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.

Do I need a “one”?

We’ll start with this, from 2001:

Written Form of Decimals

What is the CORRECT way to write decimals?

Example: 343.25 

Is it: three hundred forty-three and twenty-five hundredths - OR- 
Is it: three hundred forty-three and twenty-five one hundredths? 

The "one" is the question. Do you add "one" in front of "hundredths"? 
What about hyphens, where do they go?

Example: 46.6 

Is it: forty-six and six tenths -OR- is it forty-six and six one tenths?

Also for thousandths place?

Thank you.

Doctor Rob answered:

Thanks for writing to Ask Dr. Math, Ceci.

For 343.25, it is "three hundred forty-three and twenty-five hundredths."

For 46.6, it is "forty-six and six tenths."

For 82.554, it is "eighty-two and five hundred fifty-four thousandths."

For 0.1008, it is "one thousand eight ten-thousandths."

The word "and" is used only to designate the location of the decimal point. There are single words for numbers from 1 to 20, 30, 40, 50, 60, 70, 80, and 90.  All other numbers from 21 to 99 use a hyphen. You also must use a hyphen when talking about ten-thousandths, hundred-billionths, and similar fractional denominations.  Since hundredths and one-hundredths are the same, the shorter form is used.

I have always thought it sounds redundant to say "one one-hundredth of an inch,"  but some people do use this terminology.

We’ll be looking at “and” and the hyphen in the rest of this post. If you choose to add the “one”, you should use the hyphen as in the last sentence.

Subtle differences: how hyphens help

Now let’s move on to the hard cases. Here is a question from “Mrs. Fansler’s 6B Math Class” in 2003:

Place Value and Similar Numbers

How do you read this number: 10.00001?

We were confused because when you read 10.100 you would say "Ten and one hundred thousandths."  We believe that when you read 10.00001 it would sound the same.

We are guessing that the number would sound the same but you would write each one differently. For example:

10.100 would be written: Ten and one hundred thousandths
10.00001 would be written: Ten and one hundred-thousandth.

We would like to know if this is correct.

They had it right, so I chose to raise the stakes. I answered:

Hi, Class! Thanks for a good question.

I would like to change your question a little to make it harder. The trouble with what you asked is that 10.100 is read as "Ten and one hundred thousandths" with an "s" on the end, so the two DO sound different. Instead, let's use

  10.200 = Ten and two hundred thousandths
  10.00002 = Ten and two hundred-thousandths

Here both are plural, but as you noted, the only difference is the presence of a hyphen, which in reading might mean only that you leave a slightly smaller gap between the words. To make the difference stronger, I might tend to say (or even write)

  10.200 = Ten and two-hundred thousandths

and exaggerate the difference as much as I could.

It’s important to read it aloud very carefully to avoid being misunderstood. The hyphen can help in writing; pausing appropriately (or speeding up) can help in speaking. My”two-hundred” is not standard, but I would definitely read it aloud as if it were written that way.

You're right; there is very little difference. Two details rescue us from having an unusable number system:

1. We rarely say 10.200; usually it would be called 10.2 (though there are reasons for including the extra zeroes, when you get to studying significant digits).

2. In reality (as opposed to elementary school) we would read the numbers as

  10.200 = Ten point two-zero-zero
  10.00002 = Ten point zero-zero-zero-zero-two

This is much easier to say as you read it, easier to figure out when you hear it, and easier to copy down. Who cares if a lot of teachers would say it's illegal!

When you are reading aloud for someone to copy, digit-by-digit is the way to go! I suspect that the reasons teachers insist on the written-out-fraction form is to make sure you know what fraction the decimal represents; outside of school, you can forget it.

Why use hyphens only there? Order of operations!

Here is a very similar question, also from 2003:

Writing Numbers with Hyphens

Why do we hyphenate one hundred-millionth, but we don't hyphenate one hundred million?

