What is Place Value?
Place value is the position value of each digit in a number.
Consider the number 242, for example.
The place value of the digit 2 at ones place is 2 × 1 = 2 or 2 ones.
The place value of the digit 4 at tens place is 4 × 10 = 40 or 4 tens.
Similarly, the place value of the digit 2 at the hundredths place is 2 × 100 = 200 or 2 hundredths.
Use of Place Value in Multiplication
For the multiplication of two numbers, the place value of each digit in the numbers is considered, and individual multiplication is carried out.
Later, the results of individual multiplications are added together to get the final result.
Let’s use place value to calculate 15 × 5. We will draw a place value chart to carry out the multiplication.
Tens | Ones | X | Tens | Ones |
|---|---|---|---|---|
1 | 5 | 5 |
\(\Rightarrow\)( 5 × 5) + (5 × 10)
= 25 + 50
= 75
It can be shown in column form as follows:
In the above multiplication,
(5 × 5) = 25 (Multiply 5 and 5)
5 × 10 = 50 (Multiply 5 and 10)
10 × 10
25 + 50 = 75 (Add)
Similar steps will be taken for multiplication with numbers having digits in the hundreds or thousands place value.
Using Place Value to Multiply by 10, 100, or 1000
It is a simple application of multiplication with place value where we simplify the multiplication by expressing the numbers to be multiplied in terms of tens, hundreds, or thousands and later on carry out the standard multiplication.
Consider the following multiplication:
7 × 10 (here, 10 can be written as 1 tens)
= 7 × 1 tens
= 7 tens
= 70
Consider another example:
9 × 200 (here, 200 can be written as 2 hundreds)
9 × 2 hundreds
= 18 hundreds
= 1800
Rules for Multiplication with 10, 100, or 1000
The following are the basic rules to follow while multiplying any non-zero numbers by 10, 100, or 1000.
- When multiplying any non-zero number by 10, just add a zero at the end of that number.
For example:
5 × 10 = 50 - When multiplying any non-zero number by 100, just add two zeros at the end of that number.For example:
5 × 100 = 500 - When multiplying any non-zero numbers by 1000, just add three zeros at the end of that number.
For example:
2 × 1000 = 2000
Facts about Multiplication
- If a number is multiplied by 0, the result is 0.
10 × 0 = 0
0 × 0 = 0
112 × 0 = 0
- If a non-zero number is multiplied by 10, 100, or 1000, respectively, the product will be the number itself with 1, 2, or 3 zeros, respectively, at the end.
- In multiplication, the number being multiplied is called the multiplicand and the number by which it is being multiplied is called the multiplier.
The result of the multiplication is called the product.
10 × 7 = 70
10 → Multiplicand
7 → Multiplier
70 → Product
- If a number is multiplied by 1, the product will be the number itself.
Solved Examples
Example 1:
Find the product for each of the following multiplications.
(i) 7 × 3 ________
(ii) 7 × 30 _________
(iii) 7 × 300 _________
(iv) 7 × 3000 __________
Solution:
(i) 7 × 3 = 21
(ii) 7 × 3 tens
= 21 tens
= 210
(iii) 7 × 3 hundreds
= 21 hundreds
= 2100
(iv) 7 × 3 thousands
= 21 thousands
= 21000
Example 2:
Find the missing factor.
(i) ______× 100 = 600
(ii) 5 ×______ = 50
(iii) 9 × 20 = ______
Solution:
(i) We know that,
(Multiplicand) × (Multiplier) = Product
Since the multiplicand is multiplied by 100 giving the product 600, it means the multiplicand is equal to 6.
(ii) We know that,
(Multiplicand) × (Multiplier) = Product
5 × _____= 50
Using the multiplication rule of a number with 10, we observe that the multiplier is 10.
(iii) 9 × 20
= 9 × 2 tens,
= 18 tens
= 180
Example 3:
A shopkeeper has two varieties of glitter pens. 10 packs of one variety with 5 pens in each pack and 20 packs of the second variety with 7 pens in each pack. So, how many glitter pens does the shopkeeper have in total?
Solution:
First variety → 10 × 5 = 50 (Multiply)
Second variety → 20 × 7 = 140 (Multiply)
50 + 140
= 190 [Add]
Hence, the shopkeeper has 190 glitter pens in total.
Example 4:
Liam has 2 boxes with 20 caramel candies in each box. He also has 5 boxes with 30 chocolate candies in each box.
How many candies does Liam have in total?
Solution:
Liam has 2 boxes with 20 caramel candies in each box.
Total number of caramel candies,
= 2 × 20
= 40 [Multiply]
Liam has a total of 40 caramel candies.
Liam also has 5 boxes with 30 coffee candies in each box.
Total number of chocolate candies,
= 5 × 30
= 150 [Multiply]
He has 150 chocolate candies in total.
So, the total number of candies Liam has
= 40 + 150
= 190 [Add]
Hence, Liam has a total of 190 candies.
According to the zero property of multiplication, if a number is multiplied by zero, the product will be 0.
In math, every digit in a number has a certain place value. It can be defined as the value of a digit in a number based on its position in the number. Each place has a value of 10 times the place to its right.
If any non-zero number is multiplied by 10, 100, or 1000, the product will be the number itself, ending with 1, 2, or 3 zeros, respectively.
For example:
3 × 10 = 30
3 × 100 = 300
3 × 1000 = 3000
In the above example, it is observed that the product of 3 multiplied by 10, 100, or 1000 is the number 3, ending with 1, 2, or 3 zeros at the end, that is, 30, 300, or 3000.