Chapter 4.7, Problem 50E

To determine

To arrange $9.1\times {10}^{-4};5.2\times {10}^{-2};0.0013$ from least to greatest.

Answer to Problem 50E

  $1.97\times {10}^3<8.7\times {10}^3<3.98\times {10}^4$

Explanation of Solution

Given information: $9.1\times {10}^{-4};5.2\times {10}^{-2};0.0013$

To arrange the numbers in ascending order, denote all the numbers in their scientific format. Then compare first the exponent value of 10 in these terms. If two or more numbers have the same exponent of 10, compare the individual numbers.

If have negative exponents of 10, then the lowest negative exponent will be greater than the higher negative exponent.

Here, $0.0013$ can be denoted in scientific form as $1.3\times {10}^{-3}$

Hence, on comparing the three numbers, $1.97\times {10}^3<8.7\times {10}^3<3.98\times {10}^4$