# Question #0a2eb

May 1, 2015

The answer will have 3 sig figs.

Start by writing down the number of sig figs you have for each of the three numbers

$40 , 200.0$ $\to$ 6 sig figs;
$0.000240$ $\to$ 3 sig figs;
$2.778$ $\to$ 4 sig figs.

Now focus on the operations you have to do. Notice that you subtract the third number from the product of the first two.

Start with the multiplication first. When you multiply two numbers, the answer can only be as precise as you least precise number, which means that the product must only have 3 sig figs.

You'll get

$40 , 200.0 \cdot 0.000240 = 9.648 = \textcolor{g r e e n}{9.65}$

Now you subtract a number that has 4 sig figs from one that has 3 sig figs. When doing addition or subtraction, you only take into account the sig figs in the decimal portion.

The number with the fewest sig figs in the decimal portion will determine the number of sig figs for the decimal portion of the answer.

So, you have

$9.65$ $\to$ it has 2 sig figs after the decimal, 6 and 5;
$2.778$ $\to$ it has 3 sig figs after the decimal, 7, 7, and 8.

This means that your answer can only have 2 sig figs after the decimal. Hence

$9.65 - 2.778 = 6.872 = \textcolor{g r e e n}{6.87}$

Here is a video which discusses how to complete calculations keeping sig figs in mind!

Video from: Noel Pauller