Numbers up to 4-Digits

Numbers up to 4-Digits
Go back to  'Number Systems'

Have you ever played on an abacus and been fascinated by the beads on the rods! Watch this video to learn all about the place value for 4 digit numbers with the help of an abacus.

 

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Concept Video on Numbers

Here is how numbers are taught in Cuemath. Watch this video to understand how \(10\) Ones make \(1\) Tens, \(10\) Tens make a Hundred and \(10\) Hundreds make a Thousand.

Learn the Why? behind the What!


Introduction to Numbers up to 4-Digits

When we multiply a unit with ten, we get a two digit number.

For example, \(2\) multiplied by \(10\) gives \(20\)

For \(3\) digit numbers it’s \(\begin{align}  10 \times 10 = 100\end{align}\) 

What happens when we multiply a unit digit with \(1000\)?

In such a number, the following place values are covered:

Example of the place value of a 4 digit number 1489

Each of the above place values would have a number, and so you would get a number with 4 digits.

After 999, the first \(4\) digit number begins with \(1000\)

The next \(9000\) numbers are all \(4\) digit numbers, for example, \(3469, 9210, 2583\) etc.

Watch how a 4-digit number is formed by adding 1 to the greatest 3 digit number.


The Big Idea: Numbers up to 4-Digits

A Simple Idea: The Place Value of Numbers

When we covered \(3\)-digit numbers, we saw that the hundreds place value was the units place multiplied by a hundred.

Like you’ve already read, for four digit numbers, a new place value is introduced which is the units place multiplied by \(1000\)

It’s not that hard to visualise actually, take any \(3\) digit and multiply it with \(10\) and there you go! A four digit number!

The place values of the number 3447

How To Decompose 4-digit numbers

We already saw that a \(4\) digit number has the following place valuesThousands, Hundreds, Tens and Units. That is why the multiplier to be used for each of the digits of a \(4\)-digit number are \(1000, 100, 10\) and \(1\) respectively.

Let us examine the number \(1729\)

We can decompose the number as:

\(\begin{align} 1729 = &( 1 \times 1000 ) + \\&( 7 \times 100 ) +\\ &( 2 \times 10 ) + \\&( 9 \times 1 ) \\ &= 1000 + 700 + 20 + 9 \\&= { 1729 } \end{align}\)

Consider the number \(1792, 1279\) and \(2179\) as well.

And notice the values of the same digit in each of these numbers.

\(1729\) - \(2\) has ten's place and a place value of \(20\)
\(1792\) - \(2\) has unit's place and a place value of  \(2\)
\(1279\) - \(2\) has hundred's place and a place value of \(200\)
\(2179\) - \(2\) has thousand's place and a place value of \(2000\)

What this tells us is that the value of a digit is not the only thing that determines its place value in a \(4\)-digit number.

In \(1729\), for instance, the number 1 has a lower value than the number 2 but in terms of place value, 1 has a place value of 1000 (being the 4th digit from right) and 2 has a place value of 10 (being the second digit from right).

You can try some more 4-digit numbers here to see how they can be decomposed into their place values.

place value expansion of a 4 digit number 1234   

Here is an interactive simulation for you to try.

You can generate a \(4\) digit number, enter its expanded form and check if your answers are right.

Commas in 4-digit numbers

In every \(4\)-digit number, the \(4^{th}\) digit on the extreme left represents the thousand’s place.

It is a common convention to apply a comma between the 4th and 3rd digit (thousand’s place and hundred’s place).

So, while the 3-digit number 374 is written simply as 374, the 4-digit number 4539 is written as 4,539

There is no mathematical reason for doing this.

The 4-digit number is longer than a 3-digit or 2-digit number, and the comma only helps to make the number more readable.

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How is it Important?

Fancy 4 digit Number - The Amazing Kaprekar’s Routine

As per this amazing law, there is a magic number 6174 

Let us see how we get it.

These are the steps to be followed.

  1. Arrange any 4-digit number in ascending order of digit and descending order of digits.
  2. You get two distinct 4-digit numbers.
  3. Find out the difference between the two numbers.
  4. Repeat the above 3 steps on this number.
  5. You will reach 6174 in at most 7 iterations.

Doesn’t it sound amazing enough for us to try it out?

