Lecture 6 - Arithmetic, Rounding, and Sig Figs Flashcards
Rounding
Removing excess digits from a number so that number has a correct quantity of significant figures.
How should you round the digit next to the last digit to be reported is <5
Ex: Round to the hundredths
4.164
The last reportable digit should be left unchanged
Ex: 4.164 –> 4.16
How should you round the digit next to the last digit to be reported is >5
Ex: Round to the thousandths
8.2316
The last reportable digit should be increased by one
Ex: 8.2316 –> 8.232
How should you round the digit next to the last reported is 5
Ex: Round to the tenths
- 25
- 35
The last reportable digit should be changed to the nearest even number
- 25 –> 5.2
- 43 –> 4.4
Round the following number to the nearest hundredths:
345.9876283495
345.99
Round the following number to the thousandths:
49.38456738
49.384
What is the point of significant figures?
Used to express precision of a measurement.
The ___ digits used, the ___ precise a measurement.
The more digits used, the more precise a measurement.
What is indicated if too many significant figures are used?
Suggests result is falsely more precise
What is indicated if not enough significant are used?
Does not provide enough information, can be misleading.
How do we handle numbers that contain zeros within them?
Ex: how many significant figures in 857.0042?
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
How do we handle numbers that contain zeros at the end of the number?
Ex: how many significant figures in 301.00?
Zeros or zeros are considered to be significant.
Ex: 301.00 has 5 significant figures
How do we handle numbers that are less than 1?
Ex: how many significant figures in 0.037
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
Exactness of a group of measurements is dependent on what?
The least exact measurement
Determine the significant figures in the following equation:
10.0 mL + 15.85 mL + 7.775 mL = 33.625 mL
10.0 mL (3 sfs) + 15.85 mL (4 sfs)+ 7.775 mL (4 sfs) = 33.625 mL = 33.6 mL (3 sfs)
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.
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.
How many significant figures should the final result of an addition or subtraction problem have?
As many digits to the right of the decimal point as the least precise number involved in the problem.
Using addition and subtraction significant figure rules, determine the answer.
11.5 + 14.411 + 13.65
11.5 + 14.411 + 13.65 = 39.561 –> 39.6
Using addition and subtraction significant figure rules, determine the answer.
4.05 + 4.8
4.05 + 4.8 = 8.85 –> 8.8
Using addition and subtraction significant figure rules, determine the answer.
2.77 + 4.489 + 15.44
2.77 + 4.489 + 15.44 = 22.699 –> 22.70
What is the rule of significant figures for multiplication and division problems?
The final results cannot contain more significant figures than the number in the calculation with the least number of significant figures.
Using multiplication and division significant figure rules, determine the answer.
4.977 x 1.83
4.977 x 1.83 = 9.10791 –> 9.11
Using multiplication and division significant figure rules, determine the answer.
61.45 x 2.70
61.45 x 2.70 = 165.915 –> 166
