Numbers Up To Three Digits

What are the numbers up to three digits?

Numbers with three digits range from 100 to 999. The digits in the hundreds place of a three-digit number must be between 1 and 9. The smallest three-digit number is 100 and the largest three-digit number is 999. All in all, there are exactly 900 three-digit numbers. 

Say, for example, the number 125.

125 is a three-digit number with a units digit of 5, a tens digit of 2, and a hundreds digit of 1. 

What is the place value of a three-digit number?

All number is made up of ten digits: zero (0), one (1), two (2), three (3), four (4), five (5), six (6), seven (7), eight (8), and nine (9), and each digit has an assigned position which we call as a place value. 

The place value of a number is the position of each digit. When dealing with three-digit numbers, we have two distinct place values: ones, tens, and hundreds.

Consider the number 578. 

The digit on the outmost right of 578 is the ones digit – or the units digit. The middle digit is called as tens digit, and the digit positioned on the outmost left is the hundreds digit. Hence, 5 is the hundreds digit, 7 is the tens digit; and 8 is the ones digit.

Consider a block . If each block represents the single digit 1, then, we can represent the tens and hundreds as:

Hundreds	Tens

How to assign place values in a three-digit number?

To assign place values in a three-digit number, you must note that:

1. The number on the rightmost position is the units digit. 
2. The number positioned in the middle is the tens digit. 
3. The leftmost digit is the hundreds digit.

The table below shows an example of assigning place values in a three-digit number.

	Hundreds Digit	Tens Digit	Ones Digit
396	3	9	6
471	4	7	1
285	2	8	5
914	9	1	4
730	7	3	0
809	8	0	9
176	1	7	6
657	6	5	7
221	2	2	1
525	5	2	5

What is the significance of 0 in a three-digit number?

If the number zero is placed in a position where there are no other non-zero numbers to its left, then it contributes nothing to a three-digit number.

Consider the numbers 099, 009, 909, 990. 

• In 099, the value of the hundreds digit is 0 x 100. Hence, it makes no sense because we can simply write 099 as 99 – making it a two-digit number. 
• In 009, the value of the hundreds digit is 0 x 100 = 0, the value of the tens digit is 0 x 10 = 0 which does not contribute to the value of the number. We can simply express 009 as a single-digit number 9. 
• In 909, the value of the tens digit is 0 x 10 = 0. However, the number to the left of 0 is a non-zero digit – 9. If we decompose 909, it will be (9 x 100) + (0 x 10) + (9 x 1) which will result to a three-digit number 909.
• In 990, the value of the units digit is 0 x 1 = 0. Since the numbers to the left of 0 are both non-zero digit, then it is an example of a three-digit number.

How to decompose a three-digit number?

To decompose a three-digit number, we simply multiply the place value by its corresponding digit:

1. Multiply the number on the rightmost position by 1.
2. Multiply the middle digit by 10.
3. Multiply the digit positioned on the outmost left by 100.
4. Get the sum of the preceding steps.   

Below is an example of decomposing a three-digit number.

Example	Answer
396	(3 x 100) + (9 x 10) + (6 x 1)
471	(4 x 100) + (7 x 10) + (1 x 1)
285	(2 x 100) + (8 x 10) + (5 x 1)
914	(9 x 100) + (1 x 10) + (4 x 1)
730	(7 x 100) + (3 x 10) + (0 x 1)
809	(8 x 100) + (0 x 10) + (9 x 1)
176	(1 x 100) + (7 x 10) + (6 x 1)
657	(6 x 100) + (5 x 10) + (7 x 1)
221	(2 x 100) + (2 x 10) + (1 x 1)
525	(5 x 100) + (2 x 10) + (5 x 1)

How to write a three-digit number?

Three-digit numbers can be written in numerical form, in words, and in its expanded form. Say, for example, the three-digit number 489. 

• The numerical form of 489 is simply 489. 
• When written in words, it is four hundred eighty-nine.
• If we expand 489, it will be written as 400 + 80 + 9. 

Three-digit numbers in numerical form

The numerical form of a three-digit number is simply the combination of any three digits from 0 – 9.

The table below shows the numerical form of a three-digit number.

