# 5) How many significant figures are in the number 2.34xx10^12?

Jul 11, 2016

$3$

#### Explanation:

The thing to remember about numbers expressed in scientific notation is that you can determine how many significant figures they have by examining the mantissa.

For a number written using normalized scientific notation, you have

$\textcolor{w h i t e}{a a} \textcolor{b l u e}{m} \times {10}^{\textcolor{red}{n} \textcolor{w h i t e}{a} \stackrel{\textcolor{w h i t e}{a a a a a a}}{\leftarrow}} \textcolor{w h i t e}{a \textcolor{b l a c k}{\text{the")acolor(red)("exponent}} a a}$
$\textcolor{w h i t e}{\frac{a}{a} \textcolor{b l a c k}{\uparrow} a a a a}$
$\textcolor{w h i t e}{\textcolor{b l a c k}{\text{the")acolor(blue)("mantissa}} a}$

For normalized scientific notation, you must have

$1 \le | m | < 10$

Now, the number of sig figs for a number expressed in scientific notation is always given by the number of sig figs in the mantissa.

In this case, the mantissa is

$m = 2.34$

As you know from the rules we have for determining how many sig figs we have in a number, any non-zero digit is significant. In this case, the mantissa contains three non-zero digits, $2$, $2$, and $4$, which means that it has three sig figs.

Therefore, the number

$2.34 \cdot {10}^{12} \to$ three sig figs

will also have three sig figs, all present in the mantissa.