How many factors of 1/10 are there in the number 0.01?
The correct answer and explanation is:
To determine how many factors of 110\frac{1}{10} are present in the number 0.010.01, let’s break down the problem step by step.
Step 1: Express the numbers in terms of powers of 10
First, express both 110\frac{1}{10} and 0.010.01 as powers of 10:
- 110=10−1\frac{1}{10} = 10^{-1}
- 0.01=10−20.01 = 10^{-2}
Step 2: Set up the division
Now, we need to find how many times 110\frac{1}{10} (which is 10−110^{-1}) fits into 0.010.01 (which is 10−210^{-2}). This is equivalent to dividing 10−210^{-2} by 10−110^{-1}. 10−210−1=10−2×101=10−1\frac{10^{-2}}{10^{-1}} = 10^{-2} \times 10^{1} = 10^{-1}
Step 3: Interpret the result
The result of this division is 10−110^{-1}, which indicates that 10−110^{-1} (or 110\frac{1}{10}) fits into 10−210^{-2} (or 0.010.01) exactly once. Thus, there is 1 factor of 110\frac{1}{10} in 0.010.01.
Conclusion
There is 1 factor of 110\frac{1}{10} in 0.010.01. The problem essentially asks how many times 10−110^{-1} fits into 10−210^{-2}, and the answer is one. This is a simple division of powers of 10.