Place Value

Easy

1. Problem:

In the number 6,732, which digit is in the hundreds place? What is its value?

Solution:

The digit in the hundreds place is 3. Its value is 300.

2. Problem:

Write the number that has 8 in the tens place and 5 in the ones place.

Solution:

The number is 80 + 5 = 85.

3. Problem:

Which number has 4 in the thousands place, 9 in the hundreds place, and 2 in the tens place?

Solution:

The number is 4,920.

4. Problem:

What is the value of the digit 7 in the number 9,764?

Solution:

The value of the digit 7 in the number 9,764 is 70.

5. Problem:

In the number 3,218, which digit is in the tens place? What is its value?

Solution:

The digit in the tens place is 1. Its value is 10.

Medium

1. Problem:

Write the smallest 4-digit number using each of the digits 3, 6, 8, and 1 exactly once.

Solution:

The smallest 4-digit number using these digits is 1,368.

2. Problem:

Find the sum of the place values of the digit 7 in the number 7,896.

Solution:

The place value of 7 in the thousands place is 7,000 and the place value of 7 in the ones place is 7. So, the sum of their place values is 7,000 + 7 = 7,007.

3. Problem:

Which digit has the greatest value in the number 4,953?

Solution:

The digit with the greatest value in the number 4,953 is 9, as it is in the thousands place.

4. Problem:

If you subtract the number 2,567 from 6,789, what is the value of the digit in the thousands place of the difference?

Solution:

The difference is 4,222. The value of the digit in the thousands place is 4.

5. Problem:

How many hundreds are there in the number 8,765?

Solution:

There are 87 hundreds in the number 8,765.

Hard

1. Problem:

The difference between the greatest 4-digit number and the smallest 4-digit number formed using the digits 3, 5, 7, and 9 is subtracted from the sum of all the possible 4-digit numbers formed using these digits. What is the result?

Solution:

The greatest 4-digit number formed using these digits is 9753 and the smallest is 3579. Their difference is 9753 - 3579 = 6174.

The sum of all the possible 4-digit numbers formed using these digits can be calculated by finding the sum of the digits in each place value position and multiplying each sum by the appropriate place value. This sum is (3+5+7+9) × (1111 + 1110 + 1100 + 1000) = 24 × 4321 = 103,704.

Therefore, the result is 103,704 - 6174 = 97,530.

2. Problem:

Rohan wrote a 5-digit number. The digit in the ten thousands place is 7. The digit in the thousands place is one-fifth of the digit in the ten thousands place. The digit in the hundreds place is three times the digit in the ten thousands place. The digit in the tens place is half the digit in the thousands place. The digit in the ones place is the sum of all the other digits. What is the number?

Solution:

Let's break down the information:

- Digit in ten thousands place = 7

- Digit in thousands place = 7/5 = 1.4, but since digits must be whole numbers, it's 1.

- Digit in hundreds place = 3 * 7 = 21

- Digit in tens place = 1/2 * 1 = 0.5, but since digits must be whole numbers, it's 0.

- Digit in ones place = 7 + 1 + 21 + 0 = 29

So, the number is 71,290.

3. Problem:

A number is made by repeating a certain digit four times. If the number formed is the largest 4-digit number, what is the digit?

Solution:

The largest 4-digit number is 9999. Since this number is formed by repeating a digit four times, the digit is 9.

4. Problem:

A 5-digit number is formed using the digits 1, 3, 5, 7, and 9 without repetition. What is the difference between the greatest and the smallest numbers that can be formed using these digits?

Solution:

The greatest 5-digit number formed using these digits is 9,7531, and the smallest is 1,3579. Their difference is 9,7531 - 1,3579 = 8,3952.

5. Problem:

In the number 8,765,432,109, which digit has the highest place value? What is its value?

Solution:

The digit with the highest place value is 8, which is in the billions place. Its value is 8 billion.