The Decimal Structure

The decimal structure divides the number by positions accordingly:
ones, tens, hundreds, thousands, and ten thousands.
For example, in the number $65,792$
$2$ ones, $9$ tens, $7$ hundreds, $5$ thousands, and $6$ ten thousands.

Detailed explanation

Start practice

Test yourself on the decimal structure up to 10,000!

A thousands units is represented by the cube below:

Which number is represented by the cubes below?

Practice more now

The Decimal Structure

The decimal structure divides each digit into its group as follows:
ones, tens, hundreds, thousands, ten thousands

Each digit represents a group according to its position. For example, in the number
$34,608$
$8$ is in the ones place
$0$ is in the tens place
$6$ is in the hundreds place
$4$ is in the thousands place
and $3$ is in the ten thousands place.

In other words, we can say that in the number $34,608$ there are:
$8$ ones, $0$ tens, $6$ hundreds, 4 thousands, and $3$ ten thousands.
If we're asked what the value of each digit is, we'll need to multiply the digit by its corresponding place value. That is:
The value of the digit $8$ is $8×1=8$
We multiplied by $1$ because $8$ is in the ones place and $1$ represents ones.
The value of the digit $0$ is $0×10=0$
We multiplied by $10$ because $0$ is in the tens place and $10$ represents tens.
The value of the digit $6$ is $6×100=600$
We multiplied by $100$ because $6$ is in the hundreds place and $100$ represents hundreds.
The value of the digit $4$ is $4×1000=4000$
We multiplied by $1000$ because $4$ is in the thousands place - $1000$ represents thousands.
The value of the digit $3$ is $3×10000=30000$
We multiplied by $10000$ because $3$ is in the ten thousands place and represents ten thousands.

Interesting fact!
If we multiply each digit by its place value and add all the products, we obtain the number itself!
Let's observe –
$8×1+0×10+6×100+4×1000+3×10000=$
$8+600+4000+30000=34,608$

Fascinating Question -
We established that the digit $0$ is in the tens place and its value is $0$ because $10×0=0$
Can we remove it from the number?
The answer is absolutely not!
If we remove the digit $0$ from the number, we'll obtain the number $3,468$ which is a completely different number from our original number.
So why is the $0$ there at all?
The $0$ is holding the place for tens in the original number.
For example, if this number represents a collection of marbles and we want to add another $20$ marbles, the digit $0$ is what kept the place for these $20$ marbles, and after we add them to the collection, we'll obtain the number: $34,628$ .

And now let's practice!
Before you is the number $12495$

Questions:

How many hundreds are in the number?
What is the thousands digit in the number?
What is the value of the digit $1$ ?
What does the digit $9$ represent?
What is the value of the digit $9$ ?

Answers:

The number has $4$ hundreds because the digit $4$ represents hundreds according to its position.
The thousands digit in the number is $2$ .
The value of the digit $1$ is $10,000$
$1$ is in the ten thousands position and to know the value of the digit, we need to multiply it by $10,000$ : $1×10000=10000$
The digit $9$ represents tens because it is in the tens position.
The value of the digit $9$ is $90$ .
We multiply $9×10=90$ because $9$ represents the tens digit and also $10$ .

Another exercise:
Before you is the number $56891$
Questions:

How many ones are in the number?
What is the value of the digit $5$ ?
How many hundreds are in the number?
What does the digit $9$ represent?
How many thousands are in the number?
What does the digit $5$ represent?
What is the value of the digit $8$ ?

Answers:

The number has a ones digit $1$ . $1$ is in the ones place.
The digit $5$ represents ten thousands according to its position, so we need to multiply $5×10000=50000$ and the value of the digit $5$ is $50000$ .
The number has $8$ hundreds since it is in the hundreds place.
The digit $9$ represents the tens according to its position.
The number has $6$ thousands because the digit $6$ is in the thousands place.
The digit $5$ represents ten thousands.
The digit $8$ represents hundreds, so we need to multiply $8$ by $100$ to understand its value.
Let's multiply $8×100=800$
therefore the value of the digit $8$ is $800$ .

Join Over 30,000 Students Excelling in Math!

Endless Practice, Expert Guidance - Elevate Your Math Skills Today

Test your knowledge

Question 1

A thousand units is represented by a cube as shown below:

What number do the cubes below represent?

Question 2

A thousand units is represented by a cube as shown below:

What number is represented by the cubes below?

Question 3

A thousand units is represented by a cube, as shown below:

What number is represented by the cubes below?

