The Correct Answer and Explanation is:
The correct answer is -3 5/8.
To convert the decimal number -3.625 into a mixed number, we follow a systematic process that involves separating the integer and decimal components and then converting the decimal portion into a simplified fraction. A mixed number is a value represented by a whole number and a proper fraction combined.
The first step is to identify the whole number part of -3.625. The whole number is the integer to the left of the decimal point. For -3.625, the whole number is -3. We will temporarily set aside the negative sign and work with 3.625 to avoid confusion, reapplying the sign at the very end.
Next, we take the decimal portion, which is 0.625, and convert it into a fraction. The place value of the last digit in the decimal determines the denominator of the initial fraction. In 0.625, the first digit ‘6’ is in the tenths place, ‘2’ is in the hundredths place, and ‘5’ is in the thousandths place. Since the decimal extends to the thousandths place, we write the fraction as 625 over 1000, or 625/1000.
The third step is to simplify this fraction to its lowest terms. To do this, we find the greatest common factor that both the numerator (625) and the denominator (1000) share. We can see that both numbers are divisible by 5. Dividing both by 5, we get 125/200. This new fraction can be simplified further, as both 125 and 200 are also divisible by 5, which gives us 25/40. Repeating the process one last time, we divide both by 5 to arrive at 5/8. The numbers 5 and 8 do not share any common factors besides 1, so 5/8 is the fully simplified fraction.
Finally, we combine the whole number from the first step with the simplified fraction. Our whole number was 3, and our fraction is 5/8. Putting them together gives us the mixed number 3 5/8. Now, we reapply the negative sign from the original number, -3.625.
Thus, -3.625 written as a mixed number is -3 5/8.