Numerical Form
267
345
819
956
123
218
195
649
987
366

Three-digit numbers in words

When numbers are written in words, it helps us quickly tell the place values. US System and British have a slight difference in writing three-digit numbers in words. The smallest three-digit number is written as one hundred, while the largest three-digit number is written as nine hundred ninety-nine.

The table below shows the numerical form and how it is written in the US and British systems.

Numerical Form	Writing numbers in word US System	Writing numbers in word British System
267	Two hundred sixty-seven	Two hundred and sixty-seven
345	Three hundred forty-five	Three hundred and forty-five
819	Eight hundred nineteen	Eight hundred and nineteen
956	Nine hundred fifty-six	Nine hundred and fifty-six
123	One hundred twenty-three	One hundred and twenty-three
218	Two hundred eighteen	Two hundred and eighteen
195	One hundred ninety-five	One hundred and ninety-five
649	Six hundred forty-nine	Six hundred and forty-nine
987	Nine hundred eighty-seven	Nine hundred and eighty-seven
366	Three hundred sixty-six	Three hundred and sixty-six

Given the table, we can easily note that the only difference in writing in numbers in words in the US and British system is the conjunction “and” between the hundreds and tens place. 

Three-digit numbers in expanded form

The expansion of a number gives us information on how it is composed. A three-digit number’s expanded form can be represented in three ways. 

Basically, splitting, decomposing, or expanding a three-digit number enables us to gain a better understanding of the three-digit number. By splitting a three-digit number into hundreds, tens, and units, we can easily denote the digits of the hundreds, tens, and units place.

Consider the expanded form of the three-digit number 821.

• The first way is to write as 821 = (8 x hundreds) + (2 x tens) + (1 x ones)
• The second way is to express it as 821 = (8 x 100) + (2 x 10) + (1 x 1)
• The third and last method is to express it as 821 = 800 + 20 + 1

Example #1

Express 267 in its expanded form

Solution

The table below shows how we can express 267 in its expanded form.

Method 1	(2 x hundreds) + (6 x tens) + (7 x ones)
Method 2	(2 x 100) + (6 x 10) + (7 x 1)
Method 3	200 + 60 + 7

Example #2

What is the expanded form of 345?

Solution

The table below shows how we can express 345 in its expanded form.

Method 1	(3 x hundreds) + (4 x tens) + (5 x ones)
Method 2	(3 x 100) + (4 x 10) + (5 x 1)
Method 3	300 + 40 + 5

Example #3

How can we expand 819?

Solution

The table below shows how we can express 819 in its expanded form.

Method 1	(8 x hundreds) + (1 x tens) + (9 x ones)
Method 2	(8 x 100) + (1 x 10) + (9 x 1)
Method 3	800 + 90 + 1

Example #4

What is the expanded form of 956?

Solution

The table below shows how we can express 956 in its expanded form.

Method 1	(9 x hundreds) + (5 x tens) + (6 x ones)
Method 2	(9 x 100) + (5 x 10) + (6 x 1)
Method 3	900 + 50 + 6

Example #5

Expand the three-digit number 123. 

Solution

The table below shows how we can express 123 in its expanded form.

Method 1	(1 x hundreds) + (2 x tens) + (3 x ones)
Method 2	(1 x 100) + (2 x 10) + (3 x 1)
Method 3	100 + 20 + 3

Example #6

What is the expanded form of 218?

Solution

The table below shows how we can express 218 in its expanded form.

Method 1	(2 x hundreds) + (1 x tens) + (8 x ones)
Method 2	(2 x 100) + (1 x 10) + (8 x 1)
Method 3	200 + 10 + 8

Example #7

Expand the three-digit number 195.

Solution

The table below shows how we can express 195 in its expanded form.

Method 1	(1 x hundreds) + (9 x tens) + (5 x ones)
Method 2	(1 x 100) + (9 x 10) + (5 x 1)
Method 3	100 + 90 + 5

Example #8

Expand the three-digit number 649.

Solution

The table below shows how we can express 649 in its expanded form.

Method 1	(6 x hundreds) + (4 x tens) + (9 x ones)
Method 2	(6 x 100) + (4 x 10) + (9 x 1)
Method 3	600 + 40 + 9

Example #9

How can we expand 987?

Solution

The table below shows how we can express 987 in its expanded form.

