Scientific Notation

6.08 x 10^-7

656000 in scientific notation is written as 6.56 x 10^5.

It is: 3.12*10^-7

It is: 8.26*10^-3

.0059?

5.9 x 10^-3

It is: 2.73*10^9

0.0000585 in scientific notation is 585x10 to the 5

1053 = 1.053 x 103

2 x 10-1

1.33x101

Astronomers often have to deal with large numbers, because the universe is very large and most of the universe is very distant from the Earth. For example, the size of the Milky Way galaxy on its long axis is 200,000 light years, and a light year is about 7,000,000,000,000 miles, so if I wanted to tell you how many miles long the galaxy is on its major axis, I could say it is 14,000,000,000,000,000,000 miles, or much more conveniently, I could say that it is 1.4 x 1019 miles.

1*10100.

Scientific notation is particularly useful for numbers that are very big (eg 465 000 000 000) or very small (eg 0.000 000 003 98) because it saves you from having to write a lot of zeros. It also gives you a better feel for the magnitude of the number.

The big number above is 4.65 multiplied by 100 000 000 000. The big number to the left is a one followed by 11 zeros, and it can be written as 1011 (ten to the power of eleven). Hence the complete number is 4.65 x 1011 (4.65 times 10 to the power of 11).

Likewise, the small number above is the same as 3.98 divided by 1 000 000 000 (9 zeros), or 3.98 multiplied by 0.000 000 001.

This can be written as 3.98 x 10-9 (4.65 times 10 to the power of -9).

So the scientific notation for the two numbers is 4.65 x 1011 and 3.98 x 10-9.

Scientific notation saves you from having to count a lot of zeros, and avoids errors. Note that I have made the original numbers a bit easier to read by inserting a space between each group of three digits.

If you are happy with scientific notation, you might want to consider a variation on the system, called engineering notation.

0.6412 in Scientific Notation = 6.412 x 10-1

First non-zero digit is 5, so decimal point goes after it.

To get back to its original position requires going 3 digits to the left, so the power of 10 is -3. Thus

0.00504 = 5.04 x 10-3

0.02718 in scientific method is, 2.718 multiplied by 100.

5.5 X 10^4

87,400 in scientific notation can be expressed as 8.74 x 10^4 or 8.74E4

5.2683 x 10 to the power 4

3.1 x 10^1 m

It is: 1.64*10^1

0.0019 = 1.9 x 10-3

8.24e-4 or 8.24 x 10^-4

Scientific notation shows things to the power of 10

So 35 in scientific notation is 3.5 x 10

Other examples are 350 is 3.5 x 102

0.740 in scientific notation is 7.4 x 10^-1