×

Sig figs

So in my chemistry class, and I've been wondering,"aren't sig figs a little inaccurate"

$$\frac{2 mi}{3hr}=0.\overline{6} mph$$

Which by sig figs

$$\frac{2 mi}{3hr}=0.7 mph=\frac{7}{10} mph$$

Or even more absurdly

$$35J\cdot 1 s=40J\cdot s$$

$$\therefore 35=40$$

I do see the reason why we change numbers like $$\dfrac{1.3739}{1729.36}$$ into decimal form.

But why can't we leave the pretty things in fractional form like $$\frac{2}{3}$$

Note by Trevor Arashiro
2 years ago

Sort by:

Yes, I am also posting this in protest to my last chem test where. All 4 points I got off were because of sig figs. 😕 · 2 years ago

Here's an example to illustrate why we use sig figs:

Suppose you were to find the speed of your average walking in miles per hour, and you got that in $$2$$ miles, you walked $$3$$ hours.

Thus, you have to calculate $$2\text{ mi}/3\text{ hr}$$

This is where you are wondering why not just leave it in a pretty fraction form. This is also the part where science diverges from theoretical mathematics.

In theory, the $$2$$ miles and $$3$$ hours are exact. Thus, it is actually $$2.000\ldots$$ miles and $$3.000\ldots$$ hours.

However, in the problem, we are given only one sig fig: $$2$$ miles and $$3$$ hours.

Therefore the actual exact value could range from anything like $$1.55\text{ mi}/3.4\text{ hr}=0.46\text{ mph}$$ to $$2.45\text{ mi}/2.5\text{hr}=0.98\text{ mph}$$

Thus, saying that the miles per hour is $$\dfrac{2}{3}=0.666\ldots$$ is incorrect because the value is too precise, and does not take into regard the actual possible values.

This is why the answer is $$2\text{ mi}/3\text{ hr}=0.7\text{ mph}$$ with only one sig fig.

An important thing to note here is that $$0.7\ne \dfrac{7}{10}$$. Usually, when we use a fraction not as a division but as a numeral, the value is exact [citation needed], which is not the case here. · 2 years ago