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# Find the ratio of the larger object to the smaller one. Give your answer in scientific notation to one decimal place.

3.2*10^5     And   1.31*20^8

Hi Betsy,

Let's begin by writing the ratio of our larger object to our smaller object (the larger object will be the one with the greater power of 10):

larger object / smaller object = 1.31 x 108 / 3.2 x 105

Now let's reduce our ratio to a fraction with a denominator of 1 and, thereby, getting rid of the fraction.

We can do this by dividing the denominator into the numerator giving us a decimal value:

1.31 / 3.2 = 0.409375

Now let's take care of our power of 10 (when we divide we subtract exponents):

108 / 105 = 108-5 = 103

So our answer at this point is 0.409375 x 103

Our instructions are to put our answer in scientific notation, which means we need to express our answer as a single digit with value greater than zero before the decimal point followed by our decimal portion and a power of 10.

We can do this by multiplying the decimal portion of our value by 10 and at the same time dividing our power of 10 by 10 to maintain equality (the same value).  In effect we are multiplying our value by a form of 1 (10/10), which changes only the form but NOT tbe meaning of our value.

(0.409375 x 103) x 10 = (0.409375 x 10)(103)  / 101 = 4.09375 x 103-1 = 4.09375 x 102

Finally, we are told to leave our final answer rounded to the nearest tenth (1 decimal place):

4.09375 x 102 = 4.1 x 102 (final answer rounded to 1 decimal place)

I hope this helps you with your understanding of scientific notation.