Multiply and Divide Powers of Ten

Contributor: Ashley Nail. Lesson ID: 13886

How do you know when a video goes viral? In this lesson, you will learn to look for patterns when multiplying and dividing by powers of 10.

categories

Integers/Rational Numbers and Operations

subject
Math
learning style
Kinesthetic, Visual
personality style
Otter, Golden Retriever
Grade Level
Intermediate (3-5)
Lesson Type
Quick Query

Lesson Plan - Get It!

Audio:

Damien wants a video he made to go viral on the internet. He asks his older sister to help him write an expression to show how many people might view his video in one week.

On the first day, Damien shared his video with four friends. He thinks each friend will then share his video with 10 other people. Then, each of those people will share his video to 10 other people the next day. This will happen for seven days.

Damien’s sister tells him this is a time to let exponents and the powers of 10 do the work!

She writes the equation 4 x 107 based on the information Damien gives her.

  • How can this expression tell us how many people will view Damien’s video?
  • Will this plan make Damien’s video go viral?

Before we can help Damien calculate his number of views, we need to go over multiplying and dividing with powers of 10.

  • What is a power of 10?

A power of 10 is a base of 10 multiplied by 10 as many times as the whole number exponent says to use it in the multiplication.

For example, let’s look at some powers of 10:

10¹ = 10

10² = 10 x 10 = 100

10³ = 10 x 10 x 10 = 1,000

104 = 10 x 10 x 10 x 10 = 10,000

  • Do you notice any patterns?

Let’s look closer!

10¹ = 10

  • The exponent tells us there is only one 10.
  • The exponent is 1, so we write one zero after the 1.

10² = 10 x 10 = 100

  • The exponent tells us there are two 10s.
  • The exponent is 2, so we write two zeros after the 1.

10³ = 10 x 10 x 10 = 1,000

  • The exponent tells us there are three 10s.
  • The exponent is 3, so we write three zeros after the 1.

104 = 10 x 10 x 10 x 10 = 10,000

  • The exponent tells us there are four 10s.
  • The exponent is 4, so we write four zeros after the 1.

Now that you see the patterns, let’s check to make sure you understand the powers of 10!

You are ready to multiply and divide with the powers of 10. You are one step closer to helping Damien go viral!

Let’s see if we notice any similar patterns.

Look at the example of a decimal being multiplied by powers of 10:

decimal example

We know 10¹ is equal to 10. Therefore, we can multiply 8.7 by 10.

When multiplying by 10, we move the decimal point one time to the RIGHT.

Let’s look more closely at other examples:

multiplication examples

We know 10² is equal to 100. Therefore, we can multiply 8.7 by 100.

When multiplying by 100, we move the decimal point two times to the RIGHT.

x 10³ means we move the decimal point three times to the RIGHT.

x 104 means we move the decimal point four times to the RIGHT.

  • Do you notice a pattern?

When multiplying by a power of 10, you will move the decimal point to the RIGHT the same number of times as the exponent.

Try finding the next answer in this pattern:

  • But what about dividing by powers of 10?

It’s the same pattern; however, when you divide, a number gets smaller so we move the decimal point to the LEFT.

Look at the examples below and see if you can spot the pattern:

division examples

Now, try finding the the next answer in this pattern:

If you need more help before practicing on your own, watch Powers of Ten 5.NBT.2 | 5th Grade Math from Math with Mr. J:

When you are ready, click next to visit the Got It? section.

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