Given digits are 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. Write the smallest 9-digit number and the greatest 8-digit…

Question

Given digits are 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. Write the smallest 9-digit number and the greatest 8-digit number using these digits without repetition. Find the difference between them.

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Here are the solutions for the questions:

c) 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 are the given digits.

(i) Write the smallest number of 9-digits formed from the given digits.

Identify the smallest 9 distinct digits from the given set.
The smallest 9 digits are $0, 1, 2, 3, 4, 5, 6, 7, 8$.
Arrange these digits to form the smallest 9-digit number.
To form the smallest number, the smallest non-zero digit must be in the highest place value. So, 1 comes first, followed by 0, then the remaining digits in ascending order.
The smallest 9-digit number is 102,345,678.
$\boxed{102,345,678}$
(ii) Write the greatest number of 8-digits formed from the given digits.
Identify the greatest 8 distinct digits from the given set.
The greatest 8 digits are $9, 8, 7, 6, 5, 4, 3, 2$.
Arrange these digits to form the greatest 8-digit number.
To form the greatest number, arrange the digits in descending order.
The greatest 8-digit number is 98,765,432.
$\boxed{98,765,432}$
(iii) Find the difference of the numbers formed in (i) and (ii).
Subtract the number from (ii) from the number from (i).
$102,345,678 - 98,765,432$
Perform the subtraction.
$102,345,678 - 98,765,432 = 3,580,246$
The difference is $\boxed{3,580,246}$ .

a) If $x$ is at tens place and $y$ is at ones place, write the number formed by these digits.
The number formed is the sum of the place values of the digits.
$10x + y$
The number is $\boxed{10x + y}$ .

b) If $a$ is at hundreds place, $b$ is at tens place and $c$ is at ones place, write the number formed by these digits.
The number formed is the sum of the place values of the digits.
$100a + 10b + c$
The number is $\boxed{100a + 10b + c}$ .

c) If $p$ is at thousands place, $q$ is at hundreds place, $r$ is at tens place and $s$ is at ones place, write the number formed by these digits.
The number formed is the sum of the place values of the digits.
$1000p + 100q + 10r + s$
The number is $\boxed{1000p + 100q + 10r + s}$ .

Creative section - B
The mobile number of Sunayana's father is 9851086083.

(i) What is the place value of 5 in the number?
Identify the position of the digit 5 in the number 9851086083.
The digit 5 is in the hundred millions place.
Calculate the place value.
Place value of $5 = 5 \times 100,000,000 = 500,000,000$ .
The place value of 5 is $\boxed{500,000,000}$ .

(ii) What is the face value of 5 in the number?
The face value of a digit is the digit itself.
The face value of 5 is $\boxed{5}$ .

(iii) Find the difference between the place value and face values of 5 in the number.
Use the place value and face value found in (i) and (ii).
Place value = 500,000,000
Face value = 5
Calculate the difference.
$500,000,000 - 5 = 499,999,995$
The difference is $\boxed{499,999,995}$ .

Given digits are 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. Write the smallest 9-digit number and the greatest 8-digit number using these digits without repetition. Find the difference between them.

Step-by-step solution

Identify the smallest 9 distinct digits from the given set.

Arrange these digits to form the smallest 9-digit number.

Identify the greatest 8 distinct digits from the given set.

Arrange these digits to form the greatest 8-digit number.

Subtract the number from (ii) from the number from (i).

Perform the subtraction.

Identify the position of the digit 5 in the number 9851086083.

Calculate the place value.

Use the place value and face value found in (i) and (ii).

Calculate the difference.

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