Scientific Notation

Lily is working on a science project and needs to calculate the combined effect of two chemicals. The first chemical has a concentration of 3.2 x 10^4 parts per million (ppm) and the second chemical has a concentration of 2.5 x 10^2 ppm. What is the result when she multiplies these concentrations?

• 8.0 x 10^6

• 8.0 x 10^5

• 8.0 x 10^3

• 8.0 x 10^1

Answer explanation

To find the result, multiply the concentrations: (3.2 x 10^4) * (2.5 x 10^2) = 8.0 x 10^6. Therefore, the correct answer is 8.0 x 10^6.

Maya is working on a science project and needs to calculate the concentration of cells in a solution. She has a total of 6.4 x 10^5 cells in 8 x 10^2 microliters of solution. What is the concentration of cells per microliter?

• 8.0 x 10^3 cells/μL

• 8.0 x 10^2 cells/μL

• 8.0 x 10^1 cells/μL

• 8.0 x 10^0 cells/μL

Answer explanation

To find the concentration, divide the total cells by the total volume: (6.4 x 10^5 cells) / (8 x 10^2 μL) = 8.0 x 10^3 cells/μL. Therefore, the correct answer is 8.0 x 10^3 cells/μL.

Daniel is planning a science project and needs to calculate the total number of particles he observed under a microscope. He counted 4.5 x 10^3 particles in one slide and 2.3 x 10^2 particles in another. How many particles did he observe in total?

• 4.7 x 10^3

• 4.7 x 10^2

• 4.7 x 10^1

• 4.7 x 10^0

Answer explanation

To find the total number of particles, add the counts from both slides: 4.5 x 10^3 + 2.3 x 10^2 = 4.7 x 10^3. Therefore, Daniel observed 4.7 x 10^3 particles in total.

Liam has a bank account balance of (1.2 x 10^5) dollars and Aiden has a balance of (7.8 x 10^4) dollars. How much more money does Liam have in his account compared to Aiden?

• 4.2 x 10^4

• 4.2 x 10^5

• 4.2 x 10^6

• 4.2 x 10^7

Answer explanation

Liam has (1.2 x 10^5) dollars and Aiden has (7.8 x 10^4) dollars. The difference is calculated by subtracting Aiden's balance from Liam's, resulting in 4.2 x 10^4 dollars.

Michael is working on a science project and needs to calculate the force exerted by two moving objects. The mass of the first object is (5.6 x 10^3) kg and it is moving at (3.2 x 10^2) m/s. What is the force exerted if the acceleration is considered constant?

• 1.8 x 10^6 N

• 1.8 x 10^5 N

• 1.8 x 10^4 N

• 1.8 x 10^3 N

Answer explanation

The force exerted is calculated using the formula F = m * a, where m is the mass and a is the acceleration. Plugging in the values, F = (5.6 x 10^3) kg * (3.2 x 10^2) m/s = 1.8 x 10^6 N. Therefore, the correct answer is 1.8 x 10^6 N.

Hannah is reviewing her company's financial reports and notices that the annual revenue is 9.6 x 10^4 dollars, while the operational costs are 4 x 10^2 dollars per year. What is the ratio of the revenue to the operational costs?

• 2.4 x 10^3

• 2.4 x 10^2

• 2.4 x 10^1

• 2.4 x 10^0

Answer explanation

This is an example explanation.

Anika is calculating the total number of views on her two YouTube videos. The first video has 3.7 x 10^3 views and the second video has 1.9 x 10^2 views. What is the total number of views on both videos?

• 3.9 x 10^3

• 3.9 x 10^2

• 3.9 x 10^1

• 3.9 x 10^0

Answer explanation

To find the total number of views, add the views of both videos: 3.7 x 10^3 + 1.9 x 10^2 = 3.9 x 10^3

Elijah has a bank account balance of (1.5 x 10^5) dollars and Emma withdraws (6.2 x 10^4) dollars from it. What is the new balance in Elijah's account?

• 8.9 x 10^4

• 8.9 x 10^5

• 8.9 x 10^6

• 8.9 x 10^7

Answer explanation

To find the new balance, subtract Emma's withdrawal from Elijah's balance: (1.5 x 10^5) - (6.2 x 10^4) = 8.9 x 10^4 dollars. Therefore, the new balance in Elijah's account is 8.9 x 10^4.

Luna is calculating the total power output of two machines. The first machine has a power output of 4.3 x 10^3 watts and the second machine has a power output of 2.8 x 10^2 watts. What is the total power output when these two machines operate together?

• 1.2 x 10^6 watts

• 1.2 x 10^5 watts

• 1.2 x 10^4 watts

• 1.2 x 10^3 watts

Answer explanation

The total power output is calculated by adding the power outputs of both machines: 4.3 x 10^3 + 2.8 x 10^2 = 4.3 x 10^3 + 0.28 x 10^3 = 4.58 x 10^3 = 1.2 x 10^6 watts

Grace is reviewing her physics notes and calculates the force exerted by a rocket engine that produces 8.9 x 10^4 newtons of thrust and is opposed by an air resistance of 5 x 10^2 newtons. What is the net force exerted by the engine?

• 1.78 x 10^3

• 1.78 x 10^2

• 1.78 x 10^1

• 1.78 x 10^0

Answer explanation

To find the net force, subtract the air resistance from the thrust: 8.9 x 10^4 - 5 x 10^2 = 1.78 x 10^3 newtons. Therefore, the correct answer is 1.78 x 10^3.