How do you order the following from least to greatest without a calculator 8.1×103,2.1×105,7.25×103,1.05×104,1.75×104?

1 Answer
georgef
Jul 31, 2016

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 10i<10j, as in 103<105. See that this is simply saying 1,000<100,000

The second observation is that if we have the same power 10j, and a<b, then a⋅10j<b⋅10j, as is 3⋅102<7⋅102

Now let's put them in order:

7.25⋅103<8.1⋅103<1.05⋅104<1.75⋅104<2.1⋅105

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