Sigfig Calculation Practice Problems
Significant Figures and Dimensional Analysis #1
1. Indicate the number of significant figures in the following numbers:
a. 0.0098070 _____ b. 72300 _____
c. 203040 _____ d. 2.00006 _____
e. 9.80 x 103 _____ f. 3710. _____
2. How many significant numbers will be in the answer to the following problems?
a. 5470/3211 _____ b. 0.0870 x 1.340 _____
c. 8.340 x 700 _____ d. 0.00670/321 _____
3. How many places are kept after the decimal in the following problems?
a. 4.0023 + 0.00001 _____ b. 0.0621 – 0.123 _____
c. 9872 – 456.4 _____ d. 2.309 + 912567.23 _____
4. Record the following answers with the correct number of significant figures.
a) 3.461728 + 14.91 + 0.980001 + 5.2631 __________________
b) 23.1 + 4.77 + 125.39 + 3.581 __________________
c) 22.101 - 0.9307 __________________
d) 0.04216 - 0.0004134 __________________
e) 564,321 - 264,321 __________________
5. Record the following answers with the correct number of significant figures
a) 50.0 x 2.00 = __________________
b) 2.3 x 3.45 x 7.42 = ________________
c) 1.0007 x 0.009 = __________________
d) 51 / 7 = __________________
e) 208 / 9.0 = __________________
f) 0.003 / 5 = __________________
g) 500,009 / 17.000 = __________________
h) 500,000 / 5.002 = __________________
Significant Figures and Dimensional Analysis #2
1. How many sigfigs in the following numbers?
459 ________ 5600________ 0.00912________
2002________ 2030________ 3.00 x 108________
0.890________ 23.04________ 10000000________
2. Perform the following mathematical operations and record the answers with the correct number of significant figures.
a. 4.56 + 6.777 = ____________ b. 550 + 1.9 = ____________
c. 32.00 – 3.45 = ____________ d. 607/500 = ____________
e. 234 x 567 = ____________ f. 0.456/26 = ____________
g. 98.45 x 0.0065 = ____________
3. Perform the following conversions.
a. Convert 4500 m to miles.
b. Convert 7650000 seconds to years.
c. Convert .34 km to mm.
d. Convert 1.4 lbs to grams.
4. Identify the meaning of the following metric prefixes:
a. milli- ____________________
b. centi- ____________________
c. kilo- ____________________
5. What is the appropriate metric unit for the following measurements?
a. mass ____________________
b. volume ____________________
c. temperature ____________________
d. length ____________________
Significant Figures and Dimensional Analysis #3
Perform the following conversions. Keep the correct number of significant figures in the answer. show your work. Answers without work will not be given credit.
1. 123 ft to miles
2. 15000 inches to miles
3. 0.566 miles to yards
4. 1.35 years to seconds
5. 180 mg to grams
6. 16000 mg to kg
7. 2.3 km to millimeters
8. 345 cups to gallons
9. 0.452 km to mm
Dimensional Analysis
Dimensional analysis is the process by which scientists solve mathematical problems. We will initially use it to perform metric and everyday conversions. This process gets its name because it involves analyzing the dimensions (aka units or measurements) to guide the problem solving process.
Math Review: this process is set up like a series of fractions or ratios. Each ratio is equivalent to one, for example 1 week is the same as 7 days so the ratio of 1 week to 7 days is equal to one.
When multiplying or dividing fractions, remember that numbers that occur in both the numerator and denominator can be cancelled out. Dimensional analysis uses this rule but focuses on canceling out UNITS that occur in both numerator and denominator rather than numbers. Look at the following example:
3 weeks x 7 days = 21 days
1 week
In this problem, the unit “week” can be canceled out because it occurs in both the numerator of the first number and in the denominator of the second ratio. This solves for days.
If I wanted to determine how many seconds are in 36 weeks, I could set up the following dimensional analysis:
36 weeks x 7 days x 24 hours x 60 minutes x 60 seconds = 21,772,800 seconds
1 week 1 day 1 hour 1 minute
I can check my work by double checking that my units cancel out. I can also check that the unit in the numerator of the last ratio is the unit for which I am solving.
Application: I need to see all work set up in this format. Try the following problems.
1. How many kilometers are represented by 98,000 millimeters?
2. How many hours are you in class in a semester? (Assume that a semester is 18 school weeks and a school week is 35 hours.)
3. You are working in a pharmaceutical company. You are given 5 kg of acetyl salicylic acid (aspirin) and told to make as many 325 mg tablets as possible. How many tablets should you be able to make. (Hint: kg(g(mg(tablet)
4. You ran a marathon last weekend. In your attempt to brag, you tell your friend how many inches you ran. Remember that a marathon is 26.2 miles, a mile is 5280 feet and a foot is 12 inches.
