What is the rule in multiplying notation in scientific notation?

Answer 1

To multiply two numbers:

• Multiply the mantissae (the bits that go before the 10).
• If this number is between less than 10 then it is the mantissa of the product. If not, divide it by ten and that is the mantissa of the product.
• Add the powers. If the product of the mantissae was less than 10, this is the power for the answer. If not, add one to the sum of powers. This, then is the power for the answer.
• Combine the mantissa and power.

For example:

3.5*103 x 4.3*10-5

3.5*4.3 = 15.05. Since this is not less than 10, divide it by 10 so that the mantissa of the answer is 1.505. Also, remember to add one to the power.

Sum of powers (exponents) = 3 + -5 + 1 (from the mantissa multiplication) = -1

So the final answer is 1.505*10-1

Answer 2

Multiply the mantissas; add the exponents. Finally, normalize. Here is an example:

(5 x 103) x (3 x 102)

Multiplying 5 x 3 (= 15) and adding the exponents, 3 + 2 (= 5), you get:

15 x 105

Normalize this to get:

1.5 x 106