Solutions - Exercise 1 (A) | Number System | Class 6 Mathematics | Selina Concise Mathematics - Middle School.
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📂 Chapter 1 - Exercise 1 (A).
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# Let's Discuss :
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There are ten digits in our numbers system (0, 1, 2, 3, ....., 9) and every number is made by using one or more digits with or without repetition.
E.g. 8, 18, 361, 4863, etc.
# Place Value of a Digit in a Number :
The place value (local value) of a digit depends upon the position it occupies in the number.
Example :
Consider a two digit number i.e. 69.
69 in Expanded form can be written as (60 + 9)
Or
[ (6 x 10) + (9 x 1) ]
Here,
- Place value of 6 is Tens.
- Place value of 9 is Ones.
📌 NOTE : The place value of '0' is always 0 regardless of the place it occupies in the given number.
Similarly,
In a Six digit Number i.e. 123456.
Expanded form = 1,00,000 + 20,000 + 3000 + 400 + 50 + 6
Or
[ (1 x 1,00,000) + (2 x 10,000) + (3 x 1000) + (4 x 100) + (5 x 10) + (6 x 1) ]
Here,
- Place value of 1 is Lakhs.
- Place value of 2 is Ten Thousands.
- Place value of 3 is Thousands.
- Place value of 4 is Hundreds.
- Place value of 5 is Tens.
- Place value of 6 is Ones.
-- Place Value Table --
| Lakhs (L) | Ten Thousands (TTh) | Thousands (Th) | Hundreds (H) | Tens (T) | Ones (o) |
|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | 6 |
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# Face Value of a Digit in a Number :
The face value of a digit does not depend on the position of the digit in a number and is equal to the value of the digit itself.
Example :
Consider a two digit number i.e. 69.
Here,
- The face value of 6 is 6 itself.
- The face value of 9 is 9 itself.
Similarly,
In a six digit number i.e. 123456.
Here,
- The face value of 1 is 1 itself.
- The face value of 2 is 2 itself.
- The face value of 3 is 3 itself.
- The face value of 4 is 4 itself.
- The face value of 5 is 5 itself.
- The face value of 6 is 6 itself.
| Digits | Place Value (Local Value) | Face Value |
|---|---|---|
| 1 | 1 x 1,00,000 = 1,00,000 | 1 |
| 2 | 2 x 10,000 = 20,000 | 2 |
| 3 | 3 x 1000 = 3000 | 3 |
| 4 | 4 x 100 = 400 | 4 |
| 5 | 5 x 10 = 50 | 5 |
| 6 | 6 x 1 = 6 | 6 |
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-- EXERCISE - 1 (A) --
Q1. Fill in the blanks :
(i) In 24673, the place value of 6 is 600 (6 Hundreds)
(ii) In 8039, the place value of 8 is 8000 (8 Thousands)
(iii) In 325648, the local value of 2 is 20,000 (2 Ten Thousands)
(iv) In 6439, the local value of 3 is 30 ( 3 Tens)
Q2. Find the difference between the place values of 3 and 5 in the number 3945.
Solution :
Place value of 3 is thousands (3 x 1000 = 3000)
Place value of 5 is ones (5 x 1 = 5)
Difference = 3000 - 5 = 2995
Ans. 2995
Q3. In the number 40562,
(i) the local value of 5 = 500 (5 Hundreds)
(ii) the face value of 6 = 60 ( 6 Tens)
(iii) the sum of the place value of 5 and the face value of 6 = 560
Q4. Find the difference in the place values of the two sevens in the number 8,72,574.
Solution :
Place value of first 7 from right side is Tens (7 x 10 = 70)
Place value of second 7 from right side is Ten Thousands (7 x 10,000 = 70,000)
Difference = 70,000 - 70 = 69,930
Ans. 69,930
Q5. Find the difference between the face value of 9 and the face value of 4 in the number 324798.
Solution :
Face value of 9 is nine (09)
Face value of 4 is four (04)
Difference = 09 - 04 = 05
Ans. 05
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