10.1 Big and Small
In Unit 5, you looked into for some everyday measurements and considered some everyday problems. However, you may have to deal with much larger and much smaller quantities than you have already—particularly if you are interested in science or technology.
Activity: Biggest and Smallest Physical Objects
Think of the biggest and smallest physical objects or numbers that you can and consider how you would describe their size to someone else, making brief notes in your math notebook.
There are many different ideas that you may have come up with. Here are a few that we thought of:
- The width of the universe.
- The distance to a star.
- The number of grains of sand in the world.
- The size of a cell in your body.
- A virus.
- An atom.
A quick check on the Internet gives the width of the observable part of the universe as about 92 billion light years, where a light year is about 9.5 trillion kilometers. So to find the width of the universe in kilometers, you need to multiply 92 billion by 9.5 trillion. How would you do that? [ A trillion is one thousand billion or a million million—which means a number followed by 12 zeros. What is the biggest number you can put in your calculator?]
Well, you may want to use the calculator, but there’s a problem: 92 billion is 92,000,000,000, and while that number will work on this course's online calculator, that is too big a number for many other calculators.
What could you have done if the number were too big for your calculator? You could have worked the calculation out on paper, or multiplied 92 by 9.5 to get 874 and deduced that the distance must therefore be 874 billion trillion kilometers, or you may just have been bewildered by the enormity of the numbers. Clearly, the skills and notation we have used so far are not particularly helpful here. However, there is a way around this that builds on the work you did with exponents in Unit 4.
In Unit 4, you discovered that some large numbers could be written using power notation. For example, 100 is the same as . Here, 10 is known as the base number, and the 2 is the power. Similarly, 1,000 is the same as , and so on.
We can use this idea to help us write very small and very large numbers, but first let's have a recap on powers of 10.