3.A Understanding Decimal Notation
Chad Flinn and Mark Overgaard
We started by going through whole numbers, then we moved onto fractions, and now we will look at decimals.
We start this story with Chad. Now, Chad is not an apprentice, like the people in the first two stories, but rather someone who received his Red Seal Electrical Ticket a number of years ago. He then went on to start his own electrical company, which he still runs today.
After owning his own business for several years, Chad recognized the fact that apprentices coming through the system could use some advice about starting and running a company, especially when it came to the money portion. As Chad has some experience in this, he decided to start a course for apprentices wishing to start their own businesses.
When dealing with numbers, we don’t always have the luxury of working with just whole numbers. If we referred back to the last chapter and looked at fractions, we would see that a fraction represents a part of a whole number. Decimals are the same in that they represent a part of a whole number. The difference is that decimals are written with a different notation than fractions. Decimal notation allows us to visually quantify how much of a whole number we are dealing with.
In his first class, Chad starts off by talking about the price of tools and materials. He starts with a hammer priced at $12.47. Note that the cost of the hammer is not exactly $12, but a little more than $12. This is where decimals come into play. The numbers after the point (.) , also known as the decimal point, are called decimals.
Each dollar contains 100 cents. In fact, the word “cent” means 100. Think of a century: it has 100 years in it. All decimals are based on the number 10 and can be referred to as base 10. These numbers include 10, 100, 1000, 10000, and so on. If we were to relate this to fractions, we would be dealing with fractions that have a denominator of 10, 100, 1000, 10000, and so on.
Although we only have two decimal places to worry about when dealing with money, we can continue a decimal on for as long as we want. For instance, the number pi (3.14 or π) actually continues on forever and has no ending. Check it out:
This just shows pi to the first few dozen decimal places, but there are lots more.
What we need to do is get an understanding of the decimal system and how it works. Take a look at the following number.
Back in Chapter 1, we dealt with the place value system for whole numbers (see The Place Value System). Decimals follow a similar pattern that starts with the first number to the right of the decimal. In our example of 5.9, the pattern would begin with the 9.
Back to Chad. In Chad’s lecture, he stresses the importance of detailed accounting when dealing with your own business. Now, we all know that there are 100 cents in a dollar, and making sure that you get the cents correct when accounting is important. Rounding up or down to the nearest dollar and being “close enough” w