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I find it very strange that the top results on Google for "how to read decimal" give me a very strange way to read them - as fractions.

I have learnt to read the digits individually and it makes a lot of sense. There is no fumbling with which "-ths" the fractional part is, and there's no confusion for the listener. The ESE QA here and here also agree with me.

However, I find that the system of reading decimals as fractions is being widely taught and accepted.

The top result here has an example: What is the numerical value of "two hundred thousandths"? Three students gave the answers as follows:

  • Student 1: 200,000.
  • Student 2: 0.200
  • Student 3: 0.00002

Apparently only Student 2 is right. The explanation given is that the individual answers when converted to words would be:

  • Student 1: two hundred thousand
  • Student 2: two hundred thousandths
  • Student 3: two hundred-thousandths

And that Student 3 is wrong because the question did not contain a hyphen.

But here's what I don't understand: How do you state the hyphen when actually speaking the number out loud? Do you say "two hundred hyphen thousandths", or do you simply say "t-w-o hundredthousandths" (saying the second word as compressed as possible)?

According to other sources like this video, even the question is wrong, as the "correct" answer by Student 2 should actually be read as "two tenths", ignoring the insignificant zeros.

I am trying to understand how this system came to be and why it is accepted over the simpler system of reading out the digits individually after the decimal point:

  • Student 1: two hundred thousand.
  • Student 2: zero point two.
  • Student 3: zero point zero zero zero zero two.
  • Decimals and (common) fractions are just two ways of addressing the area of fractions; indeed , decimals may also be called decimal fractions. Essentially, they're just different mathematical languages; percentages are a third. Very few people would use any other format than decimal for things like 0.00002 (largely because it gets so fiddly and confusing, as you point out). If one had to distinguish say 'two hundred thousandths' from 'two hundred-thousandths', and I've never had to myself before today in spite of once being a maths teacher ... – Edwin Ashworth Jun 14 '14 at 8:49
  • , one would use "two .......hundredthousandths" as you suggest, possibly with 'hand-brackets' 'round' hundredthousandths. On a maths note, "two hundred thousandths" = 200/1000 = 2/10 = 1/5 (simplest form) = .2 = 0.2 (usual decimal form) = 0.200 = 0.200000000.... The simplest forms are usually preferred. But note that 0.19993 is 0.200 when rounded to 3sf / 3dp; here there can be no other way of writing the rounded number. – Edwin Ashworth Jun 14 '14 at 8:55
  • The question is badly worded. It's merely trying to illustrate the difference the hyphen makes to the grouping of the words involved. For 'What is the numerical value of ...' read 'Write down, in words, or numerals using common fractions or decimals:' Student 2's answer is not the best, but not incorrect. Your suggestions are all fine. – Edwin Ashworth Jun 14 '14 at 9:00
  • Your Google-hatred is irrelevant here, and your comment is off-topic. I don't see what they stand to gain by promoting one system of reading decimals over another. Besides what do you use to search the web? Please don't say DuckDuckGo! – ADTC Jun 14 '14 at 20:11
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There isn't really a standard term hundred-thousandths probably for the reasons you give; you can't pronounce a hyphen.

The usual terminology jumps from 10-3 (thousandths) to 10-6 (millionths)

0.2 is two tenths

0.02 is two hundredths

0.002 is two thousandths

0.0002[00] is two hundred millionths

0.00002[0] is twenty millionths

0.000002 is two millionths.

0.765 is seven hundred and sixty five thousandths.

Two hundred thousandths is 0.200, or less commonly twenty hundredths or (and I'd say this would be the preferred wording) two tenths.

Why decimal vs fractional? I guess that's historical. When all you've got is an inch, a thou makes more sense than 0.001 of an inch.

The use of fractions (with a decimal denominator) is not new, decimal fraction terminology is part and parcel of the decimal number system, tenth, hundredth, thousandth etc.

Non decimal fractional terminology has a long history too.

Before about 1700 all currencies were not decimal, the UK had pounds split into twenty shillings with twelve pence in each shilling, the US had a variable number of cents to the dollar (about ninety usually), the Spanish peso was split into eight reals and so on and those variations didn't lend themselves to decimal representations, so fractional representations were common. Almost all currencies are now representable in the same decimal form. Each country changed to a basic 1 to 100 unit at different times.

Similarly measures of length, an inch is a twelfth of a foot, a foot is a third of a yard. Going the other way an inch was (and still is) subdivided into quarters, eighths and sixteenths, even thirty-seconds and sixty-fourths, and so on.

When to use one and not the other? I don't think it matters.

I find referring to something as zero point one zero of a gallon (or even just point one of a gallon) just isn't as comfortable as saying a tenth of a gallon.

You are using a term for a decimal fractions if you say something is 72 cents because cents is a direct replacement for a hundredth of a dollar so 72 hundredths of a dollar is 72 cents.

  • Could you expand your answer more on "historical" and help explain why some cultures teach reading as fractions while others teach reading the digits individually as decimals? Also would you argue that reading as fractions is better than as decimals, and why or why not? – ADTC Jun 14 '14 at 9:57
  • @ADTC I can't imagine teachers not teaching both vulgar and decimal fractions. I've tried to add something that might show that fractions are more than just different versions of 1/10 but I'm not sure it makes the history any clearer. Why we say this or that when given a choice is rarely obvious. – Frank Jun 14 '14 at 10:51

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