Doctor Greenie answered first:

Hi, Brian -

I'm not an expert on this, but I know why I think this is the case.

When we say "one hundred million," the 'unit' of measure is millions, and we are counting one hundred of them.

When we say one hundred-millionth, the 'unit' of measure is neither hundreds nor millionths; it is hundred-millionths, and we are counting one of them.

In other words, we want to hyphenate the unit in order to hold it together, but don’t need to hyphenate “one-hundred” or “hundred-million”, which are not single entities. But why not? I offered a concurring opinion:

Hi, Brian.

Here is another perspective on the same basic idea Dr. Greenie expressed. To make it a little clearer at some points, I will use "two hundred-millionths" as my example.

We COULD hyphenate two hundred million as two-hundred million, or as two hundred-million, or even as two-hundred-million, if we wanted to, and it wouldn't change the meaning, which is two times a hundred times a million. We don't do so because it isn't necessary; multiplication is associative.

  200,000,000 = 2 * 100 * 1,000,000        two hundred million

My suggestion here is that we should only hyphenate when it is required, not just when we can do so. And since $$(2\times100)\times1,000,000 = 2\times(100\times1,000,000) = 2\times100\times1,000,000,$$ the hyphen (like the parentheses) is not needed.

But the fraction is different: it means not two times a hundred times a millionth, but two times a (hundred millionth); or alternatively, two divided by a (hundred million). Just as in algebra we use parentheses to group the parts that must be kept together, in English we hyphenate them, turning "hundred millionth" into a single word.

  2/100,000,000 = 2 / (100 * 1,000,000)    two hundred-millionths

  200/1,000,000 = (2 * 100) / 1,000,000    two-hundred millionths

In the latter case we probably would not hyphenate as I showed, for the same reason we don't have to parenthesize the expression; we assume that numbers are grouped from left to right if not otherwise specified.

In part, you might say that we can get away with not hyphenating two-hundred there, because we don’t need to do that to keep 200 together; it is the absence of a hyphen between “hundred” and “millionths” that tells us to make a break there.

So we hyphenate the fraction because division is not associative! English is not quite as irrational as it often seems.

So when you read a hyphen in a number, you can mentally put parentheses around it: “two (hundred-millionths)”. When there is no hyphen, just read from left to right: (two hundred) millionths”.

Hyphens in fractions generally

Here is one from 2004:

Use of Hyphen When Writing Fractions with Words

Is there one correct way to write a fraction in word form?  I have seen one-half and have also seen one half.  I have seen 2/3 written as two-thirds or as two thirds.  Are both ways (with a hyphen, without a hyphen) acceptable, or is only one truly correct?

I answered:

Hi, Colleen.

I usually reserve the hyphen for use in keeping the name of the denominator together.  For example,

  1/5 = one fifth

  1/25 = one twenty-fifth

  2/100,000 = two hundred-thousandths

  200/1000 = two hundred thousandths

This is the same idea that Doctor Greenie and I proposed above.

But you will also see hyphens within numbers when the entire number is used in certain special settings:

  One third of a piece

  A one-third share

  A hundred thousand dollars

  A hundred-thousand-dollar income

That may be what you have seen.

This is really a general grammar issue: We use the hyphen in phrases like this that play the role of an adjective.

After referring to two of the answers above, I added some research, as I usually do when making statements about common usage. (None of the links I used are still live.)

On the other hand, a web search reveals lots of writing style guides that seem to recommend always using the hyphen in fractions, without making a distinction as to usage.  Here is just one of many examples:

  http://owll.massey.ac.nz/writing/grammar_punctuation/hyphen.htm 

  Any two numbers or fractions that are written as words are hyphenated. 

    When she reached the age of twenty-one, Sylvia inherited
    three-quarters of a million dollars from her trust fund.

