Question

How do you order the following from least to greatest without a calculator `8.1 times 10^3, 2.1times10^5, 7.25times10^3, 1.05times10^4, 1.75times10^4`?

Answer 1

Use the power of 10 first, and then the coefficient

Explanation:

If we have powers of 10 as the ones given, the first observation is that:

if `i < j` then `10^i < 10^j`, as in `10^3 < 10^5`. See that this is simply saying `1,000 < 100,000`

The second observation is that if we have the same power `10^j`, and `a < b`, then `a*10^j < b*10^j`, as is `3*10^2 < 7*10^2`

Now let's put them in order:

`7.25 * 10^3 < 8.1*10^3 < 1.05*10^4 < 1.75*10^4 < 2.1*10^5`