Chapter 4, Problem 47CR

To determine

To complete the statement using <, > , or =. $1.08\times {10}^6\_\_1.09\times {10}^7$

Answer to Problem 47CR

  $1.08\times {10}^6<1.09\times {10}^7$

Explanation of Solution

Given information:

  $1.08\times {10}^6\_\_1.09\times {10}^7$

Calculation:

Here , the right hand side may be written as-

  $1.09\times {10}^7$

To make the exponents same on both the left & right hand side for comparison.

As the left hand side has the exponent as 6 , change the right hand side similarly

  $1.09\times {10}^7=1.09\times {10}^6\times 10$

Hence, may be written as

  $10.9\times {10}^6$

Now, left hand side is

  $1.08\times {10}^6$

And, right hand side is

  $10.9\times {10}^6$

As the powers of 10 are now same on both left and right hand side (i.e. 6), so compare the numerical aspect.

Since 1.08<10.9, hence the left hand side is less than the right hand side.

Conclusion-

  $1.08\times {10}^6<1.09\times {10}^7$