Write possible three-digit numbers using digits 4, 7, 9 and find the smallest and greatest among them. Repeat…

Question

Write possible three-digit numbers using digits 4, 7, 9 and find the smallest and greatest among them. Repeat for digits 3, 0, 8, 6.

ScanSolve AI Tutor · Accepted Answer

Here are the solutions for questions 8, 9, and 10:

8. Given digits: 4, 7, and 9.

a) Write the possible numbers of three-digits formed from the given digits.

List all permutations of the digits 4, 7, and 9.
The possible three-digit numbers are:
- 479
- 497
- 749
- 794
- 947
- 974 The possible three-digit numbers are $\boxed{\text{479, 497, 749, 794, 947, 974}}$ .
b) What are the smallest and the greatest number among these three-digit numbers?
Identify the smallest number from the list.
The smallest number is formed by arranging the digits in increasing order: 479.
Identify the greatest number from the list.
The greatest number is formed by arranging the digits in decreasing order: 974.
The smallest number is $\boxed{\text{479}}$ and the greatest number is $\boxed{\text{974}}$ .

9. Given digits: 3, 0, 8, and 6.

a) Write the four-digit number by arranging the given digits in decreasing order.
Arrange the digits 3, 0, 8, 6 in decreasing order.
The digits in decreasing order are 8, 6, 3, 0.
The four-digit number is $\boxed{\text{8630}}$ .

b) Write a four-digit number by arranging the given digits in increasing order.
Arrange the digits 3, 0, 8, 6 in increasing order.
The digits in increasing order are 0, 3, 6, 8.
Form a four-digit number.
Since 0 cannot be the first digit, place the smallest non-zero digit first, followed by 0, then the remaining digits in increasing order.
The four-digit number is $\boxed{\text{3068}}$ .

c) Write the smallest and the greatest numbers of four-digit formed by these digits.
Determine the smallest four-digit number.
Using the digits 3, 0, 8, 6, the smallest four-digit number is formed by placing the smallest non-zero digit first, then 0, then the rest in increasing order: 3068.
Determine the greatest four-digit number.
Using the digits 3, 0, 8, 6, the greatest four-digit number is formed by arranging the digits in decreasing order: 8630.
The smallest four-digit number is $\boxed{\text{3068}}$ and the greatest four-digit number is $\boxed{\text{8630}}$ .

10.

a) Find the sum of the greatest and the least numbers of 6 digits.
Identify the greatest 6-digit number.
The greatest 6-digit number is 999,999.
Identify the least 6-digit number.
The least 6-digit number is 100,000.
Calculate their sum.
$999,999 + 100,000 = 1,099,999$
The sum is $\boxed{\text{1,099,999}}$ .

b) Find the difference between the greatest and the least numbers of 7-digits formed by 3, 0, 1, 8, 5, 9, 4.
List the given digits in order
0, 1, 3, 4, 5, 8, 9.
Form the greatest 7-digit number using these digits.
Arrange the digits in decreasing order: 9854310.
Form the least 7-digit number using these digits.
Arrange the digits in increasing order, with the smallest non-zero digit first: 1034589.
Calculate the difference between the greatest and the least numbers.
$9,854,310 - 1,034,589 = 8,819,721$
The difference is $\boxed{\text{8,819,721}}$ .

Write possible three-digit numbers using digits 4, 7, 9 and find the smallest and greatest among them. Repeat for digits 3, 0, 8, 6.

Step-by-step solution

List all permutations of the digits 4, 7, and 9.

Identify the smallest number from the list.

Identify the greatest number from the list.

Arrange the digits 3, 0, 8, 6 in decreasing order.

Arrange the digits 3, 0, 8, 6 in increasing order.

Form a four-digit number.

Determine the smallest four-digit number.

Determine the greatest four-digit number.

Identify the greatest 6-digit number.

Identify the least 6-digit number.

Calculate their sum.

List the given digits in order

Form the greatest 7-digit number using these digits.

Form the least 7-digit number using these digits.

Calculate the difference between the greatest and the least numbers.

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