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Solving for Significant Figures

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Please provide assistance with the following questions:

Which of the following has three significant figures?
a. 1.00081 kg
b. 8.060 x 1011 m
c. 0.0500 mm
d. 305.0 cm
(I think the correct answer is d)

Express 0.0015671 to three significant figures.
a. 0.002
b. 0.0016
c. 0.00156
d. 0.00157
(I think the correct answer is a).

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Solution Preview

Significant figures are a scientist's way of describing how precise a measurement is. When you take a math class, most people don't pay attention to the number of digits a measurement in a problem has. For example, in math 473 and 473.04 are just numbers you use to solve the problem. However, in any physical science, the number of digits reported with the measurement gives you vital information to how good the measuring instrument was. For example, with the 473, the person making the measurement had to "guess" on the three, meaning that there was some uncertainty in the last digit. In contrast with the 473.04, the uncertainty came with the 4 in the hundredths place, making the second measurement much more precise since it could be estimated to a smaller interval. The number of significant figures are the number of measured digits reported. In the first case above, 473 has three significant figures (labelled sf) while 473.04 has 5. The only problem with determining the number of significant figures in a measurement comes when you are dealing with the number zero. Zero is a problem because for many measurements it is necessary to be included so that you have an idea of the ...

Solution Summary

This solution provides a very detailed response which clearly explains the topic of significant figures and how to both read and record numbers accurately using this method of notation. This response is about 860 words.

See Also This Related BrainMass Solution

Density, Conversions and Significant Figures

1. a: A cube of osmium metal 1.500cm on a side has a mass of 76.31 g at 25*C. What is its density in g / cm3 at this temperature?

B: The density of titanium metal is 4.51 g / m3 at 25*C. What mass of titanium displaces 65.8 mL of water at 25*?

C: The density of bezene at 15 *C is 0.8787 g / mL. Calculate the mass of 0.1500 L of benzene at this temperature.

Solutions for a,b,c

A. g/cm3
B. g
C. g

2, A cylindrical rod formed from silicon is 16.8 cm long and has a mass of 2.17 kg. The density of silicon is 2.33 g / cm3. What is the diameter of the cylinder? (the volume of a cylinder is given by TTr2h, where r is the radius and h is its length.)



Question 3: Indicate the number of significant figures in each of the following measure quanties.

A: 3.7745km___________________________
B: 205 m2 ___________________________
C: 1.700cm____________________________
D: 350.0 K _____________________________
E: 307.080 g ___________________________

Question 4. Carry out the following conversions
A: 0.105 in_______________________________mm
B: 0.870 qt_______________________________mL
C: 9.75 um/s______________________________km/hr
D: 4.733 yd3_______________________________m3
E: $3.99/lb_________________________________dollars per kg
F 8.75 lb/ft3_________________________________g/ml


5. Carry out the following operations and express the answer with the appropriate number of signigicant figures.

A: 320.55 - (6104.5/2.3)

B: [(285.3 x 105) - (1.200) x 103] x 2.8954

C: (0.0045 x 20, 000.0) + (2813 x 12)

D: 863 x [1255 - (3.45 x 108)]

6.The concentration of carbon monoxide in an urban apartment is 48 ug/m3. What mass of a carbon monoxide in grams is present in a room measuring 9.0 x 14.5 x 18.8ft?




7. By using estimation techniques determine which of the following is the heaviest and which is the lightest.

Quantity Conversion factor(s) Conversion to grams

5-lb bag of potatoes g potatoes
5-kg bag of sugar g sugar
1 gal of water (density = 1.0g/ml) g water


8.The liquid substances mercury (density = 13.5 g / mL), water (1.00 g / ml ), and cyclohexane
(0.778 g / mL) don not form a solution when mixed, but separate in distinct layers. Sketch how the liquids would position themselves in a test tude.

Question 9. Small spheres of equal mass are made of lead (density = 11.3 g / m3),
Silver (10.5 g / m3) and aluminum (2.70 g / m3). Which sphere has the largest diameter and which has the smallest?

Lead (cm) Pb sphere
Silver (cm) Pb sphere
Aluminum (cm) Pb sphere


Question 10. Automobile batteries contain sulfuric acid, which is commonly referred to as "batter acid". Calculate the number of grams of sulfuric acid in 0.500 L of battery acid if the solution has a density of 1.28 g / mL and is 38.1% sulfuric acid by mass.

________________________________________________ g H2SO4 ( . 5L)

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