Indicate the number of significant figures in each of the following measured quantities: (a) 62.

Indicate the number of significant figures in each of the...

Key Concepts

Significant Figures

Significant figures represent the digits in a number that contribute to its precision. They include all the known digits, helping to express the limit of measurement accuracy, and are crucial for reporting and comparing measured quantities in science and engineering.

Measurement Uncertainty

Measurement uncertainty is inherent in any measured quantity and refers to the doubt about the exact value of the measurement. It is closely linked to significant figures because the number of significant figures indicates how precisely a quantity is known.

Rules for Counting Significant Figures

There are established rules for identifying significant figures: nonzero digits are always significant; zeros between nonzero digits are significant; leading zeros are not significant; and trailing zeros are significant if a decimal point is present or if explicitly stated. Understanding these rules is essential when dealing with measured quantities.

Scientific Notation

Scientific notation is a method of writing numbers that clearly reflects significant figures by expressing numbers in the form a × 10^n, where all digits in the coefficient are significant. This notation is particularly useful for expressing very large or very small measured quantities while maintaining clarity about their precision.

Transcript

00:01 To be talking about significant figures and we're going to be helping to identify the number of significant figures present with each of these numbers and significant figures are each of the digits of a number that are used to express it to a certain point of accuracy and so not not all the the digits that you see in a certain number are going to be significant some of them are just their replacement and so determining the number of significant figures is a little bit crucial especially when you are very precise and you know and a little chemists do really take very careful no number of digits in their calculations.

00:36 And so here we have examples and we want to determine the number significant figures on each of these numbers.

00:41 And so for the first one, we have 62 .65 kilometers per hour.

00:47 All of these digits are in fact significant.

00:49 There are no zeros or trickling zeros that would allow us or that would prevent us from counting them as significant figures.

00:56 All these numbers are whole.

00:58 It's not a trickling decimal at all.

01:00 So all four of these digits are in fact significant.

01:03 So for that particular reason, we do have four significant figures.

01:09 Our next one, we have 78 .00k.

01:12 And the way in which these zeros are ranged there after a decimal, but because there are, maybe there is no other number after these zeros, if you were to have, for example, 78 .00003, then that would be a different case.

01:28 But because there's only two of these decim, there's only two of these zeros after the decimal point.

01:35 And they come after, of course, we have 78 .00.

01:39 Therefore, all of these numbers, all of these digits are going to be significant.

01:43 So normally, if you were thinking that it's two significant figures, it's actually going to be four.

01:49 Those zeros do, in fact, count at the end...

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