PLEASE HELP! Significant Figures...!? Will choose best answer! DESPERATE!?

Question

Please help... I don't understand this!

YOU DON'T NEED TO SOLVE EACH ONE... you can solve one and explain how you did it.

Round to the correct number of significant digits.

a. (2.3x10^6)(8.57x10^3)/4.3x10^2

b. (1.4x10^3)(2.35x10^5)/3x10^-2

c. 2.21x10^7/(4.2x10^2)(1.5x10^3)

d. .125x.73x4070/1500x.150

e. (7.53x10^3)(1x10^2)/8.75x10^4

f. 70000x60000/1500

g. .08x200x.0032/700x30000

h. 8.5x90000x.12520/.001x.0002

Answer 1

Whenever you multiply or divide two numbers we look at the number with the least significant digits.  This is how many digits the product or quotient will have.

a) (2.3x10^6)(8.57x10^3) = 1.9711x10^10  We must convert this into a 2 sig fig digits.  Since we have a 7 in the hundredths place we round up to 9 and remove all but two sig figs to get 2.0x10^10.

Now for the division:

(2.0x10^10)/4.3x10^2 = 4.6511x10^7  Again we need to chop off all but two digits.  We look at the 5 in the hundreths place and by convention we usually leave the 6 as is because it is even.

Thus we obtain a final solution of 4.6x10^7

b-e are essentially the same as a.

f)  This is a more interesting problem as some conventions seem to vary with dealing with zeroes to the right of whole number digits and to the left of the decimal.  Usually for clarification a decimal point is added to show the trailing zeroes are significant. (so for example 70000 is 70000.) We will go ahead and assume that these were indeed exact measurements so we include all of the zeroes.

Making that assumption it follows that:

70000.x60000. = 4.2000x10^9  We have 5 sig figs by our assumption.

(4.2000x10^9)/1500. = 2.800x10^6  This time we only have 4 sig figs because that is how many 1500. has.

Just to cover all my bases I suppose that those zeroes on 70000 are just filler.  In that case 70000 and 60000 have only 1 sig fig and:

70000x60000 = 4x10^9

(4x10^9)/1500 = 2.66666x10^6 which we may round to 3.000x10^6 and pull off insignificant figures to obtain 3x10^6.