Express 2.125 as an improper fraction.
The Correct Answer and Explanation is:
To express 2.125 as an improper fraction, we first need to break it down into its whole number and decimal parts. The number 2.125 consists of a whole number part (2) and a decimal part (0.125).
Step 1: Convert the decimal part (0.125) into a fraction.
To do this, observe that 0.125 is the same as 125 thousandths. So, we can write it as: 0.125=12510000.125 = \frac{125}{1000}0.125=1000125
Next, simplify the fraction. The greatest common divisor (GCD) of 125 and 1000 is 125. Dividing both the numerator and the denominator by 125: 1251000=125÷1251000÷125=18\frac{125}{1000} = \frac{125 \div 125}{1000 \div 125} = \frac{1}{8}1000125=1000÷125125÷125=81
So, 0.125 as a fraction is 18\frac{1}{8}81.
Step 2: Add the whole number part (2) to the fraction part.
Now we combine the whole number part, 2, with the fraction part, 18\frac{1}{8}81. We can write 2 as a fraction with the denominator of 8: 2=21=2×81×8=1682 = \frac{2}{1} = \frac{2 \times 8}{1 \times 8} = \frac{16}{8}2=12=1×82×8=816
Step 3: Add the two fractions.
Now, add the two fractions 168\frac{16}{8}816 and 18\frac{1}{8}81: 168+18=16+18=178\frac{16}{8} + \frac{1}{8} = \frac{16 + 1}{8} = \frac{17}{8}816+81=816+1=817
Final Answer:
Therefore, 2.125 as an improper fraction is: 178\frac{17}{8}817
This improper fraction represents the value of 2.125 as a ratio of two integers, with 17 as the numerator and 8 as the denominator.
