# Multiplier by 10, 100, 1000, 10000 | How do you Multiply by Multiples of 10 100 1000 and 10000?

In maths, multiplication is denoted by ‘×’ to find the product of two or more values. The first number is called multiplicand and the second number is called the multiplier. The multiplier will increase the value of the number. The increase in a number depends on the multiplier. It is the repeated addition of the number with respect to one another.

Multiplication is one of the fundamental topics in maths. Here we will learn about the multiplier with different numbers. Get the examples on Multiplier by 10, 100, 1000, 10000 with step by step explanation. Also, the students can know in detail about the properties of multiplication.

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## How to Multiply by 10, 100, 1000, 10000?

In this concept, we multiply the multiplicand by the non-zero digit of the multiplier. Then we add the same number of zero to the extreme right of the product as the multiplier.
We can understand this concept by following the below steps.
Step 1: We count the zeros first.
Step 2: We multiply the non-zero numbers.
Step 3: We place the same number of zero to the extreme right of the product.

### Properties of Multiplication

1. Commutative Property
2. Associative Property
3. Distributive Property
4. Identity Property
5. Zero Property

1. Commutative Property: The commutative property of multiplication, if A and B are any two integers then,
a × b = b × a
Example: 2 × 3 = 3 × 2

2. Associative Property: As per the associative property of multiplication, if a, b, c are three integers then,
a × (b × c) = (a × b) × c
Example: 2 × (3 × 5) = (2 × 3) × 5

3. Distributive Property: According to the distributive property of multiplication, if a, b and c are three integers then,
a × (b + c) = (a × b) + (a × c)
Example: 2 × (3 + 5) = (2 × 3) + (2 × 5)

4. Identity Property: As per the identity property of multiplication, if we multiply any integer by 1, then its value remains unchanged, such that,
a × 1 = 1 × a
Example: 2 × 1 = 1 × 2

5. Zero Property: Zero property of multiplication states that any number multiplied by 0 is always 0.
a × 0 = 0
Example: 5 × 0 = 0

### Examples on Multiplying by Multiples of 10 100 1000 and 10000

Let us see some examples of multiply by 10, 100, 1000, 10000 with explanations.

Example 1.
Find the product of the following
i. 12 × 10
ii. 24 × 20
Solution:
i. 12 × 10
Follow the steps to find the product of the given numbers.
Step 1: We count the zeros first.
There is one zero
Step 2: We multiply the non-zero numbers.
12 × 1 = 12
Step 3: We place the same number of zero to the extreme right of the product.
Now add zero to the extreme right.
Thus it becomes 120.
So, 12 × 10 = 120
ii. 24 × 20
Follow the steps to find the product of the given numbers.
Step 1: We count the zeros first.
There is one zero
Step 2: We multiply the non-zero numbers.
24 × 2 = 48
Step 3: We place the same number of zero to the extreme right of the product.
Now add zero to the extreme right.
Thus it becomes 480.
So, 24 × 20 = 480

Example 2.
Find the product of the following
i. 34 × 100
ii. 12 × 200
Solution:
i. 34 × 100
Step 1: We count the zeros first.
There are two zeros.
Step 2: We multiply the non-zero numbers.
34 × 1 = 34
Step 3: We place the same number of zero to the extreme right of the product.
Now add zero to the extreme right.
Thus it becomes 3400.
So, 34 × 100 = 3400
ii. 12 × 200
Step 1: We count the zeros first.
There are two zeros.
Step 2: We multiply the non-zero numbers.
12 × 2 = 24
Step 3: We place the same number of zero to the extreme right of the product.
Now add zero to the extreme right.
Thus it becomes 2400.
So, 12 × 200 = 2400

Example 3.
Find the product of the following
i. 2 × 1000
ii. 5 × 3000
Solution:
i. 2 × 1000
Step 1: We count the zeros first.
There are three zeros.
Step 2: We multiply the non-zero numbers.
2 × 1 = 2
Step 3: We place the same number of zero to the extreme right of the product.
Now add zero to the extreme right.
Thus it becomes 2000.
So, 2 × 1000 = 2000
ii. 5 × 3000
Step 1: We count the zeros first.
There are three zeros.
Step 2: We multiply the non-zero numbers.
5 × 3 = 15
Step 3: We place the same number of zero to the extreme right of the product.
Now add zero to the extreme right.
Thus it becomes 15000.
So, 5 × 3000 = 15000

Example 4.
Find the product of the following
i. 6 × 10000
ii. 15 × 50000
Solution:
i. 6 × 10000
Step 1: We count the zeros first.
There are four zeros.
Step 2: We multiply the non-zero numbers.
6 × 1 = 6
Step 3: We place the same number of zero to the extreme right of the product.
Now add zero to the extreme right.
Thus it becomes 60000.
So, 6 × 10000 = 60000
ii. 15 × 50000
Step 1: We count the zeros first.
There are four zeros.
Step 2: We multiply the non-zero numbers.
15 × 5 = 75
Step 3: We place the same number of zero to the extreme right of the product.
Now add zero to the extreme right.
Thus it becomes 750000.
So, 15 × 50000 = 750000

Example 5.
Jai earns $24 per hour. What are his earnings for 10 hours? Solution: Given that, Jai earns$24 per hour.
We have to find his income for 10 hours.
24 × 10 = $240 Thus Jai earns$240 for 10 hours.

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