# Lesson 14Multiplying, Dividing, and Estimating with Scientific Notation

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.

## 14.1True or False: Equations

Is each equation true or false? Explain your reasoning.

## 14.2Biomass

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?

## 14.3Distances in the Solar System

Use the table to answer questions about the Sun and the planets of the solar system (sorry, Pluto).

object distance to Earth (km) diameter (km) mass (kg)
Sun
Mercury
Venus
Earth N/A
Mars
Jupiter
Saturn
Uranus
Neptune

Answer the following questions about celestial objects in the solar system. Express each answer in scientific notation and as a decimal number.

1. Estimate how many Earths side by side would have the same width as the Sun.

2. Estimate how many Earths it would take to equal the mass of the Sun.

3. Estimate how many times as far away from Earth the planet Neptune is compared to Venus.

4. Estimate how many Mercuries it would take to equal the mass of Neptune.

### Are you ready for more?

Choose two celestial objects and create a scale image of them in the applet below.

object distance to Earth (km) diameter (km) mass (kg)
Sun
Mercury
Venus
Earth N/A
Mars
Jupiter
Saturn
Uranus
Neptune

Plot a point

for the center of each circle. Select the Circle with Center and Radius tool  and click on a point. When the dialog box opens, enter the radius.

## 14.4Professions in the United States

Use the table to answer questions about professions in the United States as of 2012.

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 14 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!

## Lesson 14 Practice Problems

2. How many bucketloads would it take to bucket out the world’s oceans? Write your answer in scientific notation.

Some useful information:

• The world’s oceans hold roughly cubic kilometers of water.
• A typical bucket holds roughly 20,000 cubic centimeters of water.
• There are cubic centimeters in a cubic kilometer.
3. The graph represents the closing price per share of stock for a company each day for 28 days.

1. What variable is represented on the horizontal axis?
2. In the first week, was the stock price generally increasing or decreasing?
3. During which period did the closing price of the stock decrease for at least 3 days in a row?
4. Write an equation for the line that passes through and .

5. Explain why triangle is similar to triangle