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How do I say 0.0001782% written out in English?

  • 0.1 is one tenth
  • 0.01 is one hundredth
  • 0.001 is one thousandth

Is 0.0001782 one ten-thousandth seven hundred eighty two, or seventeen hundred eighty two, ten thousandths?

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  • A tenth, hundredth, thousandth, etc., only work like that because of the decimal system (an eighth, for example, is 0.125, not 0.8). I don't know what the simplest actual "vulgar fraction" ratio for your value might be, but it's unlikely to be anything that anyone would actually say aloud as a fraction. – FumbleFingers Nov 1 '16 at 16:18
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    Just as 0.035 would be rendered thirty-five thousandths, 0.0001782 should be rendered one thousand seven hundred eighty-two ten-millionths. – Silenus Nov 1 '16 at 16:22
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    In 'casual mode', where absolute accuracy is not required, you could say "less than two ten-thousandths of a percent". – Hellion Nov 1 '16 at 16:45
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    Do you just want to know to to pronounce (speak) "0.0001782%", or do you want to find a representation that is clearer and easier to understand? – Mick Nov 1 '16 at 17:48
  • Very carefully! – Hot Licks Nov 1 '16 at 22:15
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If you just want to know how to say the number, the convention that scientists and engineers use is to call out each digit to the right of the decimal point. For your example it would be:

zero point zero zero zero one seven eight two percent

This generally not done for numbers to the left of the decimal point. For example, if you wanted to say 1,234.567, it would be:

one thousand two hundred and thirty four point five six seven

Alternatively, you can just call out all the digits:

one two three four point five six seven

  • We would only keep the percent around if we really had to for a number less than about a tenth of a percent. Better to convert into a pure fraction (divide by 100) and then use scientific notation. But yes, I agree that it's better to call out the digits than to worry about billionths. For a long enough number, we call out the digits left of the decimal, also. – EL_DON Nov 1 '16 at 17:21
  • @EL_DON That doesn't seem to be the OP's question, unless I have misread it. What to do about such an unwieldy number is another matter. Interesting job, btw. – Mick Nov 1 '16 at 17:22
  • Sure, the direct answer is to tell him how to use thousandths and millionths, but we're both recommending that no one ever do this. If we're going to talk about what scientists would usually do: list digits or quote a limited number of sig figs so we don't have to go through the whole big deal of "one thousand, five hundred and twenty five": this would instead be "about fifteen hundred" if possible. Shorter answers are more likely to be interpreted correctly. – EL_DON Nov 1 '16 at 17:34
  • @EL_DON The OP may not be interested in finding a clearer representation. He has simply asked how to say 0.0001782%, presumably as it is written. I was taught at school (and at university when I studied physics) to call out the digits to the right of the decimal point. Newsreaders and presenters on British media also do this. – Mick Nov 1 '16 at 17:41
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    I agree with that. Calling out the decades is uneccesary today. – Mick Nov 1 '16 at 18:02
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You could work out how many billionths or ten-millionths of a percent this is, but the cleanest way to express a number this small is with scientific notation. Change .0001782% into 0.000001782 into 1.782e-6. If that doesn't suit your purpose, it is clearer if you just say "point zero zero zero one seven eight two percent" than trying to work out ten-millionths of a percent. If you try to talk about millionths, especially millionths of a percent, someone is bound to have a copy error as these are not frequently used.

But to answer the question plainly, this is "one thousand, seven hundred and eighty two ten-millionths of a percent", or as a fraction: "one thousand, seven hundred and eighty two one-billionths", or: "one thousand, seven hundred and eighty two in a billion".

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