How many significant figures are in each of the following measurements? (a) 35.0445 g (b) 59.000

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

Key Concepts

Significant Figures

Significant figures are the digits in a number that contribute to its precision. They include all the nonzero digits, any zeros between them, and, under certain conditions, trailing zeros in a decimal number. They indicate the level of confidence or certainty in a measurement or calculation, enabling the expression of numerical uncertainty.

Leading Zeros

Leading zeros are the zeros that appear before the first nonzero digit in a number. These zeros serve only as placeholders and do not count as significant figures because they do not reflect the precision of the measurement.

Captive Zeros

Captive zeros, also known as embedded or sandwich zeros, are the zeros that appear between nonzero digits. These zeros are always considered significant because they provide meaningful information about the measurement's precision.

Trailing Zeros in Decimal Numbers

Trailing zeros in a number that contains a decimal point are considered significant because they indicate the precision of the measurement. The placement of the decimal point confirms that these zeros are intentional and reflect the measured accuracy.

Trailing Zeros without a Decimal Point

Trailing zeros in whole numbers without an explicitly shown decimal point can be ambiguous. Their significance depends on context or additional notation; without clarification, there is uncertainty whether they are meant to indicate precise measurement or are merely placeholders.

Scientific Notation and Significant Figures

When numbers are written in scientific notation, the significant figures are clear, as the coefficient (or mantissa) explicitly shows all the significant digits. The exponent simply sets the scale and does not affect the count of significant figures, making scientific notation a tool for unambiguously conveying measurement precision.

Transcript

00:01 We've been given six different measurements and have been asked to identify the number of significant figures in each of them.

00:07 First up, we're given the measurement 35 .0445 grams.

00:15 Now the rule on decimal numbers is that you can start counting from the left, and once you hit a non -zero digit, that digit will be significant, as will everything that comes past it.

00:30 This decimal number with a non -zero therefore this means that every zero every digit will be significant so this number will have six since there are six digits in it you can also look at it that this number both begins and ends with a non -zero and digits found between non -zero's are significant therefore everything will be let's move on to part b where we're given the measurement 59 point zero zero centimeters this employs the exact same logic as the as part a we have a decimal we begin with a non -zero so everything following it must be significant we also begin an end with non -zero's so again we have six significant figures let's move on to see where we have zero point zero three zero zero three kilograms as i said before we have a decimal we'll start hunting from the left until we hit a non -zero which is here.

01:37 That is our first significant figure and that everything past it must be as well.

01:43 So this one will have four significant figures.

01:49 Let's move on to d where we're given a similar measurement 0 .00450 meters.

02:00 Begin from the left and move on.

02:04 We have hit our first non -zero and everything that follows it will be significant as well.

02:10 Because leading zeros on a decimal number are not significant, but trailing zeros are significant.

02:17 So this measurement has three significant figures.

02:24 Moving on to e, we've been given 67 ,000 square meters.

02:34 Now, obviously these two are significant because they're non -zero's.

02:38 But what about the rest of them? we don't know.

02:41 They could be significant...

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