# ABE Math Tutorials/Whole numbers/Powers of 10

## Powers of 10 Whole numbers

Arithmetic Operations with Powers of 10: Would you like to use a calculator to study? Click here for information about the GED and calculator use.

Let's start this lesson by calculating the following sums and differences:

 40 + 20 = 80 - 30 = 90 + 10 = 120 - 50 = 300 + 500 = 900 - 200 = 45,000 + 25,000 = 110,000 - 60,000 = 4,300 + 210 7,500 - 3,000 =

Can you see a pattern here? When you add 40 + 20, you are basically just adding the 4 and the 2; then putting a "0" on the end of the answer. When you add 45,000 and 25,000, once again you are just adding the 45 and the 25, then adding 3 "0"s to the answer.

It's the same thing with subtraction. When you subtract 80 - 30, you are just subtracting 8 - 3, then putting a "0" on the end of the answer. And when you subtract 7500 - 3000, you are subtracting 75 - 30, and adding 2 "0"s to the answer. Note that you can't add 3 "0"s (zeros) to your answer, because 7500 only has 2 zeros on the end. You have to see how many zeros they have in common.}}

When you are adding or subtracting numbers that have zeros on the end, the number of zeros that they have in common stays the same:

Now, let's have a look at multiplication with powers of ten. Calculate the following products:

 4 x 100 = 40 x 20 = 4 x 10,000 = 400 x 200 = 6 x 70 = 60 x 7,000 = 25 x 40 = 250 x 40,000 =

Activity
 The numbers 10, 100, 1,000, 10,000 etc. are called powers of ten. What is the pattern when you are multiplying numbers by powers of ten? It's easy to see what is going on here. When you multiply by powers of ten, you don't have to check how many zeros the numbers have in common. You add all the zeros (from the end of each number) to the answer. In 60 x 7,000 , for example, all you had to do was to multiply the 6 x 7; and then add all 4 zeros (one from the 60 and 3 from the 7000) to the answer. If you know this little trick, it can save you a lot of long multiplication!

This is simply 4 x 3, with 3 zeros added to the answer

This is simply 2 x 25, with 4 zeros added to the answer

Now let's see how powers of ten work with division. Calculate the following quotients:

 4000 ÷ 10 = 6000 ÷ 3 = 4000 ÷ 100 = 6000 ÷ 30 = 4000 ÷ 1000 = 6000 ÷ 3000 = 540 ÷ 9 = 56,000 ÷ 800 = 540 ÷ 90 = 56,000 ÷ 8,000 =

What's the pattern when you are dividing with powers of ten? Did you notice that you ended up removing the number of zeros that the two numbers had in common? For example, when you calculated 56,000 ÷ 800, all you really had to do was to divide 560 ÷ 8. The 2 zeros on the end of each number "cancel each other out". It is easier to see this when you express the division like a fraction. (You may remember that this way of expressing a division was introduced in "Different Ways of Expressing Operations".

Ready to try some operations with Powers of 10? These questions should take you about 2 minutes (3 at the very most!):

Do NOT use a calculator for this quiz! Use the "quick arithmetic" shown in the examples above.

 (1) 200 + 500 = (7) 2800 ÷ 40 = (2) 40 x 60 = (8) 14,000 - 9,000 = (3) 2500 - 2100 = (9) 700 x 90 = (4) 70,000 ÷ 100 = (10) 72,000 ÷ 800 = (5) 5000 x 200 = (11) 580,000 - 500,000 = (6) 50 + 30 +100 = (12) 200,000 + 20,000 =