This page doesn't give an example of a fraction, but does clearly explain why you use hyphens in the cases I showed above, called "compound modifier".  An example is

  a woman-hating religion is utterly different from a woman hating religion

The number twenty-one is traditionally hyphenated, as they show (which is used as a noun); the example “three-quarters” is probably being thought of as an adjectival use, that is, a “compound modifier” consisting of two words that have to be combined just like “woman-hating”. (To me, it is functioning as a noun here.) It is entirely possible that this author forgot about other uses of fractions.

Here is a page that ALMOST agrees with me:

  Ask the Grammarian
  http://www.bewrite.net/community/tips/atg_hyphenating_numbers.htm 

  There is some controversy, though, over whether or not to
  hyphenate fractions like three-fourths.  Some sources say to
  hyphenate fractions always and others say to hyphenate them
  only when using them as an adjective, as in a one-half owner.
  I say, keep it simple, stupid: if you always hyphenate
  fractions when writing them out, you have fewer rules to
  remember.
   
    "Is a fraction always hyphenated?  No, it is not. A hyphen is
    not used with a fraction that is not serving as an adjective.
    'Today he paid one half of the tax,' not one-half."
      -- The Wordwatcher's guide to Good Writing and Grammar

They and their source say, as I do, that it is the adjective (compound modifier) that has to be hyphenated; but then they take the easy way out and say to hyphenate nouns as well.

Here is another site that says not to hyphenate all fractions; but it somehow turns the rule on its head just where it is most needed:

    http://www.thegladiator.info/grammar/grammar4.phtml 

    Hyphenation: Consult the Chicago Manual of Style.
    ...

    Fractions and hyphens:  Fractions are almost always hyphenated
    when they are adjectives.

    e.g., "He is one-quarter Irish and three-quarters Nigerian."

    But when the numerator is already hyphenated, the fraction
    itself is not, as in "ninety-nine and forty-four one
    hundredths." 

    Fractions treated as nouns are not hyphenated.

    e.g., "He ate one quarter of the turkey."

Note that “one hundredth”, from our first question in this post. Sometimes it just seems to feel right, though not necessary. But why not hyphenate it?

So both rules are to be found, but the best reason for always using hyphens is just to make it easy for people to remember the rule!  I still say our rule is best when you want to make sure every case will be understood; but then, grammar is not math (obviously!).

A little more on hyphens

This is from 2004:

Using Hyphens to Indicate Place Value

What is the difference between the following two numbers:

  five hundred thousandths
  five hundred-thousandths

They seem the same to me, but my teacher says that they are different. The 1st one is written as 0.500, but I do not know how to write the 2nd one.

Doctor Wilko wrote, nicely summarizing what we’ve already said:

Hi Joe,

Thanks for writing to Dr. Math!  This is a great question and shows why we should hyphenate the place value of decimal fractions.  You might want to start by reviewing this from our archives: 

  Writing Numbers with Hyphens
  http://mathforum.org/library/drmath/view/63129.html 

If I ORALLY told you and a friend to write the number, "five hundred thousandths" you might write 0.500 and your friend might write 0.00005.  Who would be correct?  Well, both of you could be--it's not clear which way I meant since they both SOUND the same. 

If I say (in writing) to write five hundred "thousandths", the place value that I'm stressing is thousandths.  So, write the number 500 so it ends in the thousandths place:  0.500

On the other hand, if I say to write five "hundred-thousandths", the place value that I'm stressing here is the hundred-thousandths place. So, write the number 5 so it is in the hundred-thousandths place: 0.00005

Do you see the difference now?  The hyphen helps us decide if the hundred is part of the thousandths, making it hundred-thousandths, or part of the five, making it five hundred.  Since we don't speak the hyphen, we often try to communicate it by using a slight pause as we speak.  We might say:

  five....hundred-thousandths to mean 0.00005
  five hundred....thousandths to mean 0.500

Just to drive the point a little further, write these out as fractions and convert them to decimals.

  five hundred "thousandths" = 500/1000 = 0.500
  five "hundred-thousandths" = 5/100,000 = 0.00005

Another subtle difference: “and”

The word “and” can make a big difference. Here is a question from 2004:

Use and Meaning of 'And' in Naming Decimals

Can you please tell me what the word "and" means in the word form of a decimal number?  I don't normally see it when it is not used for math!

