# Multiplication by powers of 10

6 videos

5 skills

This tutorial will be your first exposure to exponents which we will build on in later grades. In particular, we're going to think about what happens when you multiply by 10 multiple times (and think about how the number of zeroes relates to the number of times we multiply by 10). Later on, we'll do the same thing with other numbers. The key here is to help you see how numbers, exponents, and decimals create patterns when multiplied or divided. Common Core Standard: 5.NBT.A.2

### Powers of 10: patterns

VIDEO
5:34 minutes

We're going to observe a pattern that develops when we compare the number of zeros in tens with the number of zeros in the answer. What do you think will be the pattern?

### Exponents and powers of zero patterns

VIDEO
6:56 minutes

Now that we understand how to interpret an exponent and how the patterns in zeros are related to the exponent, we can solve more complicated problems!

### Multiplying and dividing whole numbers by powers of 10

PRACTICE PROBLEMS

Multiply and divide whole numbers by powers of ten

### Multiplying a decimal by a power of 10

VIDEO
3:47 minutes

You will notice in this word problem that moving the decimal to the right the same number of times as the number of zeros you multiplying by gets you the answer you desire. Check this out!

### Dividing a decimal by a power of 10

VIDEO
3:18 minutes

When we were multiplying, we moved the decimal to the right for each power of ten. Guess what? When dividing, we move the decimal to the left for each power of ten.

### Dividing a decimal by a power of 10: shortcut

VIDEO
1:51 minutes

Holy cow! A shortcut? Yep. For each ten you multiply or divide by, just shift that decimal to the right or left. Watch this and be amazed.

### Multiplying and dividing decimals by powers of 10

PRACTICE PROBLEMS

Multiply and dividing decimals by powers of 10.

### Understanding moving the decimal

PRACTICE PROBLEMS

Give the number of tens a number is being multiplied or divided by when the decimal is moved to the left or right.

### Fractions as division by power of 10

VIDEO
5:07 minutes

Keep in mind that a fraction is nothing more than a division problem. So if the denominator is 10 (or 100...or 1000), then all we need to do move the decimal in the numerator that number of zeros to the left.

### Rewriting fractions as decimals

PRACTICE PROBLEMS

Practice rewriting fractions as decimals. Fractions in these problems have denominators of 10 and 100.