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# Multiplying by 10, 100, and 1,000

When you have to multiply by 10, 100, or 1,000, you could follow the instructions for 2 or 3 digit multiplication, but there’s a short cut we’ll show you to make your life easier! For example, take this problem:

It would be acceptable to write this out and work through 2 digit by 2 digit multiplication OR you could use the following short cut. Here are the steps:

Look at the 10. Count the number of zeroes 10 has (in this case—1). Put a decimal place after the 6 in 36. This is where the decimal would come naturally. Move the decimal point one place to the right. It would look like this:

Notice that in order to move the decimal place, we had to add a zero to the end of the number. This will happen every time you multiply by 10, 100, or 1,000. You will need to add the same amount of zeroes to the end of the number to match the number of places you moved the decimal. Thus, our final answer is 360.

Let’s try this one more time. This time, we’ll be multiplying by 1,000. Here’s our problem:

Now, we’ll look at 1,000. We see that 1,000 has 3 zeroes, so we know we’ll be moving the decimal point three places (as well as adding 3 zeroes to 75). Most importantly, we need to remember to move the decimal place to the right, not to the left. Here’s what that would all look like:

Thus, our final answer is 75,000.

Let’s try a trickier one. Let’s say we were given this as our problem:

Note that this time, the first number already has a decimal place in it. But that doesn’t change what you do! You’re still multiplying by 10, which means you need to move the decimal point one place to the right. Here’s what that looks like:

Thus, our final answer is 36. Notice that in this case, we did not need to add a zero, because we only moved the decimal point one place to the right, and there was already a number there. Please note that this short cut only works when you’re multiplying by 10, 100, 1,000 (or another exponential form of 10; 10,000, 100,000, 1,000,000, etc).

Now you can try a few on your own.

4.65 x 100 =

You're multiplying by 100, which means you have two zeroes--your decimal point will be moving two places to the right. Thus, your final answer is 465.

{465.|465|465.0}

3.8 x 1000 =

You're multiplying by 1000, which means you have three zeroes--your decimal point will be moving three places to the right. Thus, your final answer is 3800.

{3800.|3800|3800.0}

One last problem--it's a tricky one!

34 x 10 =

You're multiplying by 10, which means you have one zero--your decimal point will be moving one place to the right. In the problem given, the decimal point falls after the 4, even though it is unwritten. So, starting with 34, if you move the decimal point one place to the right, you would have 340. Thus, your final answer is 340.

{340.|340|340.0}
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