Question

Question #1c6ee

Answer 1

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

ADDITION/SUBTRACTION WITH SIG FIGS

`4.ul(85)_0 - 2.ul(34)` `"g"`

`=` `2.ul(51)` `"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 `bb2` 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 `"mL"` has less significant figures than the mass in `"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 "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.

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

For example...

`0.00000ul(5)` has only one significant figure, but it has six decimal places.