Decimal Place Value Practice Problems up to 10,000

Understanding The Decimal Structure up to 10,000

Complete explanation with examples

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.

Place value chart showing the number 5,916.975 labeled by place: thousands, hundreds, tens, ones, tenths, hundredths, and thousandths, with the decimal point highlighted

Detailed explanation

Practice The Decimal Structure up to 10,000

Test your knowledge with 8 quizzes

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

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

Step-by-step solutions included

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

Choose a 4-digit number whose tens digit is equal to its thousands digit and is less than 2200.

Step-by-Step Solution

To solve this problem, we should carefully examine each of the provided choices, ensuring they meet all necessary criteria:

The number should be a 4-digit number.
The tens digit should be equal to the thousands digit.
The number should be less than 2200.

Let's analyze each option:

1. $2220$ :
Thousands digit = 2, Tens digit = 2 (Condition satisfied that they are equal)
However, the number is greater than 2200.

2. $2002$ :
Thousands digit = 2, Tens digit = 0 (Condition not satisfied as digits are different)
The number itself is less than 2200.

3. $2020$ :
Thousands digit = 2, Tens digit = 2 (Condition satisfied that they are equal)
The number is less than 2200.

4. $2222$ :
Thousands digit = 2, Tens digit = 2 (Condition satisfied that they are equal)
The number is greater than 2200.

From this breakdown, the number that satisfies both necessary conditions is $2020$ .

Thus, the correct answer is $2020$ .

Answer:

$2020$

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:

$4321$

Frequently Asked Questions

Everything you need to know about The Decimal Structure up to 10,000

What is place value in numbers up to 10,000?

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Place value is the value a digit has based on its position in a number. In numbers up to 10,000, the positions from right to left are: ones, tens, hundreds, thousands, and ten thousands. For example, in 34,608, the digit 4 is in the thousands place.

How do you find the value of a digit in a number?

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To find the value of a digit, multiply the digit by its place value. For example, in the number 34,608, the digit 6 is in the hundreds place, so its value is 6 × 100 = 600.

Why can't you remove zeros from the middle of a number?

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Zero acts as a placeholder that maintains the correct position of other digits. Removing a zero changes the entire number. For example, removing the zero from 34,608 would create 3,468, which is completely different.

What are the place value positions in a 5-digit number?

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The five positions from right to left are: 1. Ones place (rightmost) 2. Tens place 3. Hundreds place 4. Thousands place 5. Ten thousands place (leftmost)

How do you break down a number using place value?

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Multiply each digit by its place value, then add all products together. For 34,608: (3×10,000) + (4×1,000) + (6×100) + (0×10) + (8×1) = 30,000 + 4,000 + 600 + 0 + 8 = 34,608.

What's the difference between a digit and its value?

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A digit is the symbol itself (0-9), while its value depends on position. The digit 5 has different values: 5 in ones place = 5, 5 in tens place = 50, 5 in hundreds place = 500.

How do you identify place value in word problems?

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Look for keywords like 'ones,' 'tens,' 'hundreds,' 'thousands,' or 'ten thousands.' Count positions from right to left, or use the comma to separate thousands from hundreds.

What are common mistakes when working with place value?

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Common errors include: confusing digit position with digit value, ignoring zero placeholders, counting positions incorrectly, and forgetting that place values increase by powers of 10 from right to left.

Continue Your Math Journey

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