Chapter 4.4, Problem 33IP

To determine

To find: the order of numbers from least to greatest.

Answer to Problem 33IP

The order of numbers is $2.4\times {10}^{-2}<2.45\times {10}^{-2}<2.4\times {10}^2<2.45\times {10}^2$ .

Explanation of Solution

Given information:

The numbers are $3.024\times {10}^2<2805<2.81\times {10}^4<3.2\times {10}^4<2.08\times {10}^5$

calculation: to find the order it is needed to write the numbers in a standard form then compare them,

  $\begin{array}{l}2.81\times {10}^4,2805,2.08\times {10}^5,3.2\times {10}^4,3.024\times {10}^2\\ 2.81\times {10}^4=28100\text{ [move decimal point 4 places to the right]}\\ 2.08\times {10}^5=208000\text{ [move decimal point 5 places to the right] }\\ 3.2\times {10}^4=32000\text{ [move decimal point 4 places to the right]}\\ 3.024\times {10}^2=302.4\text{ [move decimal point 2 places to the right]}\\ \text{2805}\end{array}$

Now compare them,

  $302.4<2805<28100<32000<208000$

Thus, the order of numbers from least to greatest is $3.024\times {10}^2<2805<2.81\times {10}^4<3.2\times {10}^4<2.08\times {10}^5$ .