1. Face Value vs. Place Value
Every digit in a number has two types of values:
- Face Value: The actual value of the digit itself, regardless of where it sits. It never changes.
- Example: In 5,820, the face value of 8 is simply 8.
- Place Value: The value a digit represents based on its position in the number.
- Formula: Place Value = Face Value* Value of the Place
- Example: In 5,820, the 8 is in the hundreds place, so its place value is 8 * 100 = 800
EXERCISE 4(A)
Question 1.
Fill in the blanks :
(i) In 20 kg, the unit is ………….., which is taken …………. times.
(ii) In 80 m, the unit is …………., which is taken …………. times.
(iii) If a unit cm (centimetre) is taken 5 times, the corresponding quantity is …………….
(iv) If a unit km (kilometre) is taken 24 times, the corresponding quantity is ……………
(v)
Solution :
(i) In 20 kg, the unit is kg, which is taken 20 times.
(ii) In 80 m, the unit is m, which is taken 80 times.
(iii) If a unit cm (centi metre) is taken 5 times, the corresponding quantity is 5 cm.
(iv) If a unit km (kilo metre) is taken 24 times, the corresponding quantity is 24 km.
Question 2.
Fill in the blanks :
(i) In 24,673 ; the place value of 6 is ………..
(ii) In 8,039 ; the place value of 8 is …………..
(iii) In 3,25,648; the local value of 5 is ……………
(iv) In 6,439 ; the local value of 6 is ……….
Solution :
(i) In 24,673; the place value of 6 is 600
- The digit 6 is in the hundreds place.
- 6 * 100 = 600.
(ii) In 8,039; the place value of 8 is 8,000
- The digit 8 is in the thousands place.
- 8 * 1,000 = 8,000.
(iii) In 3,25,648; the local value of 5 is 5,000
- “Local value” is just another name for place value.
- The digit 5 is in the thousands place.
- 5 * 1,000 = 5,000.
(iv) In 6,439; the local value of 6 is 6,000
- The digit 6 is in the thousands place.
- 6 * 1,000 = 6,000.
Question 3.
Find the difference between the place values of 3 and 5 in the number 3945.
Solution :
Step 1: Identify the Place Values
- The digit 3 is in the thousands place.
- Place value of 3 = 3 * 1,000 = 3,000
- The digit 5 is in the ones place.
- Place value of 5 = 5 * 1 = 5
Step 2: Find the Difference
“Difference” in mathematics means we need to subtract the smaller value from the larger value.
Difference = 3,000 – 5
Difference = 2,995
Question 4.
In the number 40562
(i) the local value of 5 = …………..
(ii) the place value of 6 = ………..
(iii) the sum of the place value of 5 and the place value of 6 = …………
Solution :
(i) The local value of 5 = 500
- Since 5 is in the hundreds place, we multiply the digit by 100.
- 5 * 100 = 500
(ii) The place value of 6 = 60
- Since 6 is in the tens place, we multiply the digit by 10.
- 6 * 10 = 60
(iii) The sum of the place value of 5 and the place value of 6 = 560
- “Sum” means we need to add the two values together.
- Sum = 500 + 60 = 560
Question 5.
Read and write the following numbers in words and also in expanded form :
(i) 35,000 = …………
(ii) 76,000 = ……………
(iii) 6,23,000 = ………….
(iv) 40,075 = …………….
(v) 50,004 = ………..
Solution :
(i) 35,000
- In Words: Thirty-five thousand.
- Expanded Form: $(3 \times 10,000) + (5 \times 1,000)$
- Alternative: $30,000 + 5,000$
(ii) 76,000
- In Words: Seventy-six thousand.
- Expanded Form: (7 * 10,000) + (6 * 1,000)
- Alternative: 70,000 + 6,000
(iii) 6,23,000
- In Words: Six lakh twenty-three thousand.
- Expanded Form: (6 * 1,00,000) + (2 *10,000) + (3 * 1,000)
- Alternative: 6,00,000 + 20,000 + 3,000
(iv) 40,075
- In Words: Forty thousand seventy-five.
- Expanded Form: (4 *s 10,000) + (7 * 10) + (5 * 1)
- Alternative: 40,000 + 70 + 5
(v) 50,004
- In Words: Fifty thousand four.
- Expanded Form: (5 * 10,000) + (4 * 1)
- Alternative: 50,000 + 4
Question 6.
Find the difference in the place values of two sevens in the number 8, 72, 574.
Solution :
The first 7 (from the left): This 7 is in the Ten-thousands place.
- Place Value = 7 * 10,000 = 70,000
The second 7: This 7 is in the Tens place.
- Place Value = 7 * 10 = 70
EXERCISE 4(B)
Question 1.
Fill in the blanks :
(i) 999 + 1 = …………
(ii) 10,000 – 1 = …………
(iii) 10 coins – one coin = …………
(iv) ₹ 99 + ₹ 1 = ………..
(v) 10,000 boys – 1 boy = ………..
(vi) 1000 toys – 1 toy = ……….
Solution :
(i) 999 + 1 = 1,000
- Adding 1 to the largest 3-digit number gives the smallest 4-digit number.
- Result: 1,000
(ii) 10,000 – 1 = 9,999
- Subtracting 1 from the smallest 5-digit number gives the largest 4-digit number.
- Result: 9,999
(iii) 10 coins – one coin = 9 coins
- When dealing with units (like coins), the unit stays the same in the answer.
- Result: 9 coins
(iv) ₹ 99 + ₹ 1 = ₹ 100
- Adding 1 to 99 gives 100. Don’t forget the currency symbol!
- Result: ₹ 100
(v) 10,000 boys – 1 boy = 9,999 boys
- Subtracting 1 from 10,000 gives 9,999.
- Result: 9,999 boys
(vi) 1,000 toys – 1 toy = 999 toys
- Subtracting 1 from the smallest 4-digit number gives the largest 3-digit number.
- Result: 999 toys
Question 2.
Would the number of students in your school be a 3-digit number or a 4-digit number or
a 5-digit number?
Solution :
Note : This answer will vary from school to school.
Since, the total strength of M.G.N. Public school is 5410.
Hence, It is a 4-digit number.
Question 3.
Write the smallest number which is just more than 9, 99, 999.
Solution :
Given number = 9, 99, 999
Smallest number which is more than 1 is = 9, 99, 999 + 1 = 10, 00, 000
Question 4.
Starting from the greatest 5-digit number, write the previous five numbers in descending
order.
Solution :
Descending order means arranging numbers from the largest to the smallest.
Result: 99,999 > 99,998 > 99,997 > 99,996 > 99,995 > 99,994
Question 5.
Starting from the smallest 7-digit number, write the next four numbers in ascending
order.
Solution :
Ascending order means arranging numbers from the smallest to the largest.
Result: 10,00,000 < 10,00,001 < 10,00,002 < 10,00,003 < 10,00,004
Question 6.
How many numbers lie between the largest 3-digit number and the smallest 4-digit
number?
Solution :
Largest 3-digit number = 999
Smallest 4-digit number = 1000
Required number = (1000 – 999) = 1
Question 7.
How many 5-digit numbers are there in all?
Largest number of 5-digits = 99999 Largest number of 4-digits = 9999
Required number=99999 – 9999 = 90,000
So, 90,000 numbers are there in all.