I answered:

Hi, Emily.

You're probably thinking of the fact that, at least when we read a number the way teachers commonly insist, "and" is used only between the whole number and the fractional part.  For example, we would say "one hundred fifty-two" for "152", but "one AND fifty-two hundredths" for "1.52".  

Of course, in real life people don't always follow that rule; but it does make sense if you want to be careful in your speaking.  But the "and" there really doesn't have any different meaning there than it usually does, to connect two things together, meaning more or less the same as "plus".  What's more important is that by only using it at the decimal point, when it is NOT used you know there is NOT a decimal point there!

People will often say “one hundred and fifty-two”; that’s understandable, and in fact considered the preferred style in some places. But there’s good reason to restrict the “and”:

The value of using "and" carefully shows up mostly in fractions.  Note the distinction here:

  one hundred and three hundredths = 100 3/100 = 100.03
  -----------     ----------------

  one hundred three hundredths = 103/100 = 1.03
  -----------------

Also,

  one hundred three-hundredths = 100/300 = 1/3 !
              ----------------

If you use “and” too freely, the first two examples would read identically, with no possible way to distinguish them.

Not everyone uses “and”

After my answer above, I referred to this next answer, from 2002:

Saying Numbers Out Loud

I would like to know the correct way to say numbers.  When I say numbers and when I listen to other people say numbers, I hear them use the word "and" before the last number: for example, one hundred and one; two thousand, three hundred and seven.  I have recently been told, however, that the use of "and" is incorrect.  I am having a hard time reconciling what seems to me to be common usage and the dictate that "and" is wrong.  Can you give me some guidance, please?

Doctor Ian answered first:

Hi Sheila,

I was always taught that 'and' is used only to indicate the location of the decimal point:

  three hundred
  three hundred twenty
  three hundred twenty-nine
  three hundred twenty-nine and three tenths
  three hundred twenty-nine and thirty-six hundredths

and so on.

This is the classic American school rule.

However, the Gregg Reference Manual (5th Edition) gives this example:

  seven hundred and twenty-five    ('and' may be omitted)

So if you like the way it sounds, you can always appeal to that citation in case someone makes a fuss. 

_The Elements of Style_ (Strunk and White) says that the 'and' should be retained in the phrase 'one hundred and one', which suggests that it should not normally be included.

So Gregg says “and” here is optional, and Strunk and White imply it’s normally omitted, but is used in this particular case, where the rhythm just feels wrong without it.

In English, there are lots of ways in which 'common' usage differs from 'correct' usage. People commonly mix up 'which' and 'that'; 'compose' and 'comprise'; 'farther' and 'further'; 'quote' and 'quotation'; and so on. Experts disagree on the importance of the distinctions. And, of course, what is 'correct' changes with time. 

If you stick an extra 'and' into a number, will anyone be unable to determine what you mean? No. Might some people who would consider this to be an error make a mental note that perhaps you're less 'educated' than you ought to be? Yes. Might that affect the way they subsequently interpret what you say and do? Yes. Might that, over the course of your lifetime, end up reducing both your income and the scope of opportunities that are offered to you?  Maybe.

There was a time when I would have considered this something worth arguing about. At this point, I no longer think of it in terms of 'correct' or 'incorrect'. Rather, I think of it as one of many 'secret handshakes' for a particular club, and act accordingly.  :^D

So, do what the people around you expect.

I had a little to add:

I'd like to add to Dr. Ian's comments the fact that this usage differs from country to country. I understand that proper British usage includes the "and," while "proper" (though not necessarily common) American usage excludes it.

If people around you say it both ways, you get to decide. (We hope you choose to keep “and” for fractions.)

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