To calculate the result of 0.4662 times 67, we follow the basic principles of multiplication, taking into account that one of the factors is a decimal number. Multiplying a decimal number by an integer involves the same process as multiplying two integers, with the additional step of correctly placing the decimal point in the product.
Multiplication Process
The multiplication of 0.4662 by 67 can be performed as follows: first, ignore the decimal point in 0.4662 and multiply 4662 by 67. This step is essentially treating 0.4662 as 4662, which is the number without the decimal point. The calculation is then 4662 * 67.
Calculation Steps
The multiplication of 4662 by 67 is calculated as follows:
- First, multiply 4662 by 60: 4662 * 60 = 279720
- Then, multiply 4662 by 7: 4662 * 7 = 32634
- Add the two products together: 279720 + 32634 = 312354
This result, 312354, is the product of 4662 and 67. However, since we initially ignored the decimal point in 0.4662, we must now adjust the decimal point in 312354 to reflect the original decimal factor.
Adjusting the Decimal Point
Given that 0.4662 has four digits to the right of the decimal point, the product 312354 must be adjusted by placing the decimal point four places to the left, resulting in 31.2354.
| Operation | Result |
|---|---|
| Multiplication of 4662 by 67 | 312354 |
| Adjustment for decimal point | 31.2354 |
The accurate result of 0.4662 times 67 is 31.2354. This calculation demonstrates the importance of correctly handling decimal numbers in arithmetic operations to ensure precise outcomes.
What is the rule for placing the decimal point when multiplying a decimal by an integer?
+The rule is to multiply as if the decimal were an integer, then place the decimal point in the product so that it has the same number of decimal places as the decimal factor had. In the case of 0.4662 times 67, since 0.4662 has four decimal places, the product 312354 is adjusted to have the decimal point four places to the left, resulting in 31.2354.
Understanding and applying this rule ensures that calculations involving decimal numbers and integers are performed accurately and efficiently.
