Significant Figures - AP Chemistry

First, add up the numbers.

Because this is addition, the result of the calculation needs to have the same number of decimal places as the number with the fewest decimal places. Since 8.2 has the least number of places after the decimal point, the answer must also only have 1 digit after the decimal point.

The number of significant figures in the final answer will ultimately be determined by the term in the equation that has the fewest significant figures. Let us examine the components of the expression we are given.

Since the least precise term in the expression has only one significant figure, our final answer will have only one significant figure.

When dividing two numbers, the answer can only have as many significant figures as the number with the fewest significant figures. The mass has 6 significant figures while the volume only has 2, therefore the answer can only have 2. Don't forget to round!

Remember that all leading zeroes are not significant figures.

So for 0.00150, we start counting significant figures where the 1 is. The last 0 is a significant figure because it is a trailing zero found after the decimal point.

The digits in red are not significant. The digits in green are significant.

The digit in red is not significant because this is a leading zero. All the digits in green are significant. The first 0 is significant because it is sandwiched between two non-zero digits. The last 0 is also significant because it is a trailing zero that comes after a decimal point. Thus, this has 5 significant figures.

First, do the calculation.

Because this is addition, the result of the calculation needs to have the same number of decimal places as the number with the fewest decimal places. Since 3 has the least number of places after the decimal point, the answer must not have any decimal points. The answer will round up to 25.

First, do the calculation.

Recall that for multiplication and division, the answer uses the least number of significant figures found in the question. In this case, 3.0 has the least number of significant figures at 2. The final answer should then be rounded up to only have 2 significant figures also. Thus we round up to 270.

For multistep calculations, make sure to keep track of the number of significant figures at the end of each step so we know how many significant figures to round to at the end of the entire calculation. To maintain accuracy, do not round intermediate steps. Do the addition and subtraction in the parentheses first.

Recall that for addition, the result needs to have the same number of digits after the decimal point as the number with the fewest decimal points in the question. Our answer from the addition should then only have 4 significant figures. To remember that the answer should only have 4 significant figures, the last significant digit will be highlighted:

Next, do the subtraction.

Since the rules for significant figures for addition and subtraction are the same, our answer here should only have 2 significant figures. The last significant figure from this step will also be highlighted:

Now, divide these two numbers:

Now, this is when the highlighting of significant digits in earlier steps becomes important. Recall that for multiplication and division, the result has the same number of significant figures as the factor with the least number of significant figures.

Round the final answer to 2 significant figures to reflect the least amount of significant figures found in the division. Thus 43.40167364 rounds down to 43.

First, carry out the calculation.

Recall that for multiplication and division, the answer uses the least number of significant figures found in the question. In this case, 3.45 has the least number of significant figures at 3. The final answer should then be rounded up to only have 3 significant figures. 2023.720183 rounded to three significant figures is 2020.

For multistep calculations, make sure to keep track of the number of significant figures at the end of each step so we know how many significant figures to round to at the end of the entire calculation. To maintain accuracy, do not round intermediate steps. First, calculate what's found inside the parentheses.

Recall that for multiplication and division, the answer uses the least number of significant figures found in the question. In this case, 5 has the least number of significant figures at 1. The final answer should then be rounded up to only have 1 significant figure. The last significant digit will be highlighted:

Next, do the addition.

Because this is addition, the result of the calculation needs to have the same number of decimal places as the number with the fewest decimal places. Since 20 does not have any decimal places, our answer also cannot have any decimal places. Thus, 27.82 rounded to two significant figures is 28.

For multistep calculations, make sure to keep track of the number of significant figures at the end of each step so we know how many significant figures to round to at the end of the entire calculation. To maintain accuracy, do not round intermediate steps.

First, calculate what's found inside the parentheses.

Recall that for multiplication and division, the answer uses the least number of significant figures found in the question. In this case, both factors have 2 significant figures. The final answer should only have 2 significant figures also. The last significant digit will be highlighted: The decimal point is added after the last digit to ensure that there are 2 significant figures.

Next, do the addition.

Because this is addition, the result of the calculation needs to have the same number of decimal places as the number with the fewest decimal places. Since 20. does not have any decimal places, our answer also cannot have any decimal places. Thus 36.23 is rounded down to 36.

