- Multiply and Divide Decimals
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- Decimal Multiplication
- Multiplication of a Decimal by a Whole Number
- Decimal Multiplication: Problem Type 1
- Decimal Multiplication: Problem Type 2
- Multiplication of a Decimal by a Power of Ten
- Multiplication of a Decimal by a Power of 0.1
- Multiplication of Decimals That Have a Product Less Than 0.1
- Word Problem With Multiplication of Decimal and Whole Number
- Word Problem With Multiplication of Two Decimals
- Word Problem With Multiple Decimal Operations: Problem type 1
- Whole Number Division With Decimal Answers
- Division of a Decimal by a Whole Number
- Division of a Decimal by a 1-digit Decimal
- Division of a Decimal by a 2-digit Decimal
- Division of a Decimal by a Power of Ten
- Division of a Decimal by a Power of 0.1
- Decimal Division With Rounding
- Word Problem With Division of a Decimal and a Whole Number
- Word Problem With Division of Two Decimals
- Word Problem With Multiple Decimal Operations: Problem Type 2
- Average of Two Numbers
- Exponents of Decimals
- Squaring Decimal Bases: Products Greater Than 0.1
- Exponents and Decimals: Products Less Than 0.1
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Multiplication of a Decimal by a Power of 0.1
A power of 0.1 is 10 raised to a negative whole number as follows
0.1 = 10−1; (0.1)2 = 10−2 = 0.01; (0.1)3 = 10−3 = 0.001 and so on.
A power of a 0.1 has one preceded by zeros with as many decimal places as the power of 0.1.
For example, (0.1)2 is equal to 0.01 which has as many decimal places (2) as the power of 0.1 which is 2.
Rules
The product of a decimal multiplied by a power of 0.1 can be found by a short cut. When a decimal number is multiplied by a power of 0.1, the product is found by moving the decimal point to the left that many places as the power of 0.1
Multiply 27.43 × (0.1)2
Solution
27.43 × (0.1)2
Here the power of 0.1 is two and there are two decimal places in its value 0.01. So the decimal point in 27.43 is moved 2 places to the left and the product is obtained as shown below.
27.43 × (0.1)2 = 27.43 × 0.01 = 0.2743
Multiply 16.26 × (0.1)3
Solution
16.26 × (0.1)3
Here the power of 0.1 is three and the number of decimal places in its value 0.001 is 3. So the decimal point in 16.26 is moved 3 places to the left and the product is obtained as shown below. A zero is added before 1 to make three places shift to the left.
16.26 × (0.1)3 = 16.26 × 0.001 = 0.01626