Initial Knowledge Check Write 8.1 as a mixed number and as an improper fraction. Do not try to simplify your answers.
The Correct Answer and Explanation is:
Correct Answer:
- Mixed Number: 8.1 = 8 1/10
- Improper Fraction: 8.1 = 81/10
Explanation:
To express 8.1 as both a mixed number and an improper fraction, we begin by understanding what the number means.
Step 1: Understand the Decimal
The number 8.1 is a decimal. The digit to the left of the decimal point is 8, and the digit to the right is 1, which is in the tenths place. This tells us that: 8.1=8+1108.1 = 8 + \frac{1}{10}8.1=8+101
This is already written in mixed number form: 8 (whole number) and 1/10 (fractional part). So, the mixed number is: 81108 \frac{1}{10}8101
Step 2: Convert the Mixed Number to an Improper Fraction
To write the same value as an improper fraction, we use this method:
- Multiply the whole number part (8) by the denominator of the fraction (10):
8×10=808 \times 10 = 808×10=80 - Add the numerator of the fractional part (1):
80+1=8180 + 1 = 8180+1=81 - Keep the same denominator (10), so the improper fraction is:
8110\frac{81}{10}1081
This matches the decimal 8.1 exactly because 81 divided by 10 equals 8.1.
Why Not Simplify?
In this case, the question specifically asks not to simplify the answers. That means we leave the fraction in its current form, even if simplification were possible (which it is not here, since 81 and 10 have no common factors other than 1).
Final Answer:
- Mixed Number: 81108 \frac{1}{10}8101
- Improper Fraction: 8110\frac{81}{10}1081