For multistep calculations, make sure to keep track of the number of significant figures at the end of each step so we know how many significant figures to round to at the end of the entire calculation. To maintain accuracy, do not round intermediate steps.

First, do the two addition problems found within the parentheses.

Recall that for addition, the result needs to have the same number of digits after the decimal point as the number with the fewest decimal points in the question. Our answer from the addition should then only have 2 significant figures. To remember that the answer should only have 2 significant figures, the last significant digit will be highlighted:

Perform the second addition using the same logic as above. To remember that the answer should only have 2 significant figures, the last significant digit will be highlighted:

Now, multiply:

Because both factors only have 2 significant figures, our final answer should also only have 2 significant figures. 0.33216 is rounded to 0.33.

For multistep calculations, make sure to keep track of the number of significant figures at the end of each step so we know how many significant figures to round to at the end of the entire calculation. To maintain accuracy, do not round intermediate steps.

First, do the two multiplication problems found within the parentheses.

Recall that for multiplication, the result needs to have the same number of significant figures as the factor with the least number of significant figures. Our answer from the addition should then only have 3 significant figures since that is the number of significant figures 3.14 has. To remember that the answer should only have 3 significant figures, the last significant digit will be highlighted:

Recall that for multiplication, the result needs to have the same number of significant figures as the factor with the least number of significant figures. Our answer from the addition should then only have 1 significant figure since that is the number of significant figures 10 has. To remember that the answer should only have 1 significant figure, the last significant digit will be highlighted:

Now, multiply:

Since the factor with the least number of significant figures only has 1 significant figure, the answer must also be rounded to 1 significant figure. 5570.13393 is rounded to 6000.

For multistep calculations, make sure to keep track of the number of significant figures at the end of each step so we know how many significant figures to round to at the end of the entire calculation. To maintain accuracy, do not round intermediate steps.

First, do the two multiplication problems found within the parentheses.

Recall that for multiplication, the result needs to have the same number of significant figures as the factor with the least number of significant figures. Our answer from the addition should then only have 1 significant figure since that is the number of significant figures 0.02 has. To remember that the answer should only have 3 significant figures, the last significant digit will be highlighted:

Next, do the addition.

Because this is addition, the result of the calculation needs to have the same number of decimal places as the number with the fewest decimal places. We need to only keep 1 decimal place because of . The last significant digit from this step is highlighted:

Next, do the second addition.

Because this is addition, the result of the calculation needs to have the same number of decimal places as the number with the fewest decimal places. Since 10 does not have any decimal places, our final answer also cannot have any decimal places. 33.356 is rounded down to 33.

The student who has the accurate determination is that the student's whose average is closest to that of the "known" value of the crucible. Not be confused with precision, accuracy is how close the measured value is to the actual value, while precision is how close the measured values are to each other.

To answer this question, you need to calculate the averages of each students' weighings by summing them and dividing by five, since five measurements were taken.

Student 2's data averages out to 43.36, which rounds to 43.4. This average has the smallest difference from that of the "known" value for the crucible, 43.4273 g. Student 2's data is the correct answer.

First, add up the numbers.

Because this is addition, the result of the calculation needs to have the same number of decimal places as the number with the fewest decimal places. Since 8.2 has the least number of places after the decimal point, the answer must also only have 1 digit after the decimal point.

First, do the calculation.

Because this is addition, the result of the calculation needs to have the same number of decimal places as the number with the fewest decimal places. Since 3 has the least number of places after the decimal point, the answer must not have any decimal points. The answer will round up to 25.

The number of significant figures in the final answer will ultimately be determined by the term in the equation that has the fewest significant figures. Let us examine the components of the expression we are given.

Since the least precise term in the expression has only one significant figure, our final answer will have only one significant figure.

When dividing two numbers, the answer can only have as many significant figures as the number with the fewest significant figures. The mass has 6 significant figures while the volume only has 2, therefore the answer can only have 2. Don't forget to round!

Remember that all leading zeroes are not significant figures.

So for 0.00150, we start counting significant figures where the 1 is. The last 0 is a significant figure because it is a trailing zero found after the decimal point.

The digits in red are not significant. The digits in green are significant.