1.A The Place Value System
Chad Flinn and Mark Overgaard
Have you ever heard the term “whole number”? It might seem like a weird concept: aren’t all numbers whole? I ate six apples this week, or I charged my electric vehicle for three hours yesterday. Those are whole numbers, right?
Well, not all numbers are whole. You could have eaten 3½ apples during a particularly slow apple-eating week, and maybe you didn’t drive your electric vehicle all that much yesterday, so you only had to charge it for 2.3 hours. Those are not whole numbers.
The purpose of this chapter is to define what a whole number is and then learn to work with those whole numbers, be it by adding, subtracting, multiplying, or dividing.
All the chapters in this textbook, including this one, will have examples and exercises geared towards the trades. It contains content relevant to all trades, no matter what trade you are in.
Counting Numbers and Whole Numbers
A number of years ago, a student named Harpreet went through a plumbing apprenticeship program. After completing his schooling and receiving his Red Seal plumbing ticket, he has decided to open up his own plumbing company.
Like most new entrepreneurs, he experienced a steep learning curve, especially when it came to ordering material for jobs and organizing and scheduling when he had a number of jobs on the go.
Although he might not be thinking about counting numbers or whole numbers, he has ended up working with these when ordering materials and during the day-to-day operations of the company.
If we want to start with the very basics, we must start with counting numbers, which are sometimes referred to as natural numbers. These are the most basic units in algebra and the ones we use to count objects. For instance, Harpreet had to order one toilet, two sets of taps, three fittings, four braided hoses, and five chocolate bars (it seems like Harpreet has a bit of a sweet tooth).
One more thing: in counting numbers, there are no decimal or fraction parts. Also, there are no negatives and no zero.
Okay, so we have no zero. But what if we just decided to add a zero to the set of counting numbers? Would that be so bad? No, it wouldn’t, but then we couldn’t call them counting numbers anymore. The set of counting numbers plus zero becomes what is known as the set of whole numbers.
Counting numbers: 1, 2, 3, 4, 5, …
Whole numbers: 0, 1, 2, 3, 4, 5, …
The discovery of the number zero was a big step in the history of mathematics. Don’t ask me why, but apparently it was. As for Harpreet, let’s hope that he bids jobs properly and that his profit doesn’t amount to zero.
The Place Value System
Worried that he might estimate jobs improperly, Harpreet decides he needs some help with estimating and bidding jobs, as well as some help with the books. He calls up his friend Jamieson and asks if he wants to help. Jamieson, who has been in the plumbing industry for a number of years, has had a recurring back injury and figures this might be a good op