Accepted Formalities in writing whole numbers in words

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Accepted Formalities in writing whole numbers in words

Postby hee_aaron » Fri Jan 08, 2010 2:15 pm

This is my first article. Any comments are welcome.

Accepted Formalities in writing whole numbers in words in the Singapore Mathematics syallbus - the use of comma, hyphen, “and” and the writing of numerals from words.

It is not uncommon that Singapore children, starting from Primary 4, when they started to learn numbers up to 100 000 are confused as to when the comma, and the word and be used.

This article is to address the issue on how to write in words of the numbers according to the Singapore Mathematics syllabus.

For numbers from 21 to 99, there is always a hyphen to join the 2 words. For example, thirty-two, ninety-five. [Rule 1]

For numbers ranging from 101 to 999, and is always use to join the word denoting the value of the hundreds place and the tens place, but not between the tens and ones place.[Rule 2]

For example, for 432, it is four hundred and thirty-two not four hundred and thirty and two. For 807, it is eight hundred and seven.

This rule also applies to numbers which are increase by 10, 100, 1000 fold etc. So 110 000 is one hundred and ten thousand not one hundred, ten thousand. [Rule 3]

Note, comma will never be used in writing numbers up to 999.

From 1001 onwards, whenever there is one or more zeros between the first and last digit, and is always used to join the word denoting the higher place value and the word for the lower place value. And is also used between the words for the thousands and hundreds place. [Rule 4]

1001 One thousand and one
1100 One thousand and one hundred
32 100 Thirty-two thousand and one hundred

However, if the numbers do not end with zeros, then and is only used in joining the words denoting the hundreds place and tens place. The original and is also replaced with a comma. [Rule 5]

32 101 Thirty-two thousand, one hundred and one

When a word is needed to describe the value of the highest place and the next consecutive place, a comma is used, if the value of the next consecutive place is zero, and is used instead. [Rule 6]

40 201 Forty thousand, two hundred and one
40 010 Forty thousand and ten

Notice that the highest places in these two numbers are thousands, the next consecutive place will be hundreds, since the value for the hundreds place in 40 010 is zero, a and used instead of a comma. In the case of 40 201, the digit for the hundreds place is a two – which is non-zero, so a comma is used after forty thousand.

This rule applies for all the larger numbers; let’s look at some 6-digit numbers.

a) 110 000 one hundred and ten thousand
b) 110 009 one hundred and ten thousand and nine
c) 103 027 one hundred and three thousand and twenty-seven
d) 103 413 one hundred and three thousand, four hundred and thirteen

In example (a), the largest place is thousands, the words used to describe the digits written under this place will follow Rule 2.

In example (b), Rule 2 still applies, but the second and is used because of Rule 6, i.e. the value in the hundreds place, the next consecutive place after thousand, is zero, so to join the words describing the digits in the thousands and ones place, and is used.

For example (c), even though we have a zero in the ten thousands place. When writing in words, we only used the word thousand not ten thousands. For example, we do not write 340 000 as “three hundred, 4 ten thousands” , instead we write “three hundred and forty thousand”, notice we only use the word thousand.

In example (d), the comma appears between the group of words one hundred and three thousand and four hundred. In writing, as opposed to the places we write in a place value table, only thousand and hundred are used (and of course million, which we will talk explore later.) thousand and hundred are places that are consecutive to each other, since the value in the hundreds place (which is three) is not zero, a comma and not and is used.

Finally we look at some numbers in the million range.

e) 1 450 000 one million, four hundred and fifty thousand
f) 1 045 000 one million and forty-five thousand
g) 1 000 700 one million and seven hundred
h) 1 100 700 one million, one hundred thousand and seven hundred

In example (e), since after million, the digit in the hundred thousand place is not zero, so a comma is used instead. This is in contrast to example (f). This use of and extends to place that are 2 orders further than a million (i.e. between 1 000 000 and 700).

In example (h), one will see the comma and and used together to describe a single number.

According to the syllabus, though the use of comma is important, no stress is made in putting a full-stop at the end of the sentence as it is accepted that the line which is provided for the students to write their answers ends with one.

Last but not least is the writing of numerals from the given words. The spacing or rather the lack of at the appropriate location will renders the whole written number incorrect. The rule requires that a space be inserted for every 3 digits starting from the ones. For example, one thousand is written as “1 000” instead of “1000” and one million is written neither as “1000 000” nor “1000000” but “1 000 000”.

It may also help to clear up the confusion between the meaning of the words place value, value and place. Generally, whenever we write place, it actually refers to place value. They are the same thing, some teachers choose to drop the word value in fear that their students will be confused with the word value when used by itself. So while the place aka place value of the digit “2” in the number 321 000 is ten thousands place (place is used like a unit of measure) but it has a value of 20 000.

hee_aaron
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Postby cafelatte » Fri Jan 08, 2010 5:49 pm

Thanks for taking the time to share this.

I need a bit of time to "digest" the info but just want to point out that the confusion described is very real ! My son's first Maths worksheet has exactly the described corrections !

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Postby kiasimom » Fri Jan 08, 2010 5:57 pm

:goodpost:

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Postby hee_aaron » Sun Jan 10, 2010 11:01 am

Thank you. Though this type of question is not very common anymore in the PSLE, it cost 2 marks if it ever appears. And these are the "base" marks that students cannot afford to lose in the exam. Considering that the PSLE questions are moving more towards the application and abstract level, we cannot afford to let our children lose marks this way.

In conclusion, remember that the marking scheme for this type of question is extremely stringent, there is no half of the total mark for missing one comma.

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Postby baong » Mon Jan 11, 2010 11:04 pm

Hi hee_aaron,

:thankyou:
Thank you for posting this. Really appreciate your effort.

baong

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Postby KittyBin » Thu Jan 14, 2010 5:08 pm

Hi
I am impressed by your ability to observe such details and go into such great efforts to pen down. Most importantly, to share this knowledge with us, benefitting the entire community. Looking forward to your great articles coming up. Do keep me in the loop. Thanks. :celebrate:

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Postby buds » Thu Jan 14, 2010 5:23 pm

:goodpost:

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Postby Suz855 » Fri Jan 15, 2010 9:29 am

One question, when writing numbers in word should we begin with a capital or all small letter or it doesn't matter?

Based on My Pal text, the number word is written all in small letter, a check with most Assessment books, answer key all written with Capital.

Thanks for the clarification

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