What is 4.56 x 103 times 3.1 x 106 in correct scientific notation and proper significant figures?

Answer 1

I assume you mean 10³ and 10⁶.

Then multiplying 4.56 X 3.1 = 14.136

And multiplying the powers of ten gives 10⁹, since multiplying exponential numbers with the same base is accomplished by adding the exponents.

So 14.136 X 10⁹ is a result, but to write in proper scientific notation, the decimal part of the number needs to be between 1 and 9.9999. The value is maintained by dividing the decimal number by 10 (moving the decimal point) while multiplying the exponent part of the number by 10 (adding 1 to the power)

The result is 1.4136 X 10¹⁰.

Finally, round to the correct number of sig figs. The rule for multiplying requires that the result should have the same number of sig figs as in the number being multiplied with the least number of sig figs. In this case, 3.1 has 2 sig figs, whereas 4.56 has 3 sig figs. So the result should have 2 sig figs.

Therefore, round to 1.4 X 10¹⁰.