Very big and very small numbers can be hard to comprehend. Having visualizations and videos, like the one below, can helpful in understanding what all those zeros mean. (Although, it can still be hard to wrap your mind around the scales involved.) This videos zooms out to 1024 meters and then back in to 10-16 meters. This range is smaller than that of of the Scale of the Universe site (1027-10-35 meters) mentioned in my previous post about the very big and the very small, but it was made over 35 years ago.
What’s the biggest number you can think of? Depending on a kid’s age, they may answer 100 or a million or infinity (infinity is a concept, not a number). What’s the smallest number you can think of? Sometimes kids answer this with 1 or zero or a negative number. With elementary aged kids, I often have to remind them that there are many numbers possible between 1 and 0 (the fractions or decimals).
The problems with very big and very small numbers are (1) How do you express them? and (2) How do you conceptualize or understand them?
1. To deal with the first problem, we have scientific notation. Scientific notation is a way to write numbers that are too big or two small to write in the conventional decimal notation. (If you are doing a calculation using very big or very small numbers, it can be inconvenient to write all those zeros.) As an example, 3,000,000 written in scientific notation is 3 x 106, because this is the same as 3 x 10 x 10 x 10 x 10 x 10 x 10. Similarly, a small number such as 0.000003 would be written as 3 x 10-6, because it is the same as 3 / (10 x 10 x 10 x 10 x 10 x 10).
The table below shows some numbers in decimal notation, their American names (Did you know that a billion does not mean the same thing in all countries?), and the scientific notation. Do you have a large number that you don’t know how to name? Try this interactive site.
2. To address the second problem with very large and very small numbers – how to conceptualize them – I like to have kids play with this fun interactive website: Scale of the Universe 2. This site shows the relative sizes of things from theoretical strings and quantum foam (on the order of 10-35 meters) to the observable universe (on the order of 1027 meters). Seeing the differences in scale is pretty mind-blowing, and students enjoy finding out that the site was developed by a 14-year-old boy with help from his twin brother.
Screenshot from Scale of the Universe 2