each of these problems, complete the answer with a raised to the proper power. N

Question

each of these problems, complete the answer with a raised to the proper power. Note that each answer is expressed to the correct number of significant figures. 4. (a) 2.71 x 104 x 2.0 x 102 (a) (b) 4.523 x 104 2.71 x 10 (c) 4.8 x 104 x 3.5 x 104 (c) 4.523 x 10 (d) (d) 1.2 x 10 4.70 x 102 (e) (e) 8.42 x 10 5. Solve each of the following problems, expressing each answer to the proper number of significant figure. Use exponential notation for (c), (d), and (e) (a) 1.842 45.2 87.55 (a) (b) (b) 714.3 28.525 (c) 2.83 x 104 x 7.55 x 107 (c) (d) (d) 3.3 x 5280 8714.3 (e) (e) 7.07 x 10 x 6.51 x 10 2.92 x 10

Explanation / Answer

a) 2.71* 104*2.0*102

To solve this, the power terms should be place to one side and the numbers with decimals to the other side

            2.71*2.0*104*102 = Multiply (2.71*2.0) = 5.42 * 104*102

When there is a form of number 10a * 10b then 10(a+b)

Here a= 4 b = 2, a+b = 6

So answer is 5.420*106

b) (4.523 *104) / (2.71*102) =

Initially divide 4.523 with 2.71 i.e., 4.523/2.71 = 1.6690

Now, question changes to form : (1.6690 * 104) / 102

NOw consider 104 / 102

This is of the form 10a/10b then it can be written as 10(a-b)

Here a= 4, b=2 then a-b =4-2 = 2

So, answer is 1.669*1024.

To correct this to 2 decimal points, 1.669 can be witten as 1.67 (9 is greater than 5, so add 1 to the presceding number i.e., 6)

c) 4.8*104*3.5*104

This is similar to a). So multiply (4.8*3.5)*(104*104) = 16.8 * 108

So answer is 16.80 *108

d) (4.523* 10-4) / (1.2*102)

Divide 4.523 by 1.2 = (4.523/1.2) = 3.7691

(10-4/102) ;

This is of the form 10a/10b then it can be written as 10(a-b)

Here a= -4, b=2 then a-b =-4+2 = -2

So answer is 3.769 * 10-2

All the answers are reported with 4 significant figures

Significant figures are those which are non-zeroes, a zero between two non zero number is also taken as a significant number and a zero after a non-zero number in decimals is also taken as significant number

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