Introduction
- Multiplication is the process of repeated addition. Multiplying by powers of 10 involves multiplying a number by 10, 100, 1000, and so on.
- Understanding this concept helps us quickly shift digits to the left, creating larger numbers.
- When you multiply a number by 10,100,1000 and so on each digit shifts place to the left.
Multiplying by 10:
For Example:-45×10=450
Explanation: The digit 4 moves to the hundreds place, and 5 moves to the tens place.
Add the zero to the number which we are multiplying.
Multiplying by 100:
For Example:-37×100=3700
Explanation: The digit 3 moves to the thousands place, and 7 moves to the hundreds place.
When you multiply a number by 100, each digit shifts two places to the left.
Multiplying by 1000:
For Example:-62×1000=62000
Explanation: The digit 6 moves to the ten -thousands place, and 2 moves to the thousands place.
When you multiply a number by 1000, each digit shifts three places to the left.
Multiplying by 10000:
For Example:-86×10000=860000
Explanation: When you multiply a number by 1000, each digit shifts four places to the left.
Original Number |
Power of 10 | Result |
45 | 10 |
450 |
37 |
100 | 3700 |
62 | 1000 |
62000 |
86 |
10000 |
860000 |
Multiplying by Power of 10 :-
Multiplying a whole number by a power of 10 can be expressed using exponents.
The general form is:
aX 10n
Where :
- a is whole number
- 10 is base
- n is exponent
Here, 105 = 10x10x10x10x10
Example : 86 x 101
This is equivalent to 86 x 10 =860. Here, n=1
86x 102
This is equivalent to 86 x 100 =8600. Here, n=2.
86 x 103
This is equivalent to 86 x 1000 =86000. Here, n=3
86 x 104
This is equivalent to 86 x 10000 =860000. Here, n=4
In general, when you multiply a whole number by a power 10,you need to add zeros as per the exponent in the power 10.
Example : 64 x 10,000.
In this expression:
- 64 is whole number.
- 10 is the base.
- 4 is the exponent representing the number of zeros to add.
Now, let’s do this multiplication :
64 x 10000 = 64 x 104 =640000
The exponent 4 in the power of 10 indicates that there are four zeros to add to the original number 64 , resulting in 640,000.
Example :85 x 10,0000.
In this expression:
- 85 is whole number.
- 10 is the base.
- 5 is the exponent representing the number of zeros to add.
Now, let’s do this multiplication :
85 x 100000 = 85 x 105 =8500000
The exponent 5 in the power of 10 indicates that there are five zeros to add to the original number 85 , resulting in 850,0000.
Exercise
Find the product.
- 64 x10
- 64 x 100
- 64 x 1000
- 64 x 10000
Find the value of exponent and write the product.
- 49 x 102
- 49 x 103
- 49 x 104
- 49 x 105
Find the missing values.
- 349 x 103 = _________
- 567 x 105 = __________
- 38 x______ =380000
- 50 x 105 =________
- 71 x 106 =____________
- 57 x ______= 5700
- 10 x 1000 =_____
- 21 x 100 x 10000= ______
- Find the product of 90 x 1,00,000.
- Find the product of 20 x 10
- Find the product of 8 x 1000.
- Write the following numbers in the power format.
For example : 60000 = 6 x 104
- 6,50,000
- 87,000
- 1,000
- 9,0,00,000.
- 600000
- 10000
- 8400000
- Rahul watch 10 videos daily. How many videos he will watch 90 days?
- Sameer orders 100 boxes of dryfruits, each of cost Rs. 1000 .What will be the total cost?
- How many zeros will be there in the product of 99 x 100000.
- How many zeros will be there in the product of 40 x 10
- How many zeros will be there in the product of 57x 105
- How many zeros will be there in the product of 100 x 104
Match the following.