Chapter 4, Problem 30CT

To determine

To complete the statement using <, > , or =. $9.0\times {10}^{17}\_\_5.2\times {10}^{18}$

Answer to Problem 30CT

  $9.0\times {10}^{17}<5.2\times {10}^{18}$

Explanation of Solution

Given information:

  $9.0\times {10}^{17}\_\_5.2\times {10}^{18}$

Calculation:

To compare the two expressions, first need to make the exponent of 10 same on both left & right side.

Let us change the exponent of 10 from 17 to 18. have

  $9\times {10}^{17}$

To change the exponent to 18, move

  $0.9\times {10}^{18}$

Now, the exponent for 10 is same on both sides. now compare the numbers.

  $0.9\times {10}^{18}$ and $5.2\times {10}^{18}$

Since 0.9 is less than 5.2, so have-

  $0.9\times {10}^{18}<5.2\times {10}^{18}$

Hence,

  $9.0\times {10}^{17}<5.2\times {10}^{18}$

Conclusion-

  $9.0\times {10}^{17}<5.2\times {10}^{18}$