Problems - Powers of Ten

Question 1:
Using only those powers of ten, express the following numbers in what seems to you the most logical form for future calculations in engineering notation:
a. 15,000
b. 0.005
c. 2,400,000
d. 60,000
e. 0.00040200
f. 0.0000000002


Solution 1:
a. 15,000 = 15 x 10^3
b. 0.005 = 5 x 10^-3
c. 2,400,000 = 2.4 x 10^6
d. 60,000 = 60 x 10^3
e. 0.00040200 = 402 x 10^-6
f. 0.0000000002 = 0.2 x 10-9


Question 2:
Perform the following operations in engineering notation:
a. (100)(1000)
b. (0.01)(1000)
c. (10^3)(10^6)
d. (100)(0.00001)
e. (10^-6)(10,000,000)
f. (10,000)(10^-8)(10^28)


Solution 2:
a. (100)(1000) = 100 x 10^3
b. (0.01)(1000) = 10
c. (10^3)(10^6) = 1 x 10^9
d. (100)(0.00001) = 1 x 10^-3
e. (10^-6)(10,000,000) = 10
f. (10,000)(10^-8)(10^28) = 1 x 10^24


Question 3:
Perform the following operations in engineering notation:
a. 10/10,000
b. 0.010/ 1000
c. 10,000 / 0.001
d. 0.0000001 / 100
e. 10^38 / 0.000100
f. (100)^1/2 / 0.01


Solution 3:
a. 100/10,000 = 10 x 10^-3
b. 0.010/ 1000 = 10 x 10^-6
c. 10,000 / 0.001 = 10 x 10^6
d. 0.0000001 / 100 = 1 x 10^-9
e. 10^38 / 0.000100 = 1 x 10^42
f. (100)^1/2 / 0.01 = 1 x 10^3


Question 4:
Perform the following operations in engineering notation:
a. (100)^3
b. (0.0001)^1/2
c. (10,000)^8
d. (0.00000010)^9


Solution 4:
a. (100)^3 = 1 x 10^6
b. (0.0001)^1/2 = 10 x 10^-3
c. (10,000)^8 = 100 x 10^30
d. (0.00000010)^9 = 1 x 10^-63


Question 5:
Perform the following operations in engineering notation:
a. (-0.001)^2
b. (100)(10^-4) / (1000)
c. (0.001)^2(100) / (10,000)
d. (10^3)(10,000) / 1 x 10^-4
e. (0.0001)^3(100) / 1 x 10^6
f. [(100)(0.01)]^-3 / [(100)^2(0.001)]


Solution 5:
a. (-0.001)^2 = 1 x 10^-6
b. (100)(10^-4) / (1000) = 10 x 10^-6
c. (0.001)^2(100) / (10,000) = 10 x 10^-9
d. (10^3)(10,000) / 1 x 10^-4 = 100 x 10^9
e. (0.0001)^3(100) / 1 x 10^6 = 10 x 10^-27
f. [(100)(0.01)]^-3 / [(100)^2(0.001)]
    = 1 x 10^-1