**Significant Figures** are used to determine some level of accuracy within our recorded measurements.

The Rules for Significant Figures

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concept

## Significant Figures

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So when we're dealing with any type of question or trying to write down the answer to a question, we need to take into account significant figures now significant figures. These are the numbers that contribute to the precision associated with any value. Now we're going to say here that there is an easy way and, of course, ah, hard way to approach significant figures. Luckily for us, we're gonna focus on the easy way. Now the hard way has ah lot of rules, and it has terms that sometimes might be confusing, such as leading zeros and trailing zeroes. We're gonna avoid all of that, and we're gonna rely on three simple rules to help us determine the number of significant figures associated with any value. Now, the first rule if your number has a decimal point, so if it has a decimal point, you're gonna move from left to write. Start counting once you get to your first non zero number and keep counting until the end. So here we have our first two examples. One is written standard notation. One is written scientific notation, but that doesn't matter if we look at the first one are moving from right. I'm from left to right. We're gonna start counting when we get to our first non zero number. So 0000 Here is our first non zero number. This too. We're going to start counting there and we count all the way into the end. So one, 23 This number has three sig figs or three significant figures for the next one. It's written in scientific notation, but that doesn't matter when it's written. Scientific notation focus on the coefficient. So this part here the base which is the 10 and the power of the exponents don't matter. It has a decimal point. So we're moving from left to right. Our first non zero number is this eight way. Start counting there we count all the way until the end. So 123 So we have 366 in this one as well. Next, if you're number has no decimal point, then we're gonna move from right, So left. So we're gonna go this way. Same rules apply. Start counting once you get your first non zero number and keep counting until you get to the end. Our first non zero number is this five. So that's one to 34 So we have 46 fix here as our number significant figures. Now, this third rule, this third goes a little bit different, So this third will deals with exact numbers. Now an exact number is a value or integer, so that means it has to be a whole number that is known with complete certainty. We're going to stay here for a exact number. There are an infinite number of sig figs or significant figures. So, for example, your lecture class has 125 students. That's something we can know with certainty, because we can literally count the number of students that we see within the room or a dozen eggs equals 12 eggs. This is something that is known with complete certainty. 12 eggs. We can count each one of those individual eggs. So 125 students within Electra Hall isn't eyes has an infinite number of sick fix 12 eggs equal one dozen that can also have an infinite number of sick fix. That's because, for example, for looking at the 125 students, it could be 125 which would have three sick fix. Or it could be 125.0. That's still 725 that has four sig figs. Or it could be 125.0 which has 56 figs. And it could go on and on and on and on because technically, that is still saying 125. So just remember, the first two rules are pretty simple that deals with decimal place or no decimal place. The third role is a little bit trickier. You have to recall, if this is an exact number, something that could be counted, that you can know for certain 100% that it's that number. Those have an infinite number of significant figures. Now that we've taken a look at these three rules, let's move on to the example question in the following video and see if we could determine the number of correct significant figures

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example

## Significant Figures Example 1

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So let's take a look at the following example question here, it says determine the number of significant figures in the following value. While our value has a decimal point, when it has a decimal point, you move from left to write and we start counting. Once we get to our first non zero number. Our first non zero number is this three. So that's where we start counting. So that's gonna be one to three four. You count all the way to the end once you start counting. So here, this would just simply have four significant figures. So remember, just to rely on the three rules that we know in terms of determining the number of significant figures if it has a decimal point such as this one, we move from left to right. Start counting once you get to your first non zero number and keep counting until the end. If it had no decimal point, then we moved from right toe left and follow the same exact rules. If it was an exact number, then would have an infinite number of significant figures. Now that we've done this example question, move on to the practice question

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Problem

How many sig figs does each number contain?

a) 100. min

b) 17.3 x 103 mL

c) 10 apples

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4

Problem

Indicate the number of significant figures in the following:

A liter is equivalent to 1.059 qt.

A

0

B

1

C

3

D

4

E

infinite

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Problem

How many significant figures are contained in the following measurement?

