Final answer:
To express 3.01 (with the 1 repeating) as a mixed number, we need to convert the repeating decimal into a fraction. The repeating part of the decimal is 0.0111111..., which can be represented as 1/9. Therefore, 3.01 (with the 1 repeating) can be expressed as the mixed number 3 + 1/9.
Step-by-step explanation:
To express 3.01 (with the 1 repeating) as a mixed number, we need to understand decimal notation. Each digit after the decimal point has a place value that is a power of 10. The digit 1 repeats infinitely after the decimal point, which means it represents a fraction. To find this fraction, we can assign a variable to the repeating part and solve for it.
Let x = 0.0111111...
Multiplying both sides by 10, we get:
10x = 0.1111111...
Subtracting the second equation from the first, we can eliminate the repeating part:
10x - x = 0.1111111... - 0.0111111...
Simplifying, we get:
9x = 0.1
Dividing both sides by 9, we get:
x = 0.1/9
This gives us the fraction 1/9.
So, 3.01 (with the 1 repeating) can be expressed as the mixed number 3 + 0.01 (or 1/9).
L