# Question 1c6ee

Aug 23, 2016

I would evaluate what is in implicit parentheses first. That means the numerator should be subtracted first, and then the result should be divided.

$4. {\underline{85}}_{0} - 2. \underline{34}$ $\text{g}$

$=$ $2. \underline{51}$ $\text{g}$

When you add/subtract, you keep the number of decimal places given by the number with the greatest uncertainty. $2.34$ only has two decimal places, so you keep $\boldsymbol{2}$ decimal places.

The subscript $0$ indicates the decimal place to drop, because $2.34$ has one less decimal place and is therefore more uncertain by one decimal place.

MULTIPLICATION/DIVISION WITH SIG FIGS

Now, when you multiply/divide, you retain the least number of significant figures to account for the fact that your volume in $\text{mL}$ has less significant figures than the mass in $\text{g}$ with the greatest uncertainty.

$1.3$ only has two significant figures, so you keep two significant figures to get:

${2.5}_{1} / 1.3 \text{g"/"mL}$

= 1.9308 => color(blue)("1.9 g/mL"#

The subscript $1$ indicates the significant figure to drop, since $1.3$ has one less significant figure than $2.51$ and is therefore more uncertain by one significant figure.

NOTE: You aren't necessarily less uncertain with more decimal places.

For example...

$0.00000 \underline{5}$ has only one significant figure, but it has six decimal places.