Place value –
Place value is the value of digit, depending on its place and we can relate place with ‘place value’.
For example, In the numeral 36578, Find the place values.
first write the given numerals in place-value chart, we get.
Crores | Ten Lakhs |
Lakhs | Ten Thousands |
Thousands | Hundreds | Tens | Ones |
---|---|---|---|---|---|---|---|
3 | 6 | 5 | 7 | 8 |
Face Value and Place Value difference:
The image below explains the difference between face and place value.
Shortcut to find out place value of a digit:
Find out the place value for 86791.
Step 1: First, Write the digit for the one you want to find the place value.
(Here in this case let’s find the place value for digit “7”)
Step 2: Now, Count the number of digits which come after the digit for the one you want to find the value.
(In 86791, after “7” we have two digits “91”)
Example 1:
Find the face value and place value of the underlined digit in the number given below.
968352
Solution:
Example 2:
Find the place value of “K” in the number given below.
K25937
Given that K = 2x and x = 4.
Solution:
Example 3:
Find the place value of “K” in the number given below.
58K32
Given that K is a number which is less than 10 and exactly divisible by both 2 and 3.
Solution:
Types of numbers: There are various types of numbers. They are natural numbers, whole numbers, integers, even numbers, odd numbers, prime numbers, composite numbers, etc.
Rules for divisibility:
Sample:
Example 1:
Divide 300 by 7, list out dividend, divisor, quotient, remainder and write division algorithm.
Solution:
Division algorithm for the above division is.
⇒ 300 = 42 x 7 + 6
Example 2:
Divide 400 by 8, list out dividend, divisor, quotient, remainder and write division algorithm.
Solution:
Division algorithm for the above division is
⇒ 400 = 50×8 + 0
Example 3:
Divide 750 by 16, list out dividend, divisor, quotient, remainder and write division algorithm.
Solution:
Division algorithm for the above division is
⇒ 750 = 46×16 + 14
Prove [latex](a+b)^2 = a^2 + b^2 +2ab[/latex] in geomentry:
Hence proved [latex](a+b)^{2}[/latex] = [latex]a^{2}[/latex] + [latex]b^{2}[/latex] + 2ab
Prove [latex](a+b)^2 = a^2 + b^2 +2ab[/latex] in Algebra:
[latex](a+b)^{2}[/latex] = (a+b)*(a+b)
= (a*a + a*b) + (b*a + b*b)
= ([latex]a^{2}[/latex] + ab) + (ba + [latex]b^{2}[/latex])
= [latex]a^{2}[/latex] + 2ab + [latex]b^{2}[/latex]
Hence proved [latex](a+b)^{2}[/latex] = [latex]a^{2}[/latex] + [latex]b^{2}[/latex] + 2ab
Example 1:
Expand the term [latex](3x + 4y)^{2}[/latex] using the identity [latex](a+b)^{2}[/latex] = [latex]a^{2}[/latex] + [latex]b^{2}[/latex] + 2ab
Solution:
Example 2:
Expand the term [latex](\sqrt{2}x + 4y)^{2}[/latex] using the identity [latex](a+b)^{2}[/latex] = [latex]a^{2}[/latex] + [latex]b^{2}[/latex] + 2ab
Solution:
Example 3:
Expand the term [latex](x + \frac{1}{x})^{2}[/latex] using the identity [latex](a+b)^{2}[/latex] = [latex]a^{2}[/latex] + [latex]b^{2}[/latex] + 2ab
Solution:
Step: 2
Because Step 1 and Step 2 are true, so it can be concluded that the statement is true.
2. Face value of 7 and Place value of 9 from the given digit 38745962 is?
Solution:
3. On dividing 132 by a certain number, 12 as a quotient and 0 as a remainder is obtained. Find the divisor?
Solution:
4. What will be the units digit in the product (234 × 256 × 457 × 952)?
Solution:
5. Test which of the following is not a prime number
Solution:
6. Does the number 23679715 divisible by 11?
Solution: