# Numbers up to 3-Digits

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 1 Introduction to Numbers up to 3-Digits 2 The Big Idea: Numbers up to 3-Digits 3 How is it Important? 4 Common Mistakes 5 Know More about 3 Digit numbers and its Operations 6 Solved Examples 7 Important Notes 8 Practice Questions 9 Thinking Out of the Box! 10 Play with Numbers 11 Maths Olympiad Sample Papers 12 Frequently Asked Questions (FAQs)

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## Introduction to Numbers up to 3-Digits

We have already seen what 2 digit numbers are.

The first 2-digit number (smallest 2-digit number) is 10, and the last one is 99, so there are only 90 two digit numbers possible.

What would three digit numbers then be?

In the same way, we can define three digit numbers as those which have digits in three place values – Units, Tens and Hundreds.

These are also formed by combining any three single digit numbers.

Look at the simulation below to see how a 3-digit number is formed from the largest 2-digit number.

## The Big Idea: Numbers up to 3-Digits

### A Simple Idea: The Place Value of Numbers

When the number of guests was in single digits, you bought ice cream cups (units).

But when the requirement increased to a number more than 10, then you ordered the ice cream in a combination of tubs (equivalent to 10 ice cream cups) and cups.

Now let us take this a step further, and go to the next higher power of 10, which is 100.

So what would happen if your school was going on a picnic and you were put in charge of ordering ice creams for all 243 participants, including teachers and students?

You would first ask the shopkeeper if he has any bigger cases, and he would inform you that they do have a large carton which is equal to ten tubs. Since you already know that each tub is equivalent to ten cups, therefore

\begin{align} \text { Carton } & =\! 10 \text { tubs } \\ & =\! \mathrm { tub } \! +\! \mathrm { tub }\! +\! \mathrm { tub } \! +\! \ldots10 \text{times} \\ & =\! 10 \mathrm { cups } \! +\! 10 \mathrm { cups } \! +\! \ldots .10\!\text { times } \\ & =\! 100 \mathrm { cups } \end{align}

Now, for 243 participants, here are how the 3 digits are placed in respective values:

\begin{align}& { 2 \text { in hundreds place } } \\& { 4 \text { in tens place } } \\& { 3 \text { in units place } } \\& { 243 = ( 2 \times 100 ) + ( 4 \times 10 ) + ( 3 \times 1 ) } \\& {\quad \;\;\; = 2 \text { cartons } + 4 \text { tubs } + 3 \text { cups } } \end{align}

So you would order 2 cartons for 200 cups, 4 tubs for 40 cups and 3 cups.

### Assigning Place Values

Every three digit number’s value can be found by seeing which place value each digit has.

Let us consider the same number 243 as we saw in the ice cream example.

We need to write the number as the sum of the products of each digit and its place value.

The first digit at the rightmost position is said to be in Units place, so they would be multiplied by 1

Hence the product is

\begin{align} ( 3 \times 1 ) = 3 \end{align}

Then the second number is 4, and because it is in Tens place, it is multiplied by 10

The value, therefore, is

\begin{align} ( 4 \times 10 ) = 40 \end{align}

The third number 2 is in Hundreds place.

So 2 is multiplied by 100 and its value is

\begin{align} ( 2 \times 100 ) = 200 \end{align}

Therefore,

the number =  \begin{align} 200 + 40 + 3 = 243 \end{align}

### Decomposing a 3-digit Number

In a three digit number, there are three place values used – hundred’s, ten’s and units.

The ice cream example above showed us how the place values of a 3 digit number can help to determine what value of 10 each digit number has to be multiplied by.

What if the same digits 2, 4 and 3 were combined in a different order to get the number 324?

The digit 4 would move from ten’s place to unit’s place.

The digit 3 would move from unit’s place to hundred’s place, and the digit 2 would move from hundred’s place to ten’s place.

The three numbers to be added would be

\begin{align}( 3 \times 100 ) + ( 2 \times 10 ) + ( 4 \times 1 )\end{align}

\begin{align}= 300 + 20 + 4 \ = 324\end{align}

If you see the digits 3 and 4 in the above two numbers, you will see that the first number 243 saw their values as 3 and 40 respectively, whereas the second number 324 saw their values as 300, 20 and 4 respectively.

So the value of a particular digit in a three digit number does not depend only upon its numerical value but also on the place value it has.

The abacus below has 4 green counters representing 4 hundreds (400)

3 blue counters representing 3 tens (30)

and 2 yellow counters representing 2 ones (2)

The number is 400 +30 +2 = 432

## How is it Important?

### The Significance of Zero in 3-digit numbers

While learning numbers up to 2 digits, we saw that the smallest 2-digit number is 10

Similarly, the smallest 3-digit number is 100 and the greatest three digit number is 999

Any combination of digits can be used to form 3-digit numbers, with or without repetition.

With repetition, the following are some examples of 3-digit numbers - 225, 599, 303, 222 etc.

The number zero does not make any contribution to a 3-digit number if it is placed in a position where there are no other non-zero numbers to its left.

So how is 303 different from 033 or even 003?

In 033, the values are

\begin{align} (0 \times 100 ) + ( 3 \times 10 ) + ( 3 \times 1 )\end{align}
\begin{align} = 0 + 30 + 3= 33 \end{align}

which means that the number actually becomes a 2 digit number 33, or in the case of 003, it becomes a single digit number 3

In these two examples, the digits zero do not contribute any value to the number, so the numbers can as well be expressed as 33 or 3

## Common Mistakes or Misconceptions

Misconception 1: Children make mistakes identifying numbers when there is a zero in the unit’s place or tens place.

