## 1. What are ordinal and cardinal numbers?

### 1.1. Ordinal numbers - are those numbers defining a thing's position in a series:

- 1st - first - as a number, preceding all others in time, order, or importance;

ex: They sat in the first row. He succeeded on his first attempt. - 2nd - second - as a number, next to the first in place, time, or importance;

ex: Our second option is to take a taxi. The second problem is the lack of global financing. - 3rd - third - as a number, constituting number three in a sequence;

ex: He came third in the competition. Our house is the third from the end on the left. - 4th - fourth - as a number, constituting number four in a sequence;

ex: He could do no better than finish fourth. Take the elevator to the fourth floor. - 5th - fifth - as a number, constituting number five in a sequence;

ex: May is the fifth month of the year. Coming in fifth place is better than finishing last.

### 1.2. Cardinal numbers - are those numbers denoting quantity, as opposed to ordinal numbers.

- 1 - one - as a number, the lowest cardinal number; half of two;

ex: They have many daughters but only one son. - 2 - two; - equivalent to the sum of one and one; one less than three;

ex: The number that comes before three is two. - 3 - three - equivalent to the sum of one and two; one more than two;

ex: The bag contains three ounces of chocolate. - 4 - four - equivalent to the product of two and two; one more than three;

ex: Four people in five preferred this brand. - 5 - five - equivalent to the sum of two and three; one more than four;

ex: I am ten years old and my brother is five.

## 2. How to write cardinal numbers (those denoting quantity) out?

- First, to know how to write a cardinal number out in words it's important to know the name of the place where each digit is.
- For example, the number 12,345 has a 1 in the tens thousands place, a 2 in the thousands place, a 3 in the hundreds place, a 4 in the tens place, and a 5 in the units place.
- 12,345 in words is:

ten thousand (10,000) + two thousand (2,000) + three hundred (300) + four tens (40) + five units (5) =

ten thousand + two thousand + three hundred + forty + five =

twelve thousand three hundred forty-five.

### 2.1. Useful notes / guidelines:

- 1: Note the hyphen (or the minus sign) in "twenty-three" above. Technically, it's correct to hyphenate all compound numbers from twenty-one, 21, to ninety-nine, 99. Using a hyphen also applies to ordinal numbers between 21st and 99th (notice the "st" and "th" after the cardinal numbers).
- 2: "And" placement - in (US) American English, do not use the word "and" after "hundred" or "thousand" (In British English, the word "and" is used after "hundred" or "thousand"). So it is "one hundred twenty-three" and not "one hundred and twenty-three", though you may hear a lot of people using the last, informally. The word "and" is used only when expressing the decimal points in decimal numbers.
- 3: With figures of four or more digits, use commas, ex: 1,154, 12,345.
- 4: When writing out numbers above 999, in American English, do not use commas. Incorrect (it is correct in British English): one thousand, one hundred fifty-four (1,154). Correct: one thousand one hundred fifty-four (1,154).

## 3. How to spell ordinal numbers (those denoting order)?

#### Most ordinal numbers end in "th", so just add "th" to the end of the cardinal number:

- four - 4th - fourth
- six - 6th - sixth
- seven - 7th - seventh
- ten - 10th - tenth
- eleven - 11th - eleventh
- nineteen - 19th - nineteenth
- one hundred - 100th - (one) hundredth
- one thousand - 1,000th - (one) thousandth
- one million - 1,000,000th - (one) millionth

### 3.1. Exceptions:

- one - first - 1st
- two - second - 2nd
- three - third - 3rd
- five - fifth - 5th
- eight - eighth - 8th
- nine - ninth - 9th
- twelve - twelfth - 12th
- twenty - twentieth - 20th
- thirty - thirtieth - 30th
- forty - fortieth - 40th
- fifty - fiftieth - 50th
- sixty - sixtieth - 60th
- seventy - seventieth - 70th
- eighty - eightieth - 80th
- ninety - ninetieth - 90th

### 3.2. In compound ordinal numbers only the last digit is written as an ordinal:

- 27 = twenty-seven - 27th = twenty-seventh
- 123 = one hundred twenty-three - 123rd = one hundred twenty-third
- 1,213,498 = one million two hundred thirteen thousand four hundred ninety-eight - 1,213,498th = one million two hundred thirteen thousand four hundred ninety-eighth

### 3.3. When expressing ordinal numbers as figures, the last two letters of the written word are added to the ordinal number:

- first - 1st
- second - 2nd
- third - 3rd
- fourth - 4th
- thirty-fourth - 34th
- five thousand four hundred thirty-ninth - 5,439th

