What is 5200000000000 x 760000000000000000000000000000?

You don't want to count all those zeroes. Wouldn't it be nice if I had told you how many there were in the first place?
Scientific notation is a way to express large or small numbers without writing long strings of zeros. You express them as base numbers times 'powers of ten.'

What does 'powers of ten' mean?

We're used to using 'powers' in calculating areas. When you see an equation containing something like r², you know it means r x r. This is called 'r squared' or 'r to the second power.'

10², then, would be ten squared, or 10 x 10, or 100.

10³ would be 10 x 10 x 10 or 1000.

10⁴ would be 10 x 10 x 10 x 10 or 10,000

You can see a pattern, right? 10³⁵ would end up being 1 with 35 zeroes after it.

In the expression 10³⁵, 35 is the exponent. That means the power to which 10 is raised. It also means the number of zeroes that would be after the number, if you wanted to waste your time writing them all out.

What about numbers that aren't 100, 1000, etc.? What about numbers like 300 and 6,000,000? Well, these are all just some number multiplied by some power of ten. That's how you would say them if you read them aloud; three hundred. Six million. That's how you write them, too.

300 = 3 x 100 = 3 x 10²

6,000,000 = 6 x 10⁶

56,000,000 =

73,598,000,000 =

Numbers smaller than 1 have negative exponents. For instance:

.1 = 1 x 10^-1

This means the same thing as 1/10.

.00012 = 12 x 10 ^-5 (note the exponent is the number of places you must move the decimal
point right to get the 12)

.0004 =

.00005693 =

For more practice with this skill, click here

On your calculator and in computer programs, scientific notation is written as ‘E’. The ‘E’ stands for ‘exponent.’ For instance:

If the calculator says 2.45E-15 it means 2.45 x 10^-15

6E7 means 6 x 10⁷

Convert each of these calculator expressions to scientific notation:

62E9 =

5E-12 =

Multiplying with scientific notation:

To multiply powers of ten, you add their exponents together.
For example, you know that: 10,000 x 10 = 100,000.

In scientific notation, this would be: 10⁴ x 10¹ = 10⁴⁺¹ = 10⁵ .

For more practice with this skill, click here

To multiply two numbers in scientific notation, you multiply their base numbers and their powers of ten separately. Take a very simple example: 20 x 20 = 400

In scientific notation, this is: (2 x 10¹) x (2 x 10¹) = (2 x 2) x ( 10¹ x 10¹ ) = (4) x ( 10¹⁺¹ ) = 4x 10² = 400

Estimate the answers for the following problems:

5.41x 10⁵ x 3.8 x 10⁷ =

72.1 x 10³ x 40x10⁶ =

Make up two problems of your own and estimate their solutions.

For more practice with this skill, click here

Dividing with scientific notation:

To divide powers of ten, you subtract their exponents.
For example, you know that: 10,000/ 10 = 1,000

In scientific notation, this would be: 10⁴ / 10¹ = 10^{4 -1} = 10³

For more practice with this skill, click here

To divide two numbers in scientific notation, you divide their base numbers and their powers of ten separately. Take a very simple example: 400/20 = 20

In scientific notation, this is: 4 x 10² / 2 x 10¹ = (4/2) x ( 10² / 10¹ ) = (2) x ( 10^2-1 ) = 2 x 10¹ = 20

Estimate the answers for the following problems:

5.41 x 10⁵ / 3.8 x 10⁷ =

72.1 x 10³ / 40 x 10⁶ =

Make up two problems of your own and estimate their solutions:

Now - what is 5200000000000 x 760000000000000000000000000000?

For more practice with this skill, click here