# 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?

### Powers of ten

PRACTICE PROBLEMS
Use exponents to write powers of ten.

### 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.