### Calculator: convert ordinal numbers to (US) American English words, write them out using letters instead of numerals

## 4. Here there are the main ordinal numbers:

- cardinal: 1, one; ordinal: 1st, first;
- cardinal: 2, two; ordinal: 2nd, second;
- cardinal: 3, three; ordinal: 3rd, third;
- cardinal: 4, four; ordinal: 4th, fourth;
- cardinal: 5, five; ordinal: 5th, fifth;
- cardinal: 6, six; ordinal: 6th, sixth;
- cardinal: 7, seven; ordinal: 7th, seventh;
- cardinal: 8, eight; ordinal: 8th, eighth;
- cardinal: 9, nine; ordinal: 9th, ninth;
- cardinal: 10, ten; ordinal: 10th, tenth;
- cardinal: 11, eleven; ordinal: 11th, eleventh;
- cardinal: 12, twelve; ordinal: 12th, twelfth;
- cardinal: 13, thirteen; ordinal: thirteenth;
- cardinal: 14, fourteen; ordinal: 14th, fourteenth;
- cardinal: 15, fifteen; ordinal: 15th, fifteenth;
- cardinal: 16, sixteen; ordinal: 16th, sixteenth;
- cardinal: 17, seventeen; ordinal: 17th, seventeenth;
- cardinal: 18, eighteen; ordinal: 18th, eighteenth;
- cardinal: 19, nineteen; ordinal: 19th, nineteenth;
- cardinal: 20, twenty; ordinal: 20th, twentieth;
- cardinal: 21, twenty one; ordinal: 21st, twenty first;
- cardinal: 22, twenty two; ordinal: 22nd, twenty second;
- cardinal: 23, twenty three; ordinal: 23rd, twenty third;
- cardinal: 24, twenty four; ordinal: 24th, twenty fourth;
- cardinal: 25, twenty five; ordinal: 25th, twenty fifth;
- cardinal: 26, twenty six; ordinal: 26th, twenty sixth;
- cardinal: 27, twenty seven; ordinal: 27th, twenty seventh;
- cardinal: 28, twenty eight; ordinal: 28th, twenty eighth;
- cardinal: 29, twenty nine; ordinal masculin: 29th, twenty ninth;
- cardinal: 30, thirty; ordinal: 30th, thirtieth;
- cardinal: 31, thirty one; ordinal: 31st, thirty first;
- cardinal: 40, forty; ordinal: 40th, fortieth;
- cardinal: 50, fifty; ordinal: 50th, fiftieth;
- cardinal: 60, sixty; ordinal: 60th, sixtieth;
- cardinal: 70, seventy; ordinal: 70th, seventieth;
- cardinal: 80, eighty; ordinal: 80th, eightieth;
- cardinal: 90, ninety; ordinal: 90th, ninetieth;
- cardinal: 100, one hundred; ordinal: 100th, (one) hundredth;
- cardinal: 101, one hundred one; ordinal: 101st, one hundred first;
- cardinal: 112, one hundred twelve; ordinal: 112th, one hundred twelfth;
- cardinal: 200, two hundred; ordinal: 200th, two hundredth;
- cardinal: 300, three hundred; ordinal: 300th, three hundredth;
- cardinal: 1,000, one thousand; ordinal: 1,000th, (one) thousandth;
- cardinal: 1,001, one thousand one; ordinal: 1,001st, one thousand first;
- cardinal: 2,000, two thousand; ordinal: 2,000th, two thousandth;
- cardinal: 3,000, three thousand; ordinal: 3,000th, three thousandth;
- cardinal: 12,000, twelve thousand; ordinal: 12,000th, twelve thousandth;
- cardinal: 20,000, twenty thousand; ordinal: 20,000th, twenty thousandth;
- cardinal: 20,001, twenty thousand one; ordinal: 20,001st, twenty thousand first;
- cardinal: 50,000, fifty thousand; ordinal: 50,000th, fifty thousandth;
- cardinal: 100,000, one hundred thousand; ordinal: 100,000th, one hundred thousandth;
- cardinal: 500,000, five hundred thousand; ordinal: 500,000th, five hundred thousandth;
- cardinal: 1,000,000, one million; ordinal: 1,000,000th, (one) millionth;
- cardinal: 2,000,000, two million; ordinal: 2,000,000th, two millionth;
- cardinal: 1,000,000,000, one billion; ordinal: 1,000,000th, (one) billionth;
- cardinal: 1,000,000,000,000, one trillion; ordinal: 1,000,000,000th, (one) trillionth;
- cardinal: 1,000,000,000,000,000, one quadrillion; ordinal: 1,000,000,000,000th, (one) quadrillionth;
- cardinal: 1,000,000,000,000,000,000, one quintillion; ordinal: 1,000,000,000,000,000th, one quintillionth;
- cardinal: 1,000,000,000,000,000,000,000, one sextillion; ordinal: 1,000,000,000,000,000,000th, one sextillionth; etc...

### Calculator: convert ordinal numbers to (US) American English words, write them out using letters instead of numerals

## 5. When to write out ordinal numbers?

- Since it's ok to write ordinal numbers in figures (1st, 2nd, 3rd, ...) in informal writing to friends, colleagues, etc, we need to write them in words in formal writing - business, job applications, etc.
- When beginning a sentence, "Twentieth year of her life... " and not "20th year of her life...".
- The Chicago Manual of Style recommends spelling out the numbers zero through one hundred and using figures thereafter - except for whole numbers used in combination with hundred, thousand, hundred thousand, million, billion, and beyond (e.g., two hundredth; twenty-eight thousandth; three hundred thousandth; one millionth, one hundred millionth).