Method 1	(9 x hundreds) + (8 x tens) + (7 x ones)
Method 2	(9 x 100) + (8 x 10) + (7 x 1)
Method 3	900 + 80 + 7

Example #10

What is the expanded form of 366?

Solution

The table below shows how we can express 366 in its expanded form.

Method 1	(3 x hundreds) + (6 x tens) + (6 x ones)
Method 2	(3 x 100) + (6 x 10) + (6 x 1)
Method 3	300 + 60 + 6

What are the common misconceptions about three-digit numbers?

Sometimes students commit several common errors in writing or reading a three-digit number. One of these errors is misinterpreting a number as another number. Students must note that whether they are reading, writing, and interpreting a 3-digit number, the digit’s place value must be rightly placed. 

Listed below are some of the mistakes sometimes we commit in dealing with 3-digit numbers:

• When children are asked to create the smallest three-digit number given three digits including zero, they frequently place the zero in the leftmost position. As stated above, 0 becomes non-significant if there is no non-zero number that exists in the outmost left. If we are creating a three-digit number, zero cannot be in the hundreds place. For instance, 086 is a two-digit number and not a three-digit number. Similarly, 008 is a single-digit number.
• When there is a zero in the unit’s or tens place, some have difficulty identifying the number. Students may become perplexed when asked to read 250 and 205. 
• Oftentimes, when asked to write “two hundred twenty-one,” students immediately write the number 200 and add 21 after such that it will create a 5-digit number 20021.  This misunderstanding arises as a result of a superficial understanding of place values.

Trivia about three-digit numbers

Below is the list of cool trivia about three-digit numbers

• A three-digit number cannot start with 0. 
• 10 tens will result in 1 hundred, which is the smallest possible three-digit number – 100. 
• The smallest possible three-digit number using only 1 digit is 111.
• The smallest possible three-digit number using 3 distinct digits is 102.
• The largest three-digit number is 999. Additionally, it is also the largest number using only 1 digit. 
• The largest possible three-digit number using three distinct digits is 987. 
• There are exactly 900 numbers that exist between 100 – 999.

Some famous three-digit numbers

There are a lot of famous and significant three-digit numbers such as: 

1. 666
   Apart from being the biblical beast’s number, the three-digit number 666 has several other significant meanings for history buffs and conspiracy theorists alike, one of which was the duration of the Assyrian empire before Babylon conquered it.
2. 911 
   It is an American emergency telephone number that was established in 1968 and provides access to police, ambulance, and fire services. Moreover, it can also refer to the terrorist attack on September 11, 2001, or 911 in Twin Towers.
3. 555
   Prior to the invention of smartphones, men were forced to request a girl’s landline number. If her phone number begins with 555, they would undoubtedly be disappointed, as there is no such number. This gained popularity over the last few decades due to its use in thousands of films and novels. However, in Thailand, 555 is the same as writing “hahaha” or “lol” in messages. 
4. 365
   Apart from being the standard number of days in a year, 365 has symbolic meaning in various religions. In Judaism, 365 represents the number of negative commandments. Due to its status as the universally recognized number of days in a year, it is used extensively in computer systems, business, and financial products.
5. 108
   Renowned Vedic mathematicians viewed 108 as a representation of the totality of existence. Additionally, this number connects the Sun, Moon, and Earth: the average distance between the Sun and Moon and the Earth is 108 times their diameters. These occurrences have resulted in numerous instances of ritual significance. However, the three-digit number 108 is significant to Chicago Cubs players and baseball fans because:
   • After 108 years, they won the World Series;
   • The foul posts are 108 meters from the first base;
   • The stitch count on a major league baseball is 108; and
   • The World Series cup is made up of silver – which have an atomic number of 108.
6. 143
   The number 143 refers to the number of letters in each of the following words: I (1), love (4), and you (3). According to popular belief, the use of the number 143 to mean “I Love You” dates all the way back to 1915, when Winfield Scott Thompson was the lighthouse keeper at Minots Ledge lighthouse, located off the coast of Cohasset and Scituate, Massachusetts. Thompson’s family could see the lighthouse flashing at night because the sequence was 1-4-3. Thompson’s wife explained to their children that the flash was their father’s way of expressing his love for them. Due to the popularity of the story, the Minots Ledge lighthouse has been dubbed the “I Love You Lighthouse.”

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