# How many significant figures are in 92 * 10^3?

## Thanks!

Dec 4, 2016

Two sig figs.

#### Explanation:

For starters, it's worth mentioning that the number given to you is not written in normalized scientific notation because the mantissa is $\ge 10$.

Numbers expressed in normalized scientific notation take the general form

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

Here you need to have

$1 \le \textcolor{b l u e}{m} < 10$

In your case, the correct scientific notation for that number would be

$9.2 \cdot {10}^{4}$

The exponent increased by $1$ unit because the mantissa decreased by an order of $10$.

Now, for numbers expressed in scientific notation, the number of significant figures is always given by the number of significant figures in the mantissa.

In this case, you have

$9.2 \to$ two non-zero digits $=$ two sig figs

Therefore, the number

$9.2 \cdot {10}^{4}$

has two sig figs, $9$ and $2$. The same can be said for

$92 \cdot {10}^{3}$

which also has two sig figs, $9$ and $2$.