Arithmetic

More on 0.999…

(An archive question of the week) In collecting questions and answers about 0.999… for the last post, there were two that were too long to include, but that dig more deeply into issues that some of the standard answers tend to gloss over. So here, I want to look at those two answers, both of …

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Frequently Questioned Answers: 0.999… = 1

Having looked at two common questions in probability that are often challenged, let’s turn to the realm of numbers. Non-terminating decimals are inherently problematic, and one particular example causes difficulty for many, even after they fully accept the mathematics of it. Our FAQ page on this topic, at 0.9999… = 1, is very brief, and …

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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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