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Unit 1: Lesson 10 – Operations with Numbers in Scientific Notation

Learning Target:• Practice operations with numbers expressed in scientific

notation

Scientific Notation

d is a finite decimal 1 and 10. n is an integer

The integer n is called the order of magnitude of the decimal

𝑑𝑥10𝑛

The world population is about 7 billion. There are 4.6 × ants for every human on the planet. About how many ants are there in the world?

Example 1:

A certain social media company processes about 990 billion “likes” per year. If the company has approximately 8.9 × users of the social media, about how many “likes” is each user responsible for per year? Write your answer in scientific and standard notation.

Example 2:

The speed of light is 00, , meters per second. The sun is 𝟑 𝟎𝟎𝟎 𝟎𝟎𝟎approximately . × meters from Earth. How many seconds does it take for 𝟏 𝟓sunlight to reach Earth?

Now you try!

The mass of the moon is about . × kg. It would take approximately 𝟕 𝟑𝟐6, , moons to equal the mass of the sun. Determine the mass of the 𝟎𝟎𝟎 𝟎𝟎𝟎sun.

Now you try!

In 2010, Americans generated 2.5 × tons of garbage. There are about 2,000 landfills in the United States. Assuming that each landfill is the same size and that trash is divided equally among them, determine how many tons of garbage were sent to each landfill in 2010.

Example 3:

Actually, not all garbage went to landfills. Some of it was recycled and composted. The amount of recycled and composted material accounted for about 85 million tons of the 2.5 × tons of garbage. Given this new information, how much garbage was actually sent to each landfill?

Example 3:

The mass of Earth is . × kg. 𝟓 𝟗The mass of Pluto is 3, , , , , , , kg. 𝟏 𝟎𝟎𝟎 𝟎𝟎𝟎 𝟎𝟎𝟎 𝟎𝟎𝟎 𝟎𝟎𝟎 𝟎𝟎𝟎 𝟎𝟎𝟎Compared to Pluto, how much greater is Earth’s mass than Pluto’s mass?

Now you try!

Using the information in Exercises 2 and 3, find the combined mass of the moon, Earth, and Pluto.

Now you try!

How many combined moon, Earth, and Pluto masses (i.e., the answer to Exercise 4) are needed to equal the mass of the sun (i.e., the answer to Exercise 2)?

Now you try!

Lesson Wrap Up

Today we reviewed how to compare numbers in scientific notation using the order of magnitude.

We also looked at how to perform all operations for numbers expressed in scientific notation or standard notation.

Today’s Independent Work:

Practice IXL skills G.3 and G.4. Submit your smartscore to the dropbox.