Measurement
How is quantity measured?
Quantity is measured by comparing the object measured to quantity in another object, called the unit.
(A measurement is a number, how many times the unit fits into the object, and a unit, the thing used to measure.)
Is the range 500 ft–800 ft or 574 ft–578 ft more precise?
574 ft–578 ft, since it is a smaller range.
(More precise does not mean more accurate.)
How many significant figures are in 240?
2
12.1 m + 3.27 m
15.4 m
(Adding follows the least precise decimal place. 12.1 is precise to 0.1, so 15.37 m rounds to 15.4 m.)
Suppose a desk is 7 pencils high. If 1 pencil is 6 inches, how many inches high is the desk?
42 in
(7 pencils = 7 (6 in) = 42 in)
Which is most precise: 3,000,000. mm, 300,000. cm, 3000. m, or 3 km?
3,000,000. mm
(All allow deviation in the 1s place, but 1 mm is the smallest deviation.)
What do significant figures show?
The precision of a measurement or calculated value.
(All else being equal, more significant figures means more precision.)
A table is 4.2 m long and 3.05 m wide. What is its area?
13 m²
(Multiplying follows the fewest significant figures. 4.2 has 2 and 3.05 has 3, so A = (4.2 m)(3.05 m) = 12.81 m2 = 13 m2 (rounding to 2 SF).)
What is the difference between quantity and quality?
Quantity can be divided, but quality cannot.
(Quality exists wholly in every part of a substance, but some quantity is here and some is there.)
How are systematic and random error eliminated?
Systematic error is reduced by changing the measurement setup, and random error by averaging many measurements.
How many significant figures are in 3030.?
4
(The right 0 counts because it’s the rightmost digit and there’s a decimal point.)
A hiker walks 2.50 km, then another 850 m. What is the total distance in kilometers?
3.35 km
(850 m = 0.85 km (2 SF, 0.01 place)
2.50 km + 0.85 km = 3.35 km (already 0.01 place, so stays the same))
How is the intensity of a quality measured?
The change in the intensity of a quality must be connected to some change in a quantity, and measuring the quantity gives information about the quality.
(A unit of quality is a change that produces a regular change in the connected quantity.)
The true value is 95 km. Which range is both accurate and precise compared to the others: 84–101 km, 96–98 km, or 93–96 km?
93–96 km
(84–101 km is imprecise and 96–98 km is inaccurate. Technically, accuracy means the true value is close to the middle of the range, not just that it is within the range.)
How many significant figures are in 0.090050?
5
(The leading zeros are insignificant. The middle 0s are between significant figures, and the final 0 is the rightmost digit after the decimal.)
A room is 4.20 m wide and (6.5 m - 82 cm) long. What is its area in m²?
Answer: 24 m²
(6.5 m - 0.82 m = 5.68 m (should be in 0.1 place, so 2 SF)
A = (4.20 m)(5.68 m) = 23.856 m2 = 24 m2 (rounding at the end to 2 SF from 5.68 m))