Arithmetic

Significant Digits: Measurements and Exact Numbers

To conclude this series on significant digits, I want to look at some details of their application. Specifically, we will consider questions about how they related to measured values, and to fixed constants. Measured values I’ll start with a question from 2011 about measurement and unit conversion: Changing Units … and Significant Figures? Suppose I …

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Significant Digits: Operations

Last time, we introduced what we mean by significant digits (or figures), and touched on why they are defined as they are. Here we will look at how significant digits and decimal places differ, and how they are affected by operations (primarily addition and multiplication). This is another aspect of why they are defined at …

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Significant Digits: Introduction

Our next series of posts will be about the concept of significant digits (also called significant figures), which are important in scientific or engineering calculations to keep track of the precision of numbers (although, as we’ll see, they are not what you would use when you need to be especially careful). We’ll start with the …

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Zero Divided By Zero: Undefined and Indeterminate

Back in January, I discussed the issue of division by zero. There is a special case of that that causes even more trouble, in every field from arithmetic to calculus: zero divided by zero. I’ll look at several typical questions that we answered at different levels. Conflicting rules for division? Let’s start here: Zero Laws …

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Six Distinguishable People in Four Distinguishable Rooms

(An archive question of the week) Last time we looked at some elementary problems in combinatorics, where we counted the number of ways to choose or arrange elements of a set. Let’s look at a somewhat more complicated problem, which will demonstrate issues that come up in interpreting such a problem and in choosing a …

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Permutations and Combinations: An Introduction

We have seen a number of questions recently about combinatorics: the study of methods for counting possibilities. These topics are studied at all levels of mathematical education, from elementary (where they might just be called counting) to high school (where they are often learned along with probability) to college (where they are part of “discrete …

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Greatest Common Divisor: Extending the Definition

Having just talked about definition issues in geometry, I thought a recent, short question related to a definition would be of interest. We know what the Greatest Common Divisor (GCD, also called the Greatest Common Factor, GCF, or the Highest Common Factor, HCF) of two numbers is; or do we? Negative GCD? Here is the …

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