Ok, so let’s say I choose the number 2873

The digits arranged in ascending order give us 2378 and 8732

What is 8732 - 2378? The answer is 6354

Again this gives two numbers 3456 and 6543

What is 6543 - 3456? The answer is 3087

After that, 8730 - 0378 = 8325

Finally, 8532 - 2358 = 6174 !!\(\)

Whatever 4 digit number you choose, you will reach 6174 within at most 7 iterations.

Now what happens after 6174 is reached?

It gives the two numbers 7641 and 1467, and the difference between these two numbers is 6174 again, so this sequence keeps getting repeated ad infinitum.

This interesting phenomenon was first observed and formalized by the Indian mathematician Kaprekar.

That is why this sequence is known as the Kaprekar routine.

Fancy 4 digit Number -  Ramanujam Number

An Interesting Story to End

Ramanujam was one the greatest Indian mathematicians.

One day he fell ill, and his friend Hardy came to visit him.

Hardy decided to tease his mathematician friend by saying that the cab I came in had a very uninteresting number plate – 1729

Even though he was not keeping well, Ramanujam’s sharp brain was still working, and he immediately retorted that 1729 was actually a very interesting number, because it was the smallest number which could be expressed as the sum of two cubes in two different and unique ways !!

If this was how sharp he was when unwell, imagine what his brain was capable of when functioning fully.

In honor of this incident, the number 1729 has been referred to as the Hardy–Ramanujam number.

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Solved Examples

Example 1

 

 

Find the sum and difference of the greatest four digit number and the smallest 4 digit number.

Solution:

The greatest four digit number is 9,999

The smallest four digit number is 1,000

Their sum is \( 9,999 + 1,000 =  10,999\)

Their difference is \(9,999 - 1000 =  8,999\)

\(\therefore\) Sum = 10999 & Difference = 8999
Example 2

 

 

Write 9875 in its expanded form.

Solution:

We see that 9 is in the Thousands place, 8 in the Hundreds place, 7 in the Tens place and 5 in the Ones place.

Therefore, the number 9,875 in the expanded form is:

\(9 \times 1000 + 8 \times 100 + 7 \times 10 + 5 \times 1\)
Example 3

 

 

To the sum of 7 thousands 5 hundreds and 2 ones and 2 thousands and 5 ones, subtract 2 thousands 5 hundreds and 6 tens.

Solution:

7 thousands 5 hundreds and 2 ones is 7,502

2 thousands and 5 ones is 2,005

2 thousands 5 hundreds and 6 tens is 2,560

\(7502 + 2,005 - 2,560  = 6,947\)

\(\therefore\) 6947 is the answer.
Example 4

 

 

Fill in the blanks of the given 4-digit addition problem.

find the missing digits so the sum is 7063

Solution:

Let us solve from the units place and fill all the blanks.

  Fill in the blanks of the addition problem whose sum is 7063

\(\therefore\) The missing digits are 9, 2, 1 and 5
Example 5

 

 

Find the sum.

Find the sum of the two 4-digit numbers shown in the abacus.

Solution:

Addend1 = 3,245

Addend2 = 2,413

\(3,245 + 2,413 = 5,658\)

\(\therefore\) The sum is 5658
 
Challenge your math skills
Challenging Questions
  1. How many 4-digit numbers are even numbers?
  2. If 3_12 is a 4-digit number which is a multiple of 3, what all possible digits can take the Hundreds place?
  3. How many 4-digit number can be made with the digits 1, 0, 2 and 3?

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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

 
 
 
 
 
 
 
important notes to remember
Important Notes
  1. There are 4 numbers (any number from 0-9) in a 4-digit number.
  2. The Thousands place in a 4-digit number cannot be 0
  3. The smallest 4 digit number is 1000 and the greatest 4 digit number is 9999
  4. There are 9000 four digit numbers in all.

Frequently Asked Questions (FAQs)

1. How many 4 digit numbers are there?

There are \(9000\) 4-digit numbers in all from \(1000-9999\) including both of them.

2. How do you write 4 digit numbers?

A 4-dight number has 4 numbers (digits) in it.

The right extreme is the Thousands place followed by Hundreds then Tens and finally Units.

We put a comma ", " just after the thousands place.

For example, four thousand three hundred twelve is written as \(4,312\)

3. Which is the smallest 4 digit number?

The smallest \(4\) digit number is \(1,000\) 

When we add 1 to the greatest 3-digit number 999, we get \(1000\) which is the smallest 4-digit number.

  
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