Significant Figures
How many significant figures does the number 12 have?
2
Explanation:
The decimal is Absent, so you approach from the "Atlantic" (right) side and would remove zeros if there were any. Since there are none, you can just count the digits of the number to get 2 significant figures.
How many meters are in a kilometer?
1000
How many minutes are in 1 century? Answer rounding to the correct significant figures.
50000000 (5*10^7) minutes
century -> yr -> day -> hr -> min (conversions may vary)
1 * (100/1) * (365/1) * (24/1) * (60/1)
52560000 -> 50000000
How many significant figures does 0.07 have?
1
Explanation:
The decimal is Present, so you approach from the "Pacific" (left) side and remove the two zeros before the hundredths digit. You can then count that there is one remaining digit, meaning that this number has one significant figure.
How long is exactly 8 hours in seconds?
28800 seconds
Explanation:
Hours -> minutes -> seconds
8 * (60/1) * (60/1) = 28800
No significant figures work needed because it is "exactly" 8 hours
If a bridge is 3.01 miles long, how long is it in milimeters? Remember to round to the correct number of significant figures.
4,840,000 (4.84*10^6) mm
Explanation:
Same conversion as before, but rounded to 3 sig figs
How many significant figures does 308.209 have?
6
Explanation:
The decimal is Present, so you approach from the "Pacific" (left) side but do not remove any zeros because none of the digits with a zero are leading zeros, which would come consecutively before the first non-zero digit(s). You can then count that there are 6 remaining significant digits, meaning that this number has six significant figures.
How far is a distance of exactly 3.01 miles in milimeters?
4844125
Explanation: (conversion factors may slightly vary)
miles -> kilometers -> meters -> milimeters
3.01 * (1.60934/1) * (1000/1) * (1000/1)
4844113.4 mm
A car is traveling at 60 mi/hr. How fast is it traveling in feet per second?
90 ft/sec
Explanation:Same calculation as earlier just with 1 significant figure
A given solid weighs 45 grams and displaces 21.0361 ml of water when its volume is measured with water displacement. With the correct number of significant figures, what is its density in g/ml?
2.1 g/ml
Explanation:
For context, the formula for density is mass divided by volume and, when dividing or multiplying, you round the calculated result using only as many significant figures as your least precise measurement (the one with the fewest significant figures). In this problem, this means that your answer should not have more than 2 significant figures (because of the 45g measurement), so while you might typically give "2.13917979093..." as your answer, you should only respond with 2 significant figures of that calculation, leading to the answer of 2.1 g/ml.
A car is traveling at 60 mi/hr. How fast is it traveling in feet per second? Ignore significant figures, give the exact calculated answer.
88 ft/sec
Explanation:
mi/hr -> ft/hr -> ft/min -> ft/sec
60 * (5280/1) * (1/60) * (1/60)
88 ft/sec
A book exerts 0.92 g/cm^2 of pressure sitting on a table. How many pounds per square foot does it exert?
0.45 lbs/ft^2
Explanation:
Same calculation, just with 2 sig figs
How many grams of NaCl do you have after combining three samples of 102.0g, 11.994g, and 6.28g? Respond with appropriate significant figures.
120.3g of NaCl
Explanation:
When adding observed, non-counted quantities, you always answer with only as many decimal places as the quantity with the fewest. In this problem, you might add these numbers to get 120.274g, but you should only answer with one decimal point of precision (after rounding), giving you the correct answer of 120.3g of NaCl
A book exerts 0.92 g/cm^2 of pressure sitting on a table. How many pounds per square foot does it exert? (Ignore significant figures, give exact calculation)
0.449183876739 lbs/ft^2
Explanation:
g/cm^2 -> kg/cm^2 -> lbs/cm^2 -> lbs/in^2 -> lbs/ft^2
0.92 * (1000) * (1/2.20462) * (1/6.4516) * (1/144)
0.449183876739 lbs/ft^2
After accelerating at a rate of 1000 km/sec^2 for 2 minutes, how fast is a spaceship traveling in light years/year? Respond with appropriate significant figures.
(assume no relativistic effects)
km/sec^2 * (minutes -> seconds) = km/sec
km/sec -> light years/sec -> light years/min -> light years/hr -> light years/day -> light years/year
1000 km/sec^2 * (2*60 seconds) =120000 km/sec
120000 * (1/(9.461*10^12)) * (60/1) * (60/1) * (24/1) * (365/1)
0.4 light years/year