Evaluate and give the answer in scientific notation. Assume that the factors are approximations.

Question

 

 

[(6.4*10^-3)(8.2*10^5)]/(2.1*10^-2)

Answer 1

(6.4)(8.2)/(2.1)

52.48/(2.1)

24.99047619

 

(10^[-3])(10^5)/(10^[-2])

(10^[-3])(10^5)(10^2)   10^[-2]=1/10^2 and dividing by 1/10^2 is the same as multiplying by 10^2

(10^[-3+5+2])=10^4

24.99047619*10^4

divide by 10 to move the decimal point 1 place to the left and multiply by 10 to offset the division by 10

2.499047619*10^5

Answer 2

Evaluate the product:   (6.4*10^-3)(8.2*10^5)]/(2.1*10^-2)

 

We first multiply all the leading factors of 6.4, 8.2, 2.1 together, 

6.4 x 8.2 x 2.1 = 110.208

 

Next we can multiply all the powers of ten, by adding exponents

10^-3 x 10⁵ x 10^-2  =  10 ^(-3+5-2)  = 10⁰ = 1

 

so we have 110.208 x 1, or in scientific notation  1.10208 x 10²   (decimal moved left by 2, so we mult 10²)