What is the number of significant figures in each of the following measured quantities? (a) 902.

What is the number of significant figures in each of the...

Key Concepts

Significant Figures

Significant figures are used to indicate the precision of a measured quantity. They include all the digits that are known reliably plus one final digit that is estimated. This concept is crucial in scientific measurements as it communicates how accurate a measurement is, and it helps in maintaining consistency during calculations by reflecting the precision of the measured values.

Counting Rules for Significant Figures

There are several rules for counting significant figures that apply regardless of the measurement's units or context. For example, any non-zero digit is always significant, zeros between significant digits are significant, leading zeros (zeros before the first nonzero digit) are not significant, and trailing zeros in a number containing a decimal point are significant. Understanding these rules is essential for correctly determining and utilizing significant figures in scientific work.

Scientific Notation and Significant Figures

Scientific notation is a method of writing numbers that allows one to clearly define the number of significant figures. In scientific notation, the coefficient (the number written before the exponent) is used to represent the significant figures of the measurement. This notation simplifies both the process of identifying significant digits and performing calculations, especially when dealing with very large or very small numbers.

Transcript

00:01 Talking about significant figures and just to kind of get a refresher as to what significant figures are or significant digits.

00:07 Either way, you can say it.

00:09 They are each of the digits of a number that are used to express it to a certain point of accuracy.

00:14 And there are certain rules that when it comes to expressing significant figures, depending on the number you have.

00:20 So there are rules involved, but they're not extremely complicated.

00:24 You'll eventually start noticing a trend.

00:26 And the more practice you do with these, the better you're going to get at determining significant.

00:30 Figures especially when you are doing math problems and you have to adjust the number of significant figures as needed so i have a couple examples here we have six and we want to determine the number of significant figures for each of these the first one we have 902 .5 and so for this particular problem or for this particular number the number of significant figures that we are going to have is we're going to have four so here we do have a zero in between the nine and and the two.

01:01 So that is allowing the zero to be counted.

01:03 And we do have a number after the decimal.

01:07 We don't have a zero after it or anything other than that.

01:11 And so for this particular reason, that's why we count all four of these digits.

01:16 So this number, 902 .5, does have four significant figures.

01:21 The next one is 0 .00003 meters.

01:26 Or you can also write it as 3 times 10 to negative 6.

01:30 Meters.

01:31 And so for this one of the rules is if you have there are if there are zeros after your decimal point and followed by a number, those zeros do not count as significant figures.

01:42 And so the only significant figure is going to be our three here.

01:46 So in this number, there's only going to be one significant digit, which is our three.

01:51 Our third example is 0 .0096.

01:55 So kind of like our second example.

01:58 The we there are zeros followed...

Please give Ace some feedback