Final answer:
To multiply 20.5 by 36.482, perform the multiplication as with whole numbers, then place the decimal point in the product so that the total number of decimal places equals the sum from both original numbers. Round the final product to three significant figures, since that is the least number of significant figures in the given numbers.
Step-by-step explanation:
To solve the multiplication problem 20.5×36.482, first, let's understand how multiplication with decimals works. If we know that 9.86 multiplied by something equals 36.482, we could use this to simplify our calculation. However, since we don't know the exact multiplier for 9.86 to get 36.482, we need to carry out the long multiplication. As we perform this calculation, we should keep track of the decimal places to ensure our final answer is correct.
To multiply 20.5 by 36.482, align the numbers by the decimal point and perform the multiplication as if they were whole numbers. Once you've calculated the product of the whole numbers, count the total number of decimal places in the factors (20.5 has one decimal place, and 36.482 has three), which means our final answer should have four decimal places. Therefore, the calculation should look like this:
- Multiply 205 by 36482 as if they are whole numbers.
- Add the four decimal places back into the result by moving the decimal point four places to the left.
To ensure we respect significant figures in our answer, the final step is to round our answer to the correct number of significant figures if necessary. Given the numbers involved, our answer should be rounded off to the lowest number of significant figures present in the question. Since 20.5 has three significant figures and 36.482 has five, our result should be rounded to three significant figures after the multiplication is performed.
The complete step-by-step calculation without a calculator would be lengthy and is often better done with the aid of a calculator, especially for complex decimal multiplication like this. If we carried out the multiplication using a calculator, we would directly get the product, to which we then apply our rounding rules for significant figures as the final step.