Example: When asked to read 130 and 103, students may not recognise and read these two numbers correctly.
It helps to get them to model the numbers through Base-10 blocks.
That way they can see the ten’s and one’s place value explicitly.

Misconception 2When asked to write “one hundred twenty three," students often write 100 first and then attach 23 to it thus ending up with the number “10023”
Fact: This misconception arises due to a superficial understanding of place values.
Using the base-10 blocks or abacus show children that a digit has different values based on its position.

Misconception 3: Sometimes when asked to form the smallest 3-digit number given three digits that include zero, children place the zero in the left-most position.
Fact: This is incorrect.
Zero cannot be in the hundreds place if we are creating a 3-digit number.
e.g. The smallest 3-digit number using all digits of 5, 0 and 7 is 507 and not 057

## Know More about 3 Digit Numbers and its Operation

• Get students to skip count by 10 and 100 to build fluency with 3-digit numbers.
First, start at 100
Then start from any random 3-digit number like 136

• Help children spot the pattern that when skip counting by 10, the digit in the ones place value does not change.
Similarly, when skip counting by 100, the digits in the ones place and tens place does not change

• Use a 100-square grid to build fluency.
Let students spot the pattern that moving one row up or down is the same as skip counting by 10. Moving columns (left or right) increases or decreases numbers by 1

• Often children are given three digits and asked to find the largest and smallest number three-digit number using all digits.
The trick here is to arrange all digits in descending order to find the largest number.
To find the smallest number, arrange all digits in ascending order
.
But keep in mind that if zero is one of the digits, it cannot be placed to the left.
E.g. Using the digits 7, 3 and 6, the largest number is 763 (digits in descending order) and the smallest number is 367 (digits in ascending order).
Using the digits 4, 0 and 8, the largest number will be 840 but the smallest 3-digit number is 408 and not 048.

Help your child score higher with Cuemath’s proprietary FREE Diagnostic Test. Get access to detailed reports, customised learning plans and a FREE counselling session. Attempt the test now.

## Solved Examples

 Example 1

Choose the smallest three digit number from the given options.

a. 101
b. 100
c. 010
d. 111

Solution:

Thus, option c is a 2-digit number.

Now we are left with options a, b and d.

Arranging them in ascending order, we see that 100 is the first 3-digit number.

 $$\therefore$$ Smallest three digit number is 100
 Example 2

How many 3-digit numbers are there?

Solution:

For a 3-digit number, the hundreds place cannot be 0

It can be any other digit from 1-9

Hence, there can be 9 digits in the hundreds place.

In the tens place and the ones place, there can be any digit from 0-9

Thus, there are $$9 \times 10 \times 10 = 900$$ three digit numbers in all.

 $$\therefore$$ There are 900 three digit numbers in all.
 Example 3

If the green counters represent hundreds, the blue counters represent tens and the yellow counters represent ones, what is the number represented in the following abacus?

Solution:

There are 5 green counters, so there are 5 hundreds.

There are 7 blue counters, so there are 7 tens.

There are 2 yellow counters which represents 2 ones.

Therefore, the number is 500 + 70 + 2 = 572

 $$\therefore$$ The abacus represents the number 572
 Example 4

By how much is 4 hundreds and 5 tens greater than 4 hundreds, 4 tens and 9 ones?

Solution:

4 hundreds and 5 tens is 400 + 50  = 450

4 hundreds, 4 tens and 9 ones is 400 + 40 + 9 = 449

450 - 449 = 1

 $$\therefore$$ 450 is greater than 449 by 1
 Example 5

To which hundreds is the number 7 hundreds, 8 tens and 3 ones closer to?

Solution:

7 hundreds, 8 tens and 3 ones is 700 + 80 + 3 = 783

It is closer to 8 hundreds.

 7 hundreds, 8 tens and 3 ones is closer to 800
 Example 6

A teacher wrote a puzzle on the board.

"Add the smallest 2 digit number to the smallest 1 digit number. Subtract the sum from one less than the greatest 3 digit number".

Anu said that the answer was 987

Rahul said that it was 997

Who was right?

Solution:

Smallest 2 digit number = 10

Smallest 1 digit number = 1

Sum of these two numbers = 11

One less than the greatest 3 digit number is 998

Subtracting 11 from 998, we get

$$998 - 11 = 987$$

 $$\therefore$$ Anu's answer is correct.

Important Notes
1. 100 is the smallest 3-digit number and 999 is the greatest 3 digit number.
3. 10 tens make 1 hundred which is the smallest 3 digit number and 10 hundreds make a thousand which is the smallest 4 digit number.

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## Practice Questions

Here are a few activities for you to practice. Select/Type your answer and click the "Check Answer" button to see the result.

Think Tank
1.  I am a 3-digit even number.

My ones place is double my tens place and my hundreds place is half my tens place. Who am i?
2. How many 3-digit numbers are even?

## Play with Numbers

Here is an interesting place value game we play at Cuemath!

Form the number with the counters and check your answer if it is correct!

IMO (International Maths Olympiad) is a competitive exam in Mathematics conducted annually for school students. It encourages children to develop their math solving skills from a competition perspective.

## 1. How many 3 digit numbers are there?

There are a total of 900 three digit numbers.

These include the smallest 3 digit number - 100 to the largest 3 digit number - 999

## 2. Which is the largest 3 digit number?

The largest 3 digit number is 999

Adding 1 more to it will make it a 4 digit number.

## 3. What is the sum of the three largest 3 digit numbers?

The three largest 3 digit numbers are 997, 998, 999

Their sum is 2994

$$997 +998 +999 = 2994$$

More Important Topics
Numbers
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