Scientific Notation


Discussion of Powers of Ten (not the movie)

Ref: from L. Krauss – Fear of Physics (Basic Books)


  1. We have to develop a feeling for numbers – then we can decide what we can ignore and what we cannot. It’s difficult to grasp numbers and be able to relate them to everyday life. We can easily relate to up to about 20 but it gets more difficult for us above that.

To use an example (from the book Fear of Physics) – Suppose you want to know the result of 40 x 40 roughly – which answer is better, 160 or 2000? Neither is correct, but the latter is much closer to the correct answer of 1600. (If this were money, $2000 would be $400 off, but 160 is $1440 off)


To help avoid mistakes and to concentrate on the important part of numbers, we use a different way of writing numbers – called scientific notation.


How do we write other numbers. Remember the exponent is the important part. 230 is written as 2.3 x 102. Or if we are sure of the zero, 2.30 x 102.


The number of molecules in 18 grams of water (18cc) is 6.023 x 1023. This is a much better way of writing the number than 602300000000000000000000 and also it tells us we are sure of 6023 – not the zeros which follow the 3. The 6023 are said to be "significant figures" because we are sure of them. After that the number is just rounded off.

Notice that the important part of the number is the 1023 –let's call it the magnitude. The first part (6.023) is always chosen between 1 and 10 so it can never affect the magnitude by more than +1. e.g. 9.9 x 1023 = 1024.


Write an order of magnitude #’s (powers of ten only) for

# of students at DePaul – 15,000 ______________

# of people in the Metro Chicago – 6 million ______________

# of people in US – (200 million) ______________

# of people in China ( 2 billion ______________

# of people in the world – almost 6 billion ______________


Movie – Laser Disk (10 minutes)

Watch Powers of Ten! Notice how much each factor of 10 changes things. Don’t try to memorize the values.