Chapter 4, Problem 10CST

To determine

To determine which list of numbers is in order from least to great

Answer to Problem 10CST

I. $6.3\times {10}^2,3.28\times {10}^3,8.2\times {10}^3,1.4\times {10}^6$

Explanation of Solution

Given information:

List of Numbers-

F. $1.4\times {10}^6,3.28\times {10}^3,6.3\times {10}^2,8.2\times {10}^3$

G. $6.3\times {10}^2,8.2\times {10}^3,3.28\times {10}^3,1.4\times {10}^6$

H. $1.4\times {10}^6,6.3\times {10}^2,3.28\times {10}^3,8.2\times {10}^3$

I. $6.3\times {10}^2,3.28\times {10}^3,8.2\times {10}^3,1.4\times {10}^6$

Formula Used: Exponents Comparison

Calculation:

To identify which list has the correct order, arrange the numbers available with us. There are four numbers.

Number 1- $1.4\times {10}^6$

Number 2- $3.28\times {10}^3$

Number 3- $6.3\times {10}^2$

Number 4- $8.2\times {10}^3$

The first step is to arrange the numbers on the basis of the exponent value of 10. The available exponents of 10 are 2,3,3 and 6. So at first, the numbers may be arranged in the following sequence (from least to great)-

Number 3- $6.3\times {10}^2$

Number 2 & Number 4- $3.28\times {10}^3$ & $8.2\times {10}^3$

Number 1- $1.4\times {10}^6$

Now for numbers 2 & 3, both have the exponent for 10 as 3. Since the exponent is same, now compare the two numbers i.e. 3.28 and 8.2.

Since 3.2 is less than 8.2, so the final sequence will be-

Number 3- $6.3\times {10}^2$

Number 2 - $3.28\times {10}^3$

Number 4- $8.2\times {10}^3$

Number 1- $1.4\times {10}^6$

So the final sequence is −

  $6.3\times {10}^2,3.28\times {10}^3,8.2\times {10}^3,1.4\times {10}^6$

Hence I is correct.

Conclusion-

I. $6.3\times {10}^2,3.28\times {10}^3,8.2\times {10}^3,1.4\times {10}^6$