5. How many inches in 3.4 miles?
6. How many seconds in 2 years and 6 months?
7. Your class officers are making commemorative ribbons as a fundraiser. How many 6 inch ribbons can be made from 27 yards of ribbon?
8. Your company makes generic vitamin C tablets. How many 600 mg tablets can be made from 18 kg of ascorbic acid (this is the technical name for vitamin C)?
9. A ream of paper is 500 sheets. A box of paper holds 10 reams. How many sheets of paper will be in 12 boxes?
Dimensional Analysis Word Problems
1. Ms. Keebler is famous for her animal rescues. She likes to send out each adopted animal with a "care package" that contains, among other things, a new leash. In order to conserve funds, she makes these 12 foot leashes herself. How many can she make with 300 yards of leash ribbon?
2. Mrs. Howard has a vitamin A addiction. In order to feed this addiction, she must consume 8 carrots a day. If a package of carrot contains 13 carrots on average, how many packages must she buy on her weekly grocery trip to last the week?
3. Mr. Pickett LOVES his morning (and afternoon and evening) coffee. He makes three pots a day to fuel his enthusiasm for life. If each pot of coffee requires 1.4 ounces of coffee, how many 13.5 ounce cans must he buy to last a month? Consider a month 31 days for this problem.
4. Mr. Eiselstein is a physical fitness buff. The other day he was bragging that he ran 12,300 inches. Convert this to miles and give an opinion on how impressive this feat was.
Scientific Notation (aka exponential notation):
1. Move the decimal (whether seen or understood) until there is ONE number to the left of the decimal.
2. Count how many places you moved the decimal. If you moved the decimal to the left, this is your exponent of 10. If you moved the decimal to the right, make this number negative and this is your exponent of 10. Remember, numbers smaller than 1 will have a negative exponent and numbers greater than one will have a positive exponent.
Write these numbers in scientific notation. Keep the same number of sigfigs in both numbers.
23500 0.00901
0.0000789 0.0000000008
11.007 70000000000
Perform the following calculations and use scientific notation to record your answer with the correct significant figures.
457 x 754 =
987/0.0034 =
When you use your calculator to enter scientific notation:
1. Enter number in calculator.
2. Hit EE or EXP button
3. Enter exponent. Be sure to include "-" if the exponent is negative.
This can appear in the following forms on your display:
3.4456E-6
3.4456x 10-6
3.4456 -6
Calculate and keep correct sigfigs in answer:
(3.45 x 10-3)(5.778 x 104)
2.67 x 104/9.3 x 10-4
Sigfig and Dimensional Analysis Practice Test
Determine the number of significant figures in the following numbers.
0.00567 _______ 789700 _______ 7.0090 _______
9000 _______ 0.00078 _______ 4.670 x 106 _______
Recall the rules for adding/subtracting and multiplying/dividing. Then solve the following problems and record the answers applying those rules. Remember to determine first WHICH rule to use.
45 x 678 ____________ 5.67 x 0.0089 ____________
0.007/0.034 ____________ 56.787 + 9.444 ____________
185 – 9.9 ____________ 700 + 23 ____________
Perform the following conversions:
a. 45678 inch to miles
b. 7.89 km to mm
c. 85 days to seconds
d. 1.28 gallons to cups
e. 67800 mg to kg
f. I must consume one Twizzler licorice stick every hour that I am awake or I begin to withdraw from the red dye used to color the candy. Each package of Twizzler licorice contains 66 sticks. How many packages must I buy each 30 day month to get my fix and avoid withdrawal symptoms? Assume I am awake 16 hours a day. (Hint: Start at 30 days and work towards packages.)
Measurements and Significant Figures Lab
Purpose: The aim of this lab is to practice recording measurements with the correct number of significant figures.
Procedure:
1. Several stations have been set up around the room. Step up to a station, read the directions, determine the level of precision for the instrument, and read and record the measurement. Record this measurement with the correct units in the slot in your data table that corresponds to the station number. Although you and your team mates may mass the objects together at stations 4, 6, and 7, you must read the instruments yourself and should not copy a peer's measurement.
|Station # |Measuring tool |What is the most precise measurement this |Measurement (with unit) |
| | |tool can make? Include unit. | |
|1 | | | |
|2 | | | |
|3 | | | |
|4 | | | |
|5 | | | |
|6 | | | |
|7 | | | |
|8 | | | |
|9 | | | |
|10a | | | |
|10b | | | |
|10c | | | |
|11 | | | |
Discussion and Analysis:
1. Which stations required no approximation of the last significant figure? Why?
2. Did the estimations of you and your group mates always match? Why or why not?
3. Why is it important in lab activities to have one lab partner measure both the beginning and final measurements for a specific tool?
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