3,482,005 mg

A

0

B

5

C

6

D

7

E

infinite

Additional resources for Significant Figures

PRACTICE PROBLEMS AND ACTIVITIES (44)

- The three targets from a rifle range shown below were produced by: (A) the instructor firing a newly acquired ...
- A scientist uses an uncalibrated pH meter and measures the pH of a rainwater sample four times. A different pH...
- Assume that you have two graduated cylinders, one with a capacity of 5 mL (a) and the other with a capacity of...
- Indicate which of the following are exact numbers: (a) the mass of a 3- by 5-in. index card, (b) the number o...
- Indicate which of the following are exact numbers: (a) the mass of a 32-oz can of coffee, (b) the number of s...
- What is the number of significant figures in each of the following measured quantities? (e) 92.03 km
- What is the number of significant figures in each of the following measured quantities? (d) 2.94 * 103 m2
- What is the number of significant figures in each of the following measured quantities? (b) 3 * 10-6 m
- Indicate the number of significant figures in each of the following measured quantities: (e) 89.2 metr ic ton...
- Round each of the following numbers to three significant figures and express the result in standard exponenti...
- Round each of the following numbers to three significant figures and express the result in standard exponentia...
- (a) The diameter of Earth at the equator is 12756.27 km. Round this number to three significant figures and ex...
- Two students determine the percentage of lead in a sample as a laboratory exercise. The true percentage is 22....
- Is the use of significant figures in each of the following statements appropriate? (a) The 2005 circulation of...
- For each number, underline the zeroes that are significant and draw an x through the zeroes that are not. a. 1...
- How many significant figures are in each number? a. 0.1111 s b. 0.007 m c. 108,700 km d. 1.563300 * 1011 m e...
- How many significant figures are in each number? a. 0.1111 s b. 0.007 m c. 108,700 km d. 1.563300 * 1011 m e...
- Which numbers are exact (and therefore have an unlimited number of significant figures)? a. p = 3.14 b. 12 in ...
- Which numbers are exact (and therefore have an unlimited number of significant figures)? a. p = 3.14 b. 12 ...
- Round each number to three significant figures. a. 79,845.82 b. 1.548937 * 107 c. 2.3499999995 d. 0.000045389
- Which of the following statements uses exact numbers? (a) 1 ft = 12 in. (b) 1 cal = 4.184 J (c) The height o...
- How many significant figures are in each of the following measurements? (f) 3.8200 * 103 L
- How many significant figures are in each of the following measurements? (e) 67,000 m2
- How many significant figures are in each of the following measurements? (d) 0.004 50 m
- How many significant figures are in each of the following measurements? (c) 0.030 03 kg
- How many significant figures are in each of the following measurements? (b) 59.0001 cm
- How many significant figures are in each of the following measurements? (a) 35.0445 g
- How many significant figures are in each of the following measurements? (f) 10 students
- How many significant figures are in each of the following measurements? (e) 5.10 * 102 J
- How many significant figures are in each of the following measurements? (d) 510 J
- How many significant figures are in each of the following measurements? (b) 2000.003 g
- How many significant figures are in each of the following measurements? (a) $130.95
- How many significant figures are in each of the following measurements? (c) 5 ft 3 in.
- The Vehicle Assembly Building at the John F. Kennedy Space Center in Cape Canaveral, Florida, is the largest b...
- The diameter of the Earth at the equator is 7926.381 mi. (a) Round off this quantity to four significant figur...
- Round off the following quantities to the number of signifi-cant figures indicated in parentheses. (d) 2.309 8...
- Round off the following quantities to the number of signifi-cant figures indicated in parentheses. (c) 4.995 *...
- Round off the following quantities to the number of signifi-cant figures indicated in parentheses. (b) 68.507 ...
- Round off the following quantities to the number of signifi-cant figures indicated in parentheses. (a) 35,670....
- Round off the following quantities to the number of signifi-cant figures indicated in parentheses. (d) 2,300,0...
- Round off the following quantities to the number of signifi-cant figures indicated in parentheses. (c) 13.2151...
- Round off the following quantities to the number of signifi-cant figures indicated in parentheses. (b) 1.605 k...
- Round off the following quantities to the number of signifi-cant figures indicated in parentheses. (a) 7.0001 ...
- Judge the following statements as true or false. If you believe a statement to be false, provide a corrected v...