1. In this case, round off to the “tens” place: 3600 + 30 mg.
QUESTION:
The amount of acid present in a sample was measured several times, the average was found to be mg, with an uncertainty of +30 mg. To how many significant figures should the average be reported? A. 2, B. 3, C. 4, D. 5
The location of first nonzero digit of the uncertainty is the location of the last significant digit in the average value.
In this case, round off to the “tens” place: mg.
If uncertainty is not quoted, report it as 3.60x103 mg, since “3600 mg” will be assumed as having only two significant figures.
SCRIPT
The amount of acid present in a sample was measured several time and the average was found to be three thousand six hundred one point two milligrams,
with an uncertainty of plus-or-minus thirty milligrams.
To how many significant figures should the average be reported…two, three, four, or five?
CLICK
The location of the first nonzero digit in the uncertainty is the location of the last significant digit in the average value.
The first nonzero digit in the uncertainty is 3, which is in the tens place.
HIGHLIGHT 3 in 30
Therefore, we must round off the average value to the tens place. In other words, the number in the tens place
HIGHLIGHT 0 in
is the last significant digit.
CALLOUT “Last s.f. in tens place”
This means that there are three significant digits in the average,
The first nonzero digit…three,….six,… and the last significant digit…zero.
HIGHLIGHT 3, 6, and 0 in as the numbers are called out
The correct answer is three.
HIGHLIGHT CHOICE B
To properly report the average, we must round it off to the tens place…
We report the amount of acid as three thousand six hundred plus-or-minus thirty milligrams
BOX mg
If we were to just quote the average value, and decide to leave out the uncertainty, we should write it in scientific notation
…. Three point six zero times ten to the third milligrams. We cannot simply report it as thirty six hundred milligrams. Without the uncertainty, people would assume that the trailing zeros are not significant and that there are only two significant figures.

2. Video ID: 1A-3-1 © 2008, Project VALUE (Video Assessment Library for Undergraduate Education), Department of Physical Sciences Nicholls State University Author: Glenn V. Lo Narrator: Glenn V. Lo Funded by Louisiana Board of Regents Contract No. LA-DL-SELECT-13-07/08