The Correct Answer and Explanation is:
The correct answer is 39/32.
To find the fractional equivalent of the decimal 1.21875, we can follow a clear, step-by-step conversion process. This method involves separating the number into its whole and decimal components and then converting the decimal part into a simplified fraction.
First, we can express the number 1.21875 as the sum of its whole number part and its decimal part: 1 + 0.21875. The primary task is to convert the decimal portion, 0.21875, into a fraction. We do this by placing the decimal digits over a power of 10. Since there are five digits after the decimal point (2, 1, 8, 7, 5), the denominator will be 1 followed by five zeros, which is 100,000. This results in the fraction 21875/100000.
The next crucial step is to simplify this large fraction. We need to find the greatest common divisor of the numerator and the denominator to reduce it to its lowest terms. Both 21875 and 100000 are divisible by 5. Repeatedly dividing both by 5, or recognizing a larger common factor like 3125, simplifies the calculation. Dividing the numerator and denominator by 3125 gives us:
21875 ÷ 3125 = 7
100000 ÷ 3125 = 32
Thus, the simplified fraction for 0.21875 is 7/32.
Finally, we combine the whole number part, 1, with this fraction. We can write 1 as a fraction with a denominator of 32, which is 32/32. Adding the two parts together gives us:
32/32 + 7/32 = 39/32.
Therefore, the decimal 1.21875 is equal to the improper fraction 39/32. A quick verification by dividing 39 by 32 on a calculator confirms the result is 1.21875.
