- Average of Two Numbers
- Word Problem With Multiple Decimal Operations: Problem Type 2
- Word Problem With Division of Two Decimals
- Word Problem With Division of a Decimal and a Whole Number
- Decimal Division With Rounding
- Division of a Decimal by a Power of 0.1
- Division of a Decimal by a Power of Ten
- Division of a Decimal by a 2-digit Decimal
- Division of a Decimal by a 1-digit Decimal
- Division of a Decimal by a Whole Number
- Whole Number Division With Decimal Answers
- Word Problem With Multiple Decimal Operations: Problem type 1
- Word Problem With Multiplication of Two Decimals
- Word Problem With Multiplication of Decimal and Whole Number
- Multiplication of Decimals That Have a Product Less Than 0.1
- Multiplication of a Decimal by a Power of 0.1
- Multiplication of a Decimal by a Power of Ten
- Decimal Multiplication: Problem Type 2
- Decimal Multiplication: Problem Type 1
- Multiplication of a Decimal by a Whole Number
- Decimal Multiplication
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Exponents of Decimals
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Exponents and Decimals: Products Less Than 0.1
In numbers such as (0.44)3, the decimal 0.44 is the base and 3 is the exponent. Such numbers are repeated products of the base.
Rules
We see that raising a decimal base to an exponent is same as multiplying the decimal by itself as many times as the exponent.
We treat the decimals as whole numbers by ignoring the decimal points and multiply.
After counting the total number of decimal places in these numbers, we put a decimal point after that many places from the right in the answer.
Here we are considering exponents of decimals where the products are less than 0.1.
Evaluate (0.31)2
Solution
Step 1:
Consider (0.31)2; Here, we are raising the decimal base 0.31 to a power of 2.
(0.31)2 = 0.31 × 0.31 = 0.0961
Step 2:
We see that squaring a decimal base is in fact same as multiplying the decimal by itself. We treat the decimals as whole numbers by ignoring the decimal points and multiply.
31 × 31 = 961
Step 3:
After counting the total number of decimal places which is four in these numbers, we put a decimal point after four places from the right in the answer.
So, 0.31 × 0.31 = 0.0961
We see that that the product is less than 0.1
Evaluate (0.46)3
Solution
Step 1:
Consider (0.46)3; Here, we are raising the decimal base 0.46 to a power of 3.
(0.46)3 = 0.46 × 0.46 × 0.46
Step 2:
We see that cubing a decimal base is in fact same as multiplying the decimal by itself three times. We treat the decimals as whole numbers by ignoring the decimal points and multiply.
46 × 46 × 46 = 97336
Step 3:
After counting the total number of decimal places which is six in these numbers, we put a decimal point after six places from the right in the answer.
So, 0.46 × 0.46 × 0.46 = 0.097336
We see that that the product is less than 0.1