Question

Answer this question with sig figs: 100 + 10.1 + 0.01=?

I DONT GET SIG FIGS. i got the answer 100 because apparently you need to round to the lowest number fo sig figs and the lowest number is 1 so its should be 100 because 100 has one sig fig although the answer is 110.11? yes? because i feel like thats wrong SOMEONE HELP ME

Answer 1

It is just `100`.

Explanation:

When adding numbers, you use the least precise value. The least precise value is 100, where the most precise figure you know is the hundred's place. Therefore, after we add the numbers, we will round to the nearest hundred. Note that this works differently with multiplication.

`100+10.1+.01=110.11`
Rounding to the nearest hundred:
`100`

Here's why we do it this way. If you write down `100`, we know that there's a `1` in the hundred's place because you wrote it there. However, we don't know anything about the ten's place, unit's place, etc. All we know is that the number is about `100`. Because we don't know what the other digits really are (we just know that the number is roughly equal to `100`), we only consider the hundred's place and less precise numbers.

The idea is that any measurement can only be so precise. If you have a ruler and measure something to be `3.0` centimeters, you know that it isn't really exactly `3.0` centimeters. but that the number is about `3.0`. If you say that it is exactly `3` centimeters, you are claiming to know more about the measurement than you actually do, and this will skew your results.