Learn English – How to read ISO numbers

Avoid saying "and" in the middle of a number

Bob the zealot is correct that you should avoid saying "and" in the middle of numbers. It is common for Americans to include "and" or "'n" in the middle of a number, especially after the word "hundred". American grade school math teachers discourage this, because it is unclear whether the student has stated a number, or stated a math problem.

As Bob the zealot suggests, you usually should say "and" between a whole number and a fraction. For example, 1½ = "one and a half"; 1.5 = "one point five"; 1¾ = "one and three quarters"; 1.75 = "one point seven five" or "one point seventy five". Similarly, $ 1.75 = "a dollar seventy five" or "one dollar and seventy five cents". Dollars and cents are discussed in another ELL post.

Big round numbers

There are a few different ways to say numbers like 1,000,000,000,000,000.

This number can be unambiguously expressed as "ten to the fifteenth", or less formally as "one followed by fifteen zeroes". Unfortunately, this is not the usual name for the number.

Americans usually express this number as "a quadrillion"; I am told that British speakers used to call it "a thousand billion" (and some still do).

Americans will correctly understand "a million billion"; I am told that some British speakers will think that you mean 1,000,000,000,000,000,000 instead.

Americans use the sequence: thousand, million, billion, trillion, quadrillion, quintillion, sextillion, septillion, octillion, nonillion, decillion, ….

I am told that the corresponding British sequence was: thousand, million, thousand million, billion, thousand billion, trillion, thousand trillion, quadrillion, thousand quadrillion, quintillion, thousand quintillion, ….

I list several ways Americans express large numbers in this Math Educators.Stack Exchange answer: https://matheducators.stackexchange.com/questions/4448/math-activities-for-gifted-second-and-third-grade-math-circle-students/6097#6097

Sizes.com has a history of big numbers, with citations.

Teens

The original post uses examples of most of the words in typical large numbers: units (like "one" or "two"), tens (like "ten", "twenty", "thirty"), hundreds, and large round numbers. The numbers between eleven and nineteen are a bit weird:

• "eleven" = 11
• "twelve" = 12
• "thirteen", "fourteen", "fifteen", "sixteen", "seventeen", "eighteen", and "nineteen" are 13, 14, 15, 16, 17, 18, and 19 respectively.

Examples

Here is how I say the original poster's examples. As Cort Ammon suggests, there is a pause before each triplet of digits. I have indicated the pauses with commas:

999,999 = "Nine hundred ninety-nine thousand, nine hundred ninety-nine"

123,909,909 = "One hundred twenty-three million, nine hundred nine thousand, nine hundred nine"

The closest way I know of is to say one number is "over" another. For example:

• "Three-hundred thirty-four over eleven" for 334/11

But that doesn't seem quite right to me, because one number being "over" another isn't really what makes a fraction, since that's notation.

But you're "reading aloud" notation, so it's not really clear to me why this troubles you. I wonder if you have a similar problem, for example, with saying "period" to mean - that's final. Do you ever read aloud slashes/strokes? What about the phrase "in inverted commas"?

"Over" is, in any case, widely used and understood. I would definitely go with this in the general case.

Because of this I like to say:

• "Three-hundred thirty-four by eleven" for 334/11

When I first read this, my brain went 'no, don't do that, "by" means "times."' And it certainly can mean "times." Although its most common usage is in dimensions. If you said to me "334 by 11" out of context, I'd assume you were talking about something rectangular.

However, after pausing for thought, I realised that "by" does get used for fractions. It's quite common when using radians - if you know what they are? So sin(π/4) would be read "sine pi by four."

Additionally, the notation for the derivative dy/dx is usually read by us Brits as "dy by dx". This is not a fraction, and the people over at math.SE would lynch me if I didn't stress that, but I think it's worth mentioning.

I would say "by" is far too ambiguous for general, out of context usage, especially with plain fractions. As your question seems to imply, you know people use "over" and you are inclined to use it too. So use it. Don't overthink it. The key to successful communication is to use the words that people in your speech community will understand and expect to hear - not to use the words you've decided you think they should use.

Sometimes I use the inflection "-ths" after any number, but I worry this sounds unusual. For example:

• "Three-hundred thirty-four elevenths" for 334/11

But I worry this might be incorrect.

Strictly speaking, of course, this is fine, although have fun with 334/21 and 334/22, for example, but it's pretty clunky as, clearly, you realise. The bigger the denominator, the sillier it gets.

Is there an accepted standard way

Yes. "Over." Well, of course, I should stress that's based on my experience of a good few years in maths classrooms in London, England. Other people may do things differently, but the wording of your question really makes it sound like people in your part of the world also use "over." This is also very much "the standard way", you will get "by" used with some fractions, e.g. the angle π/4 radians (see above). There may even be a rule I'm just not yet familiar with. But if you're looking for a common-or-garden reading that's unambiguous and always works: just use "over"