times 20}{20} = \frac{40}{20}2=202×20=2040
Now add the two fractions:
4020+1720=40+1720=5720\frac{40}{20} + \frac{17}{20} = \frac{40 + 17}{20} = \frac{57}{20}2040+2017=2040+17=2057
Step 4: The improper fraction
So, 2.85 as an improper fraction is 5720\frac{57}{20}2057.
Conclusion
The numerator of the improper fraction 5720\frac{57}{20}2057 is 57.
