Question

Express in scientific notation. Make sure your answer has the same number of significant figures as the starting value. (6.0 x 104) (3.1 x 10-1) = _____
a1.86x10 4
b 1.9x10 4
c 1.8x10 4

Answer 1

Since both numbers contain 2 significant digits the answer will contain 2 significant digits:

Answer: b 1.9 x 104

Answer 2

Answer : The correct option is, (b) $1.9\times 10^4$

Explanation :

Significant figures : The figures in a number which express the value -the magnitude of a quantity to a specific degree of accuracy is known as significant digits.

Scientific notation : It is the representation of expressing the numbers that are too big or too small and are represented in the decimal form with one digit before the decimal point times 10 raise to the power.

For example :

5000 is written as $5.0\times 10^3$

889.9 is written as $8.899\times 10^{-2}$

In this examples, 5000 and 889.9 are written in the standard notation and $5.0\times 10^3$  and $8.899\times 10^{-2}$  are written in the scientific notation.

If the decimal is shifting to right side, the power of 10 is negative and if the decimal is shifting to left side, the power of 10 is positive.

The rule apply for the multiplication and division is :

The least number of significant figures in any number of the problem determines the number of significant figures in the answer.

As we are given :

$(6.0\times 10^4)\times (3.1\times 10^{-1})$

$\Rightarrow 1.9\times 10^4$

In the given expression, $(6.0\times 10^4)$ has 2 significant figures and $(1.3\times 10^{-1})$ has 2 significant figures. From this we conclude that 2 is the least significant figures in this problem. So, the answer should be in 2 significant figures.

Thus, the answer will be $1.9\times 10^4$