Here’s a Free Practice Powers of 10 Worksheet

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A Short Guide to Powers of 10 in Math

A Powers of 10 is any set of numbers written in exponential form that has a base of 10 raised to an exponent. Powers of 10 is convenient because it easily allows you to write small or large numbers. The exponent on the Powers of 10 tells you which way and how many times you move the decimal point. The number of the exponent on the Powers of 10 tells you how many times the decimal point moves. If the exponent on the Powers of 10 is positive, the decimal moves right. If the exponent on the Powers of 10 is negative, the decimal moves left. Numbers written in Powers of 10 are helpful for approximating very large or very small numbers.

Common Core Standard: 8.EE.A

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Explaining how to do Powers of 10

So exactly what are powers of 10? Powers of 10 is when a base of ten is being raised to a power. Powers of 10 are helpful because they allow you to easily move a decimal. The power tells you how many spaces you will move the decimal. If the power is positive, the decimal moves right and if the power is negative, the decimal moves left. Powers of 10 help with really large or really small numbers.

3 Steps to Multiply by Powers of 10

Move the decimal in your number according to the number of the power.
When the power is negative you will move the decimal left by the amount of the exponent.
When the power is positive you will move the decimal right by the amount of the exponent.

Power of 10 Practice Problems Quiz

A Short Video on Completing our Powers of 10 Worksheet

Watch our free video on how to solve Powers of 10. This video shows how to solve problems that are on our free Powers of Ten worksheet worksheet that you can get by submitting your email above.

Watch the free Powers of 10 video on YouTube here: Powers of 10

Video Transcript:

This video is about our powers of 10 worksheets. You can get the multiplying by powers of 10 worksheet we use in this video for free by clicking on the link in the description below.

Before we do a couple practice problems on our powers of 10 worksheet, we’re going to go over the basics of what a power of 10 is. A power of 10 is written as 10 to an exponent, and we’re just going to write X for the exponent. Our base will always be 10, so this will always be 10, and then our exponent will change. The exponent can be positive or negative.

What a power of 10 is really saying is it’s telling you how many times you have to move a decimal. For example, if we have a number that is being multiplied times a power of 10. This exponent is going to tell you how many times you move the decimal and it’s also going to tell you which way you move the decimal. Is it going to move left or is it going to move right?

If the exponent is positive, it will move the decimal right. And if the exponent is negative, it will move the decimal left. Let’s jump down and do some practice problems on our powers of 10 worksheet.

The first problem we’re going to go over is number five. Number five gives us 4 times 10 to the third power. Now we know that this 10 to the third power is going to move the decimal that is behind the 4 right here. The 3 indicates that we’re going to move it three times and because the 3 is positive that means we’re going to move it to the right. We will move the decimal three times right. Our number is 4, we know that the decimal is located behind the 4 because it’s a whole number and we’re going to move it three times to the right so it will go one, two, three times. Our new decimal will be right here and any spot that is missing a number you have to add 0 as a place holder. Our answer to 4 times 10 to the third would be 4,000 because that’s after we moved the decimal three times to the right.

Number six gives us seven times 10 to the negative fifth. Now we know that this 10 to the negative fifth indicates that we’re going to have to move the decimal. The five means we have to move it five times and then because the five is negative that means the decimal will move left. We will move this decimal five times left. We have our seven, we know the decimal is behind the seven because it’s a whole number. Now we have to move the decimal five times to the left so it will go one, two, three, four, five times to the left. We’ll put our new decimal in and everywhere there’s a space we have to add zero as a placeholder. Our new answer will be point zero zero zero zero seven. That’s our simplified solution.

The last problem we’re going to do on our powers of 10 worksheet is number seven. Number seven gives us point eight three five times ten to the sixth power. 10 to the six power indicates we’re going to move the decimal six places, or six times, and the six is positive so we’ll move the decimal six times to the right. In order to do this we’ll rewrite our number point eight three five and this time we know the decimal is located before the eight because it’s given to us. And we’re going to move the decimal six times to the right. We’ll go one, two, three, four, five, six. We’ll write our new decimal here and everywhere there’s a blank we will add a zero for a placeholder. Our simplified answer will be eight hundred and thirty five thousand.