How many significant figures are in each of the following? a. 100 b. 1.0 ×10^2 c. 1.00 ×10^3 d.

step 1 So this problem is just one of those. We'll get the number, how many significant figures does it

How many significant figures are in each of the following?...

Key Concepts

Significant Figures

Significant figures are the digits in a number that carry meaning contributing to its measurement resolution. They include all non-zero digits, any zeros between them, and, in certain contexts, trailing or decimal zeros. Understanding significant figures is essential for determining precision in scientific calculations and measurements.

Scientific Notation

Scientific notation is a way of expressing numbers, particularly very large or very small ones, in the form a × 10^n. This notation helps in clearly indicating the number of significant figures, as the coefficient (the value of a) contains all the significant digits while the exponent (n) simply shifts the decimal point.

Leading Zeros

Leading zeros are the zeros that precede all non-zero digits in a decimal number. They are not considered significant because they serve only as placeholders to indicate the relative scale of the number. Their presence does not reflect the precision of the measurement.

Trailing Zeros

Trailing zeros in a number may or may not be significant depending on the context, such as whether there is a decimal point present. In numbers with a decimal point, trailing zeros are significant as they indicate the precision of the measurement. Without a decimal, trailing zeros can be ambiguous and are usually not considered significant unless specified by other notation.

Decimal Points

The presence of a decimal point in a number clarifies the significance of trailing zeros. A decimal point confirms that zeros following a non-zero digit are intended to be precise measurements rather than placeholders, thereby affecting the count of significant figures.

Transcript

00:01 So this problem is just one of those.

00:02 We'll get the number, how many significant figures does it have? there are a lot of rules that you have to remember when it comes to establishing the numbers of significant figures in a number, and it can get pretty tricky.

00:13 So i'll try to explain the rule that i'm referencing while i'm walking through these examples.

00:19 I'm also going to hop around a little bit because some of these are related to each other.

00:24 So, for example, we're going to start with a versus d.

00:27 They look very similar, but this decimal point changes the rule.

00:32 So you have this one and you have these two zeros in 100.

00:37 So these two zeros are what's known as trailing zeros.

00:41 So they are only significant if there's a decimal point here.

00:45 So the one is always significant.

00:47 These zeros are significant depending on the presence of a decimal.

00:52 In a, there's no decimal.

00:54 In d, there is a decimal.

00:55 Therefore, the trailing zeros will not be significant in a, but they will be significant in d.

01:04 So you'll notice some significant figures in the scientific notation portion as well.

01:10 So let's go from, let's do b, c, g, and h now, because they're all pretty similar.

01:17 Most important thing to remember, the 10 and the exponent, whether it's positive or negative, are not significant ever.

01:25 You would follow the normal rules for significant figures when looking at scientific notation.

01:32 So right? so 1 .0, this is a trailing zero, but there's a decimal...

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