Chapter 9.4, Problem 45PPS

To determine

To explain: Pattern between the negative powers of $10$ and their decimal equivalents as mentioned in the problem.

Answer to Problem 45PPS

Yes. We observe a pattern between negative powers of $10$ and their decimal representation.

Explanation of Solution

Given information:

As mentioned in the problem the negative power of $10$ is ${10}^{-1},{10}^{-2},{10}^{-3},{10}^{-4},{10}^{-5}$ .

Formula used:

For negative exponents to decimal expression of $10$ we have ${10}^{-1}=\frac{1}{10}=0.1$

Calculation:

Consider the statement that Pattern between the negative powers of $10$ and their decimal equivalents as mentioned in the problem.

Recall that for negative exponents to decimal expression of $10$ we have ${10}^{-1}=\frac{1}{10}=0.1$ .

Therefore ${10}^{-1}=0.1,{10}^{-2}=0.01,{10}^{-3}=0.001,{10}^{-4}=0.0001,{10}^{-5}=0.00001$ .

Here we observe the pattern that number of zeros after decimal is just one less than its negative power.