Lesson 13Multiplying, Dividing, and Estimating with Scientific Notation

Learning Goal

Let’s multiply and divide with scientific notation to answer questions about animals, careers, and planets.

Learning Targets

  • I can multiply and divide numbers given in scientific notation.

  • I can use scientific notation and estimation to compare very large or very small numbers.

Lesson Terms

  • scientific notation

Warm Up: True or False: Equations

Problem 1

Is each equation true or false? Explain your reasoning.

Activity 1: Biomass

Problem 1

Use the table to answer questions about different creatures on the planet. Be prepared to explain your reasoning.

creature

number

mass of one individual (kg)

humans

cows

sheep

chickens

ants

blue whales

Antarctic krill

zooplankton

bacteria

  1. Which creature is least numerous? Estimate how many times more ants there are.

  2. Which creature is the least massive? Estimate how many times more massive a human is.

  3. Which is more massive, the total mass of all the humans or the total mass of all the ants? About how many times more massive is it?

  4. Which is more massive, the total mass of all the krill or the total mass of all the blue whales? About how many times more massive is it?

Activity 2: Info Gap: Distances in the Solar System

Problem 1

Your teacher will give you either a problem card or a data card. Do not show or read your card to your partner.

If your teacher gives you the problem card:

  1. Silently read your card and think about what information you need to answer the question.

  2. Ask your partner for the specific information that you need.

  3. Explain to your partner how you are using the information to solve the problem.

  4. Solve the problem and explain your reasoning to your partner.

If your teacher gives you the data card:

  1. Silently read the information on your card.

  2. Ask your partner “What specific information do you need?” and wait for your partner to ask for information. Only give information that is on your card. (Do not figure out anything for your partner!)

  3. Before telling your partner the information, ask “Why do you need that information?”

  4. After your partner solves the problem, ask them to explain their reasoning and listen to their explanation.

Pause here so your teacher can review your work. Ask your teacher for a new set of cards and repeat the activity, trading roles with your partner.

Activity 3: Professions in the United States

Problem 1

Use the table to answer questions about professions in the United States as of 2012. Express each answer in scientific notation.

profession

number

typical annual salary (U.S. dollars)

architect

artist

programmer

doctor

engineer

firefighter

military—enlisted

military—officer

nurse

police officer

college professor

retail sales

truck driver

  1. Estimate how many times more nurses there are than doctors.

  2. Estimate how much money all doctors make put together.

  3. Estimate how much money all police officers make put together.

  4. Who makes more money, all enlisted military put together or all military officers put together? Estimate how many times more.

Lesson Summary

Multiplying numbers in scientific notation extends what we do when we multiply regular decimal numbers. For example, one way to find is to view 80 as 8 tens and to view 60 as 6 tens. The product is 48 hundreds or 4,800. Using scientific notation, we can write this calculation as To express the product in scientific notation, we would rewrite it as .

Calculating using scientific notation is especially useful when dealing with very large or very small numbers. For example, there are about 39 million or residents in California. Each Californian uses about 180 gallons of water a day. To find how many gallons of water Californians use in a day, we can find the product , which is equal to . That’s about 7 billion gallons of water each day!

Comparing very large or very small numbers by estimation also becomes easier with scientific notation. For example, how many ants are there for every human? There are ants and humans. To find the number of ants per human, look at . Rewriting the numerator to have the number 50 instead of 5, we get . This gives us . Since is roughly equal to 7, there are about or 7 million ants per person!