# Mentally Multiplying & Dividing Decimals by 10 & 100

Instructor: Thomas Higginbotham

Tom has taught math / science at secondary & post-secondary, and a K-12 school administrator. He has a B.S. in Biology and a PhD in Curriculum & Instruction.

In life, we don't always carry our calculators, smartphones, or even paper and pencil, yet we are constantly required to do math. Multiplying and dividing by 10 and 100 are two of the more commonly used math applications, which this lesson will show you how to do quickly and accurately 'in your head.'

## Using Mental Math

You're at a restaurant celebrating your outstanding report card, especially your improvement in math. The bill for \$48.72 arrives, and you're ready to show off your skills. 'I'll figure the tip,' you say. 'Twenty Percent, right?'

You know that to get to 20%, you find 10% and double it. You're great with your doubling, but start to panic when it comes to finding 10% of the bill. It's a decimal number, and you know you have to move the decimal point, but you can't remember the number of places, or whether you should move it to the right or the left. Aggghhh!!!

Decimal numbers use decimal points to indicate whole numbers, which fall to the left of the point, and 1/10ths, which fall to the right of the point. In this lesson, we'll learn a few never-fail, easy-to-remember strategies for multiplying and dividing decimals by 10 and 100 without using a calculator or your smartphone.

## Placing the Decimal Point

Are you ready to learn one of the easiest, but most useful math tricks? When multiplying or dividing by 10 or 100, or any power of ten, for that matter, move the decimal point the same number of places as there are zeros in the power of ten factor. For example, how many zeros are in 10? One. How many zeros in 100? Two. That's how many places you move the decimal point. Now, let's look at a few multiplication examples.

• 3.48 x 10 = 34.8
• 3.48 x 100 = 348
• 7 x 10 = 70
• 7 x 100 = 700
• 0.0480 x 10 = 0.480
• 0.0480 x 10 = 4.80

Keep in mind that whole numbers have an implied decimal point, as shown here: 7 = 7.000000000...

But which way does it move, left or right?

## Multiplying and Dividing Decimals

We already know how many places to move the decimal when we multiply or divide by 10 or 100. Now we need to figure out which direction it moves.

When we multiply by numbers greater than one, the product will always be larger than the original factors. For instance, 7 x 2 = 14. Here, the product 14 is larger than the factors 7 and 2. When we move a decimal to the right, we're making the result larger, as shown here: 7 < 70 < 700. Therefore, when multiplying, move the decimal to the right.

The inverse is true as well. When we divide a number by greater than one, that number decreases in size. For instance: 24 / 6 = 4. Here, the quotient 4 is smaller than the dividend 24. When we move a decimal to the left, we're making the result smaller, as shown here: 700 > 70 > 7 > 0.7 When dividing, move the decimal to the left.

To summarize:

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