The Decimal Structure up to 10,000 - Examples, Exercises and Solutions

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:

Therefore, the cubes represent a total of 2000 units.

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

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 $6,000$.

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 $1235$.

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 $4140$.

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:

1. $4321$:
   - Thousands digit is 4.
   - Hundreds digit is 3 (which is less than 4).
   - This choice satisfies both conditions.
2. $3321$:
   - Thousands digit is 3.
   - This does not satisfy the condition of having a thousands digit of 4. Therefore, it's incorrect.
3. $1200$:
   - Thousands digit is 1.
   - This does not satisfy the condition of having a thousands digit of 4. Therefore, it's incorrect.
4. $4789$:
   - 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 $4321$.

To solve this problem, choose a number from the options where the unit digit is three times the tens digit:

• Option 1: $8642$
  Tens digit: $4$, Units digit: $2$.
  Units is not three times tens. Reject.
• Option 2: $5846$
  Tens digit: $4$, Units digit: $6$.
  Units is not three times tens. Reject.
• Option 3: $3257$
  Tens digit: $5$, Units digit: $7$.
  Units is not three times tens. Reject.
• Option 4: $1426$
  Tens digit: $2$, Units digit: $6$.
  Six is three times two. Accept.

Thus, the correct number in question is $1426$.

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 $2020$.