Introduction to Multiplying Decimals by Powers of 10:
The decimals are the number which represents a real number and every decimal place after the decimal point is called a multiple of a negative power of 10. The powers of 10 are 1, 10, 100, 1000, and 10000 etc. these powers can be written using the exponents such as 1 = 100, 10 = 101, 100 = 102, 1000 = 103, etc. Let us see about multiplying decimals by powers of 10 in this article.
For multiplying decimals we need to move only the decimal place.
Multiply the number by the power of 10 like 10, 100, 1000, and etc, we have to move the decimal point right to appropriate places in a real number.
To multiply the number by 10 we have to move right to one place.
To multiply the number by 100 we have to move right to two places.
To multiply the number by 1000 we have to move right to three places.
Example Problems to Multiplying Decimals by Powers of 10
Example 1:
4.78 × 10
Solution:
For multiplying 4.78 by 10 we have to move the decimal place to right for one appropriate place, we get,
4.78 × 10 = 47.8
The solution for multiplying 10 to the decimal 4.78 is 47.8.
Example 2:
3.86 ×100
Solution:
For multiplying 3.86 by 100 we have to move the decimal place to right for two appropriate places, we get,
3.86 × 100 = 386
The solution for multiplying 100 to the decimal 3.86 is 386.
Problems to Practice for Multiplying Decimals by Powers of 10
1. Solve 6.7 × 10
Key: 67
2. Solve 7.8 × 103
Key: 7800
3. Solve 12.47 × 104
Key; 124700
4. Solve 87.2356 × 106
Key: 87235600
The decimals are the number which represents a real number and every decimal place after the decimal point is called a multiple of a negative power of 10. The powers of 10 are 1, 10, 100, 1000, and 10000 etc. these powers can be written using the exponents such as 1 = 100, 10 = 101, 100 = 102, 1000 = 103, etc. Let us see about multiplying decimals by powers of 10 in this article.
Exponents Used for Multiplying Decimals Powers of 10
Definition of Exponents:
The exponent is said to be how many times the number multiplied by it.
For example:
102 = 10 × 10
103 = 10 × 10 × 10
Exponents for Decimals in Powers of 10:
The fractions 1/10, 1/100, 1/1000, 1/10000, and etc is called powers of 10.
The above fractions can be written in terms of decimals.
0.1, 0.01, 0.001, 0.0001, and etc.
The exponent is said to be how many times the number multiplied by it.
For example:
102 = 10 × 10
103 = 10 × 10 × 10
Exponents for Decimals in Powers of 10:
The fractions 1/10, 1/100, 1/1000, 1/10000, and etc is called powers of 10.
The above fractions can be written in terms of decimals.
0.1, 0.01, 0.001, 0.0001, and etc.
Algebra is widely used in day to day activities watch out for my forthcoming posts on solving linear equations by graphing and how to solve linear equations with fractions. I am sure they will be helpful.
Rules for Multiplying Decimals by Powers of 10
For multiplying decimals we need to move only the decimal place.
Multiply the number by the power of 10 like 10, 100, 1000, and etc, we have to move the decimal point right to appropriate places in a real number.
To multiply the number by 10 we have to move right to one place.
To multiply the number by 100 we have to move right to two places.
To multiply the number by 1000 we have to move right to three places.
Example Problems to Multiplying Decimals by Powers of 10
Example 1:
4.78 × 10
Solution:
For multiplying 4.78 by 10 we have to move the decimal place to right for one appropriate place, we get,
4.78 × 10 = 47.8
The solution for multiplying 10 to the decimal 4.78 is 47.8.
Example 2:
3.86 ×100
Solution:
For multiplying 3.86 by 100 we have to move the decimal place to right for two appropriate places, we get,
3.86 × 100 = 386
The solution for multiplying 100 to the decimal 3.86 is 386.
Problems to Practice for Multiplying Decimals by Powers of 10
1. Solve 6.7 × 10
Key: 67
2. Solve 7.8 × 103
Key: 7800
3. Solve 12.47 × 104
Key; 124700
4. Solve 87.2356 × 106
Key: 87235600
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