Examples with solutions for The Decimal Structure up to 10,000

Exercise #1

A thousands units is represented by the cube below:

Which number is represented by the cubes below?

Step-by-Step Solution

To solve this problem, we need to calculate the number of units represented by the provided cube diagrams.

Let's follow these steps:

Step 1: Identify that each cube represents 1000 units.
Step 2: Look at the given diagram, which shows two 1000-unit cubes placed side by side.
Step 3: Count the number of cubes in this diagram and multiply by 1000 to determine the complete value.

Now, proceeding with the solution:

Step 1: The diagram shows 2 large cubes.
Step 2: Since each cube represents 1000 units, we multiply:

2 \times 1000 = 2000

Therefore, the cubes represent a total of 2000 units.

Thus, the number represented by the cubes is $2000$ .

Answer

$2000$

Exercise #2

A thousand units is represented by a cube as shown below:

What number is represented by the cubes below?

Step-by-Step Solution

To solve this problem, we'll follow these steps:

Step 1: Identify the number of cubes in the representation.
Step 2: Calculate the total number represented by multiplying the number of cubes by 1,000.
Step 3: Match the result with the provided options.

Let's work through these steps:

Step 1: Counting the Cubes
The diagram shows a total of 6 cubes arranged in a 2-layer grid. This can be verified by counting each cube distinctly in the grid shown.

Step 2: Calculate the Total Number
Each cube stands for 1,000 units. Therefore, the total number represented by 6 cubes is:

$6 \times 1,000 = 6,000$

Step 3: Matching the Result
Out of the provided options, this matches with choice number 4: $6,000$ .

Therefore, the number represented by the cubes is $6,000$ .

Answer

$6000$

Exercise #3

Choose a number greater than 1029 whose thousandth digit is 4 less than its units digit.

Step-by-Step Solution

To solve this problem, we will evaluate each choice to find the number where the thousandth digit is 4 less than its units digit, and the entire number is greater than 1029.

Choice 1: $1037$
Thousandth digit is 1, unit digit is 7. The difference is $7 - 1 = 6$ , which does not satisfy the condition (needs to be 4).
Choice 2: $408$
This does not meet the requirement of being greater than 1029.
Choice 3: $1025$
Thousandth digit is 1, unit digit is 5. The difference is $5 - 1 = 4$ , which meets the condition. However, $1025$ is not greater than $1029$ .
Choice 4: $1235$
Thousandth digit is 1, unit digit is 5. The difference is $5 - 1 = 4$ , and the number is greater than $1029$ . This satisfies all conditions.

Therefore, among the given options, the correctly chosen number is $1235$ .

Answer

$1235$

Exercise #4

Which number has the same thousands digit and tens digit?

Step-by-Step Solution

To solve the problem, we will examine each number given and evaluate the digits in the thousands and tens places:

$5105$ : The thousands digit is $5$ and the tens digit is $0$ . They are not the same.
$4140$ : The thousands digit is $4$ and the tens digit is also $4$ . They are the same.
$2333$ : The thousands digit is $2$ and the tens digit is $3$ . They are not the same.
$1121$ : The thousands digit is $1$ and the tens digit is $2$ . They are not the same.

Based on the analysis above, the only number in which the thousands digit is the same as the tens digit is $4140$ .

Therefore, the solution to the problem is $4140$ .

Answer

$4140$

Exercise #5

Which number has a thousands digit of 4 and a hundreds digit that is smaller than its thousands digit?

Step-by-Step Solution

To solve this problem, let's start by considering the criteria:

The thousands digit of the number must be 4, which represents values in the format $4XXX$ .
The hundreds digit must be less than 4, meaning it can be 0, 1, 2, or 3.

Given these constraints, let's consider the provided choices:

$4321$ :
- Thousands digit is 4.
- Hundreds digit is 3 (which is less than 4).
- This choice satisfies both conditions.
$3321$ :
- Thousands digit is 3.
- This does not satisfy the condition of having a thousands digit of 4. Therefore, it's incorrect.
$1200$ :
- Thousands digit is 1.
- This does not satisfy the condition of having a thousands digit of 4. Therefore, it's incorrect.
$4789$ :
- Thousands digit is 4.
- Hundreds digit is 7 (which is not less than 4).
- This choice does not satisfy the condition of having a hundreds digit less than the thousands digit. Therefore, it's incorrect.

Therefore, the number that meets all the conditions is $4321$ .

Answer

$4321$

Start practice