Last time, we looked at what fractions are, and saw that fractions and decimals are two different ways to handle numbers less than 1 (or between integers). Here, we’ll look at several questions about why we need both forms, and whether one is better than the other. The comparison and contrast turns out to be …
We’ve looked at some specific ideas about fractions (their proper definition, their relationship to decimals, and how to divide them); it’s time to go through this topic from the beginning. Here we’ll look at how they are introduced to beginners, and how to keep them from hurting our brains!
Here is another puzzle we have received and answered many times. (I count 7 that have been archived.) It has several variations, which make it even more interesting. The story varies, too; sometimes the monkeys are the stars, other times they just get the leftovers. Someone could to an interesting folklore study on this one.
(An archive question of the week) My title is tongue-in-cheek, as we’ll be looking at the Chinese Remainder Theorem, which is really a Chinese theorem about remainders, not a theorem about “Chinese remainders”. But we’ll work on a problem that can be solved with or without knowledge of the theorem, and with various doses of …
We have looked at how to calculate, apply, and undo a percent increase or decrease. Here we will look at some special terms used in business for percent increases, which have been a source of many questions over the years.
Having discussed how to calculate the percent change between two numbers, and how to apply such a change to one number to get a new number, we need to look at what may be one of the most common types of questions we get: reversing a percent change (increase or decrease) to find the original …
A question we got in March asked about working with percent increases. As I replied to this rather common topic, referring to an archived answer, I was reminded that this would is a very common type of question, and would be a good topic to cover in the blog. So that will be the topic …
(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 …
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 …
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.