Solve each problem and write your answer in scientific notation.
1.(6.0x10^5)x(3.0x10^4)
A.18x10^20
B.18x10^9
C.1.8X10^20
D.1.8x10^10
2.(5x10^-2) ÷(2x10^3)
A.2.5x10^-5
B.2.5x10^-1
C.25x10^1
D.25x10^2
3.(2.56x10^6)x(3.56x10^2)
A.9.1136x10^12
B.91.136x10^8
C.9.1136x10^8
D.91.136X10^12
4.In a recent year, the population of California was about 2.52x10^7 people. Its land area is about 4.05x10^5km^2. What was the average number of people per square kilometer?
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To solve each problem and write the answer in scientific notation, we multiply or divide the numbers and then adjust the result to be in the form of a number between 1 and 10 multiplied by a power of 10.
1. (6.0x10^5) x (3.0x10^4):
To multiply numbers in scientific notation, multiply the coefficients (6.0 x 3.0 = 18.0) and add the exponents (10^5 x 10^4 = 10^9). Therefore, the answer is 18.0x10^9.
2. (5x10^-2) ÷(2x10^3):
To divide numbers in scientific notation, divide the coefficients (5 ÷ 2 = 2.5) and subtract the exponents (10^-2 ÷ 10^3 = 10^-5). Therefore, the answer is 2.5x10^-5.
3. (2.56x10^6) x (3.56x10^2):
To multiply numbers in scientific notation, multiply the coefficients (2.56 x 3.56 = 9.1136) and add the exponents (10^6 x 10^2 = 10^8). Therefore, the answer is 9.1136x10^8.
4. Average number of people per square kilometer:
To calculate the average number of people per square kilometer, divide the population by the land area.
Population: 2.52x10^7
Land area: 4.05x10^5 km^2
Dividing the two values gives (2.52x10^7) ÷ (4.05x10^5) = 6.22222222222 (approximately)
To write the answer in scientific notation, we need to adjust it to a number between 1 and 10 multiplied by a power of 10. Therefore, we can write it as 6.22x10^0 km^-2, or simply 6.22 people per square kilometer.