Lecture 6 - Arithmetic, Rounding, and Sig Figs

Question 1

Rounding

Answer 1

Removing excess digits from a number so that number has a correct quantity of significant figures.

Question 2

How should you round the digit next to the last digit to be reported is <5

Ex: Round to the hundredths
4.164

Answer 2

The last reportable digit should be left unchanged

Ex: 4.164 –> 4.16

Question 3

How should you round the digit next to the last digit to be reported is >5

Ex: Round to the thousandths
8.2316

Answer 3

The last reportable digit should be increased by one

Ex: 8.2316 –> 8.232

Question 4

How should you round the digit next to the last reported is 5

Ex: Round to the tenths

5. 25
6. 35

Answer 4

The last reportable digit should be changed to the nearest even number

5. 25 –> 5.2
6. 43 –> 4.4

Question 5

Round the following number to the nearest hundredths:

345.9876283495

Answer 5

345.99

Question 6

Round the following number to the thousandths:

49.38456738

Answer 6

49.384

Question 7

What is the point of significant figures?

Answer 7

Used to express precision of a measurement.

Question 8

The ___ digits used, the ___ precise a measurement.

Answer 8

The more digits used, the more precise a measurement.

Question 9

What is indicated if too many significant figures are used?

Answer 9

Suggests result is falsely more precise

Question 10

What is indicated if not enough significant are used?

Answer 10

Does not provide enough information, can be misleading.

Question 11

How do we handle numbers that contain zeros within them?

Ex: how many significant figures in 857.0042?

Answer 11

The zero or zeros are considered to be significant to that number and are never dropped out of the number.

Ex: 857.0042 has 7 significant figures

Question 12

How do we handle numbers that contain zeros at the end of the number?

Ex: how many significant figures in 301.00?

Answer 12

Zeros or zeros are considered to be significant.

Ex: 301.00 has 5 significant figures

Question 13

How do we handle numbers that are less than 1?

Ex: how many significant figures in 0.037

Answer 13

Any zeros that are before or after a decimal point but before the first nonzero number within the number are NOT considered to be significant

Example: 0.037 has 2 significant figures

Question 14

Exactness of a group of measurements is dependent on what?

Answer 14

The least exact measurement

Question 15

Determine the significant figures in the following equation:

10.0 mL + 15.85 mL + 7.775 mL = 33.625 mL

Answer 15

10.0 mL (3 sfs) + 15.85 mL (4 sfs)+ 7.775 mL (4 sfs) = 33.625 mL = 33.6 mL (3 sfs)

Question 16

The sum or difference of a group of numbers cannot be any ___ precise than the ___ precise number in the group of numbers that were added or subtracted.

Answer 16

The sum or difference of a group of numbers cannot be any more precise than the least precise number in the group of numbers that were added or subtracted.

Question 17

How many significant figures should the final result of an addition or subtraction problem have?

Answer 17

As many digits to the right of the decimal point as the least precise number involved in the problem.

Question 18

Using addition and subtraction significant figure rules, determine the answer.

11.5 + 14.411 + 13.65

Answer 18

11.5 + 14.411 + 13.65 = 39.561 –> 39.6

Question 19

Using addition and subtraction significant figure rules, determine the answer.

4.05 + 4.8

Answer 19

4.05 + 4.8 = 8.85 –> 8.8

Question 20

Using addition and subtraction significant figure rules, determine the answer.

2.77 + 4.489 + 15.44

Answer 20

2.77 + 4.489 + 15.44 = 22.699 –> 22.70

Question 21

What is the rule of significant figures for multiplication and division problems?

Answer 21

The final results cannot contain more significant figures than the number in the calculation with the least number of significant figures.

Question 22

Using multiplication and division significant figure rules, determine the answer.

4.977 x 1.83

Answer 22

4.977 x 1.83 = 9.10791 –> 9.11

Question 23

Using multiplication and division significant figure rules, determine the answer.

61.45 x 2.70

Answer 23

61.45 x 2.70 = 165.915 –> 166