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#?

1 Answer
Jul 31, 2016

Answer:

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#