Multiple Choice
Solve each problem and write your answers in scientific notation.
(6.0 x 105) x (3.0 x 104) =
A. 18 x 1020
B. 18 x 109
C. 1.8 x 1020
D. 1.8 x 1010
(5 x 10–2) ÷ (2 x 103) =
A. 2.5 x 10-5
B. 2.5 x 10-1
C. 25 x 101
D. 25 x 102
(2.56 x 106) x (3.56 x 102) =
A. 9.1136 x 1012
B. 91.136 x 108
C. 9.1136 x 108
D. 91.136 x 1012
In a recent year, the population of California was about 2.52 x 107 people. Its land area is about 4.05 x 105 km2. What was the average number of people per square kilometer?
A. 0.62 x 105
B. 6.2 x 101
C. 0.62 x 1014
D. 6.2 x 109
To solve the first problem (6.0 x 10^5) x (3.0 x 10^4), we need to multiply the numbers and add the exponents. Here's how you can do it step by step:
1. Multiply the numbers: 6.0 x 3.0 = 18.0
2. Add the exponents: 10^5 x 10^4 = 10^(5+4) = 10^9
So the answer in scientific notation is 18.0 x 10^9. However, we can simplify this by moving the decimal point one place to the left and changing the exponent accordingly. Therefore, the answer is 1.8 x 10^10.
Therefore, the correct answer is D. 1.8 x 10^10.
To solve the second problem (5 x 10^-2) ÷ (2 x 10^3), we need to divide the numbers and subtract the exponents. Here's how you can do it step by step:
1. Divide the numbers: 5 ÷ 2 = 2.5
2. Subtract the exponents: 10^-2 ÷ 10^3 = 10^(-2-3) = 10^-5
So the answer in scientific notation is 2.5 x 10^-5.
Therefore, the correct answer is A. 2.5 x 10^-5.
To solve the third problem (2.56 x 10^6) x (3.56 x 10^2), we need to multiply the numbers and add the exponents. Here's how you can do it step by step:
1. Multiply the numbers: 2.56 x 3.56 ≈ 9.1136
2. Add the exponents: 10^6 x 10^2 = 10^(6+2) = 10^8
So the answer in scientific notation is 9.1136 x 10^8.
Therefore, the correct answer is B. 91.136 x 10^8.
To solve the fourth problem, we need to divide the population by the land area:
1. Divide the numbers: (2.52 x 10^7) ÷ (4.05 x 10^5) = 2.52 ÷ 4.05 ≈ 0.62
2. Subtract the exponents: 10^7 ÷ 10^5 = 10^(7-5) = 10^2
So the average number of people per square kilometer is 0.62 x 10^2.
Therefore, the correct answer is B. 6.2 x 10^1.