# What is the estimated value of 7.94/2.01 to 1 significant figure?

May 29, 2017

#### Answer:

$4$

#### Explanation:

Start by performing the division

$\frac{7.94}{2.01} = 3.950248756$

Now, you're dealing with division, so the answer can only have as many significant figures as the value with the least number of sig figs.

In this case, you have

• $7.94 \to$ three non-zero digits $=$ three sig figs
• $2.01 \to$ two non-zero digits + a zero sandwitched between two non-zero digits $=$ three sig figs

This means that usually, the result of this division should be rounded to three sig figs. However, you must round this value to one significant figure.

Start with the first digit and count two digits, one more than the number of sig figs that you must have for the answer. You should stop at $9$, the second digit

$3.9 \textcolor{red}{\cancel{\textcolor{b l a c k}{50248756}}}$

You now have

$\frac{7.94}{2.01} = 3.9$

Next, compare the second digit to $\textcolor{red}{5}$.

• $\text{second digit} \ge \textcolor{red}{5} \implies$ you add $\textcolor{b l u e}{1}$ to the first digit
• $\text{Second digit} < \textcolor{red}{5} \implies$ you leave the first digit unchanged

In both cases, you must drop the second digit after you make the comparison.

In your case, you have

$9 \ge \textcolor{red}{5}$

so you must add $1$ to the first digit to get

$3 + \textcolor{b l u e}{1} = 4$

The final result will be

$\frac{7.94}{2.01} = 4 \to$ rounded to one significant figure