Multiplication concept is a more interesting concept than addition and subtraction for the students. Do you wish to learn the Multiplication of a decimal by 10, 100, 1000? Then this is the right place where you will get complete knowledge on Step by Step procedure for Multiplication of Decimals by 10, 100, 1000. 5th Grade Math Students have to know about what is meant by Multiplication of a decimal by 10, 100, 1000 and how to multiply by 10, 100, 1000 with a brief explanation, Some example problems, and so on.
Also, Read: Properties of Multiplication of Decimal Numbers
What does multiplying a decimal by 10 100 or 1000 mean?
When a decimal number is multiplied by 10, 100, 1000, the digits within the product are the same as within the decimal number but the decimal point within the product is shifted to the right by as many places as there are zeros over one.
How to Multiply a Decimal by 10, 100, and 1000?
The below are the steps to follow for the multiplication of decimals by 10, 100, 1000 as:
Step 1: On Multiplying a decimal by 10, we shift the decimal point to the right by one place.
Step 2: While, you Multiply a decimal number by 100, we have to shift the decimal point to the right by two places.
Step 3: When we Multiply a decimal number by 1000, the product is the number with the decimal point of 3 places to its right.
Multiplying Decimals by 10 100 and 1000 Examples
Problem 1.
Find the product of 118.62 x 10
Solution:
As given in the question, the values are 118.62, and 10.
Now, we will multiply the value 118.62 with 10 then we get the product value.
So, the values are,
118.62 x 10 = 1186.2
After multiplication, the decimal point is shifted from one place to the right.
Therefore, the product value is 1186.2
Problem 2.
What is the value of 36.74 x 100?
Solution:
Given the values,
Now, we have to multiply the value 36.74 with 100.
Multiply a number with 100, we get the product value with 2 decimal places of right.
Then the value is,
36.74 x 100 = 3674.
Thus, the value of the given numbers is 3674.
Problem 3.
Multiply the following given values :
(i) 25.401 x 10
(ii) 45.766 x 100
(iii) 83.71 x 10
(iv) 0.0677 x 1000
Solution:
As given in the question,
(i) 25.401 x 10
Multiply the value by 10, shift the decimal point to the right by one place.
Now, we have to multiply 25.40 with 10, then the value is
25.401 x 10 = 254.01
Thus, the multiplication value is 254.01.
(ii) 45.766 x 100
When we multiply a decimal value by 100, shift the decimal point to the right by two places.
Now, find the multiplication value,
45.766 x 100 = 4576.6
After multiplication, the final value is 4576.6
(iii) 83.71 x 10
while we multiply a value by 10, shift the decimal point to the right by one place.
So, the values are,
83.71 x 10 = 837.1
Therefore, the final product value of given numbers is 837.1
(iv) 0.0677 x 1000
Now, we have to find the final value.
Multiply the decimal value by 1000, then shifted the decimal point to the right by three places.
So, the values are,
0.0677 x 1000 = 67.7
Hence, the final multiplication value is 67.7
Problem 4.
Multiply the given value by 1000 and write the final product value. The given value is 82.3
Solution:
As given in the question, the value is 82.3
Now, multiply the value by 1000 to get the product value.
When we have to multiply a value by 1000, then the decimal point is shifted to the right by three places.
82.3 x 1000 = 82,300
Therefore, the final product value of the given numbers is 82300.
FAQ’s on Multiplication of Decimal Numbers by 10 100 and 1000
1. How will you multiply decimals by 10 100 and 1000?
A simple trick to help you remember how many places the digits need to move at the zeros in 10, 100, and 1000. Consider an example, there are 2 zeros in 100, so we need to move the digits 2 places to the left to multiply by 100.
2. What is the rule for multiplying a decimal value by 100?
For multiplying a decimal value by 100, moves every 2 digits to its left.
3. What happens when we multiply by 10?
When you multiply a decimal number by 10, then the value of every digit becomes ten times bigger, so each digit moves one place to the left.
4. Why can we write zeros after a number when we multiply by 10, 100, or 1000?
The working rule of multiplication of a decimal by 10, 100, or 1000 is, when the multiplier is 10, 100, or 1000, we have to move the decimal point to the right by as many places as a number of zeros after 1 within the multiplier.