Arithmetic with Roman Numerals

Have you ever wondered how to add, subtract, multiply, and divide using Roman numerals? On one hand, we’ll give the simple answer that the Romans didn’t actually do what you think; on the other hand, we’ll consider what they actually did.

How Roman Numerals Work

Roman numerals are very different from the “Arabic” system we use; there is no “place value”. And yet, as we’ll see, the two systems have more in common than you might think.

Inverse Trig Notation: What Do sin^-1 and arcsin Mean?

Since we’ve been looking at an example of ambiguity in notation, let’s look at a very different one. There is a lot to be confused by in inverse trigonometry! We’ll try to untangle the notations of \(\sin^{-1}\) and \(\arcsin\).

What Do dx and dy Mean?

We’ve looked at the meaning of the derivative, and of its various notations, including dy/dx. This leads to the next question: What does dx or dy mean on its own? This was touched on last time, but there’s a lot more to say that I couldn’t fit there. We’ll look at more advanced approaches to …

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What Derivative Notations Mean

Last week we looked at the meaning of the derivative. In doing so, we mostly used the notation “”, but mentioned another in passing. Here I want to look at our answers to several questions about the different notations you will see.

Decimals, Commas, Thousands, and Lakhs

I’ll finish this series on place value and writing numbers, with a question that’s not quite as simple as you might think: why we use commas and decimal points as we do. Americans may be surprised at some of the answers – and some of the questions.

Decimals in Word Form: Subtleties

Last time we looked at how to convert a number between decimal and word form. Now we’ll move into some tricky cases such as where to use “and” or a hyphen, to eliminate ambiguity.