1. Add 3.6 × 10^{7} + 5.1 × 10^{7} and write your answer in scientific notation.
2. Subtract 8.4 × 10^{8} − 3.2 × 10^{8} and write your answer in scientific notation.
3. Think About the Process
a. Describe the procedure for multiplying two numbers in scientific notation.
A. Multiply the first factors, then add the exponents of the powers of 10.
B. Multiply the first factors, then subtract the exponents of the powers of 10.
C. Add the first factors, then multiply the exponents of the powers of 10.
D. Add the first factors, then add the exponents of the powers of 10.
b. Find the product of (8.1×10^{−5})(6×10^{−5}).
4. Simplify the expression (7×10^{−6})(7×10^{−6}). Write the answer in scientific notation.
5. A certain star is 4.3×10^{2} light years from the Earth. One light year is about 5.9×10^{12} miles. How far from the earth (in miles) is the star?
6. Divide fraction 7.2 times , 10 super negative 8 end super , over 3 times , 10 super negative 2 end super end fraction . . Express your answer in scientific notation.
7. Estimation You are given the following expression and asked to find the sum.
3.4×10^{4}+2.58×10^{5}
a. Round each decimal to the nearest integer. Use these rounded numbers to estimate the sum.
A. 3×10^{4}
B. 6×10^{5}
C. 3×10^{5}
D. 6×10^{4}
b. Find the sum. Write your answer in scientific notation.
8. In one year, the total amount of garbage generated in a certain country was 6.958×10^{10} pounds. In the same year, the country's population was 4.57×10^{6} people. Determine the pounds of garbage produced per person in that country in one year.
9. Think About the Process
a. Find the quotient of the first factors of fraction 2.2 times , 10 to the fifth , over 4.4 times , 10 super negative 3 end super end fraction . . What do you notice?
A. The quotient of the first factors is greater than 1 but less than 10.
B. The quotient of the first factors is greater than 10.
C. The quotient of the first factors is less than 1.
b. Find fraction 2.2 times , 10 to the fifth , over 4.4 times , 10 super negative 3 end super end fraction . .
c. How does this affect the exponent of the quotient?
10. Writing Subtract 2.4×10^{5}−5×10^{4}. Describe the process of rewriting the numbers in this problem with the same power of 10.
11.
a. Reasoning Subtract 3.95×10^{−2}−3.36×10^{−2} and write your answer in scientific notation.
b. Can you write the result using different exponents? Explain.
12. On a certain planet, Continent X has area 6.23×10^{6} square miles and Continent Y has area 6.36×10^{6} square miles. Which continent is larger? By how many square miles is its area greater?
A. The area of Continent X is ▪ square miles greater than the area of Continent Y.
B. The area of Continent Y is ▪ square miles greater than the area of Continent X.