# 数学技能 I: 推理与交流 Mathematical Skills I: Reasoning & Communication MAT00011C

the problem was $\frac{10^{2}}{10^{5}}$. Both bases have positive indices so to divide, we subtract the indices. Therefore
$$\frac{10^{2}}{10^{5}}=10^{2-5}$$

We cannot normally subtract 5 from 2 , but, just as we have negative indices, we can subtract and have a negative or minus result as an answer, We say that $2-5=-3$. Check it the long way:
$$\frac{10^{2}}{10^{5}}=\frac{100}{100000}=\frac{1}{1000} \text { or } 10^{-3}$$

## MAT00011C COURSE NOTES ：

We have now worked out that:
$$10^{2} \div 10^{4}=10^{-2}$$
If you are told that:
$$10^{-4} \div 10^{2}=10^{-6}$$
and that:
$$10^{-3} \div 10^{2}=10^{-5}$$
can you see that the subtractions of the indices of the dividing bases are as follows:
\begin{aligned} &10^{2} \div 10^{4}=10^{2-4}=10^{-2} \ &10^{-4} \div 10^{2}=10^{-4-2}=10^{-6} \ &10^{-3} \div 10^{2}=10^{-3-2}=10^{-5} \end{aligned}