"solve each problem and write your answers in scientific notation."
1. (6.0•10^5) •(3.0•10^4)
2.(5•10^-2)/(2•10^3)
3.(2.56•10^6)•(3.56•10^2)
4. "In a recent year , the population was about 2.52•10^7 people. Its land area is about 4.05•10^5 km^2. What was tbe average number of people per square kilometer?
anyone got the answers?
To solve each problem and write the answers in scientific notation, we will follow these steps:
1. For multiplication and division, multiply or divide the coefficients and add or subtract the exponents.
2. If necessary, adjust the coefficient by moving the decimal point to the appropriate position to express it as a number between 1 and 10.
3. Write the coefficient and exponent in scientific notation format.
Let's solve the given problems one by one:
Problem 1: (6.0•10^5) • (3.0•10^4)
Multiply the coefficients: (6.0) * (3.0) = 18.0
Add the exponents: 10^5 * 10^4 = 10^(5+4) = 10^9
The answer is 1.8•10^9.
Problem 2: (5•10^-2)/(2•10^3)
Divide the coefficients: (5 / 2) = 2.5
Subtract the exponents: 10^-2 / 10^3 = 10^(-2-3) = 10^-5
The answer is 2.5•10^-5.
Problem 3: (2.56•10^6) • (3.56•10^2)
Multiply the coefficients: (2.56) * (3.56) ≈ 9.1136
Add the exponents: 10^6 * 10^2 = 10^(6+2) = 10^8
The answer is 9.1136•10^8.
Problem 4: "In a recent year, the population was about 2.52•10^7 people. Its land area is about 4.05•10^5 km^2. What was the average number of people per square kilometer?"
To find the average number of people per square kilometer, we need to divide the population by the land area:
Average = Population / Land Area
Average = (2.52•10^7) / (4.05•10^5)
Divide the coefficients: (2.52 / 4.05) ≈ 0.622222...
Subtract the exponents: 10^7 / 10^5 = 10^(7-5) = 10^2
The answer is approximately 0.622•10^2.
Therefore, the average number of people per square kilometer is approximately 0.622•10^2.
multiply the numbers
if multiplying, add exponents
if dividing, subtract exponents.
For example
4*10^2 * 3*10^3 = 12*10^5
but, to keep it in scientific notation, the number cannot be 10 or more, so
12*10^5 = 1.2*10^6
For the last problem, you want pop/km^2, so divide
2.52•10^7 by 4.05•10^5 = (2.52/4.05)*10^(7-2) = ...