How many significant figures are in each of the following? a. 3.1416 m b. 59600700 g c. 300 .

step 1 This question covers the concepts of significant figures. Significant figures are essentially fi

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

Key Concepts

Rules for Counting Significant Figures

There are specific rules to determine which digits are significant: nonzero digits are always significant; zeros between significant digits are significant; leading zeros (zeros to the left of the first nonzero digit) are not significant; trailing zeros in a number with a decimal point are significant; and trailing zeros in a whole number without a decimal point are ambiguous unless additional notation, such as a decimal point or scientific notation, is provided.

Trailing Zeros and Decimal Points

Trailing zeros can indicate precision in a measurement. When a number is written with a decimal point, trailing zeros are considered significant since they imply measured or intended precision. Conversely, trailing zeros in whole numbers without a decimal point are often ambiguous, as they might be placeholders rather than measurements of precision.

Significant Figures

Significant figures are the digits in a number that carry meaningful information about its precision or accuracy. This concept is important in scientific measurements because it reflects the certainty of the measured value.

Transcript

00:01 This question covers the concepts of significant figures.

00:05 Significant figures are essentially figures that allow us to know what part of our measurement of our number includes meaningful numbers.

00:16 And the last digit in the significant figure in a number that's measured lets us know that that number was an estimate and there's a degree of uncertainty.

00:25 So sig figures allow us to know what's meaningful and allows us to understand the uncertainty.

00:31 In our figures.

00:33 So there's a few different rules that we're going to go through that allow us to know what is significant and what is not.

00:40 And we're going to start off here by just exposing those rules.

00:45 And these rules allow us to know which numbers are actually significant.

00:52 So i'll highlight that in green right here.

00:55 So sig -fig positive.

01:01 Okay.

01:03 So a number is not a number is significant if it it is not a zero.

01:08 So any non -zero number is significant.

01:10 A number significant if it's zero between non -zero digits.

01:15 For instance, if we have 707.

01:18 Okay, that zero is significant.

01:20 A number is also significant if it's a zero at the end of a decimal number.

01:28 So if we have 70 decimal point, then that zero here is significant.

01:34 So here we have two significant figures.

01:36 And a number is also significant.

01:38 If it's in the coefficient of a number written in scientific notation.

01:42 So if we have 1 .70 times 10 to the eighth, all our non -zero is always significant, and the zero is also significant because it's a coefficient in a number written in scientific notation, which means we would have three significant figures in this notation.

02:02 And then there's a couple of times where zeros are not going to be significant.

02:08 Zeros are not significant.

02:11 Let me just write this out here.

02:16 No sig -figs...

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