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Multiplication and division with significant figures

Rule: When we multiply or divide numbers, we should round the result to the same number of digits as the number with the least number of significant figures (the least precise value in terms of multiplication and division).

(a) Multiply 0.6238 cm by 6.6 cm.

(b) Divide 421.23 g by 486 mL.

Solution

(a) 0.6238 cm × 6.6 cm = 4.11708 cm 2 result is 4.1 cm 2 ( round to two significant figures ) four significant figures × two significant figures two significant figures answer

(b) 421.23 g 486 mL = 0.86728... g/mL result is 0.867 g/mL ( round to three significant figures ) five significant figures three significant figures three significant figures answer

Check your learning

(a) Multiply 2.334 cm and 0.320 cm.

(b) Divide 55.8752 m by 56.53 s.

Answer:

(a) 0.747 cm 2 (b) 0.9884 m/s

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In the midst of all these technicalities, it is important to keep in mind the reason why we use significant figures and rounding rules—to correctly represent the certainty of the values we report and to ensure that a calculated result is not represented as being more certain than the least certain value used in the calculation.

Calculation with significant figures

One common bathtub is 13.44 dm long, 5.920 dm wide, and 2.54 dm deep. Assume that the tub is rectangular and calculate its approximate volume in liters.

Solution

V = l × w × d = 13.44 dm × 5.920 dm × 2.54 dm = 202.09459 ... dm 3 ( value from calculator ) = 202 dm 3 , or 202 L ( answer rounded to three significant figures )

Check your learning

What is the density of a liquid with a mass of 31.1415 g and a volume of 30.13 cm 3 ?

Answer:

1.034 g/mL

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Experimental determination of density using water displacement

A piece of rebar is weighed and then submerged in a graduated cylinder partially filled with water, with results as shown.

This diagram shows the initial volume of water in a graduated cylinder as 13.5 milliliters. A 69.658 gram piece of metal rebar is added to the graduated cylinder, causing the water to reach a final volume of 22.4 milliliters

(a) Use these values to determine the density of this piece of rebar.

(b) Rebar is mostly iron. Does your result in (a) support this statement? How?

Solution

The volume of the piece of rebar is equal to the volume of the water displaced:

volume = 22.4 mL 13.5 mL = 8.9 mL = 8.9 cm 3

(rounded to the nearest 0.1 mL, per the rule for addition and subtraction)

The density is the mass-to-volume ratio:

density = mass volume = 69.658 g 8.9 cm 3 = 7.8 g/cm 3

(rounded to two significant figures, per the rule for multiplication and division)

From [link] , the density of iron is 7.9 g/cm 3 , very close to that of rebar, which lends some support to the fact that rebar is mostly iron.

Check your learning

An irregularly shaped piece of a shiny yellowish material is weighed and then submerged in a graduated cylinder, with results as shown.

This diagram shows the initial volume of water in a graduated cylinder as 17.1 milliliters. A 51.842 gram gold colored rock is added to the graduated cylinder, causing the water to reach a final volume of 19.8 milliliters

(a) Use these values to determine the density of this material.

(b) Do you have any reasonable guesses as to the identity of this material? Explain your reasoning.

Answer:

(a) 19 g/cm 3 ; (b) It is likely gold; the right appearance for gold and very close to the density given for gold in [link] .

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Accuracy and precision

Scientists typically make repeated measurements of a quantity to ensure the quality of their findings and to know both the precision    and the accuracy    of their results. Measurements are said to be precise if they yield very similar results when repeated in the same manner. A measurement is considered accurate if it yields a result that is very close to the true or accepted value. Precise values agree with each other; accurate values agree with a true value. These characterizations can be extended to other contexts, such as the results of an archery competition ( [link] ).

Questions & Answers

what is d meaning of organic chemistry
Elizabeth Reply
it's a compound that comprises of hydrocarbon
Omoru
what iz alkanol
icha Reply
alkanol there are organic compounds with the functional group of ROH and relative molecular formula (CnH2n+1+OH)
Omoru
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icha
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Sam. A
frbsaz
What's alkaline soil
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a system in which only energy is transferred between the system and the surrounding is called?
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which Element exhibit diagonal relationship with aluminum
Ani
following processes: Solid phosphorus pentachloride decomposes to liquid phosphorus trichloride and chlorine gas b. Deep blue solid copper(II) sulfate pentahydrate is heated to drive off water vapor to form white solid copper(II) sulfate
Hisham Reply
Ssskma
frbsaz
How to know periodic table oftend
Ahmed Reply
u can know it through singing it as song it simple
Elizabeth
how to get atomic number of an element
Ogunleye Reply
how do you solve the examples in a much more explanatory way
Ogunleye
it seems by multiplying d number of d element by 2
Elizabeth
E.g like carbon 6*2=12 so d atomic number is 12
Elizabeth
The reaction of aceto nitrile with propane in the presence of the acid
Sskma
frbsaz
Explain this paragraph in short
Manish Reply
What is solid state?
Manish Reply
What is chemical reaction
Manish
transforming reactants to product(s)
Andre
process
Andre
solid state is composed of tightly particles and it has a definite shape and volume
Elizabeth
Example of Lewis acid
Chidera Reply
Example of Lewis acid
Chidera
Chlorine
Mikidad
Anything with an empty orbital... the hydrogen ion is the most common example. BH3 is the typical example, but any metal in a coordination complex can be considered a Lewis acid.
Eszter
okay thanks
Jovial
aluminium and sulphur react to give aluminium sulfide.How many grams of Al are required to produce 100g of aluminium sulphide
Soni Reply
aluminium and sulphur react to give aluminium sulphide how many grams of Al are required to produce 100g of aluminium sulphide?
Soni
aluminium and sulphur react to give aluminium sulphide how many grams of Al are required to produce 100g of aluminium sulphide?
Soni
2Al+3S=Al2S3
galina
m(Al)=100×27×2/150=36g
galina
150 comes from?
Soni
thank you very much
Soni
molar mass of Al2S3
galina
150.158
thiru
what's periodic table
Agnes
Why can't atom be created or destroyed
Jacaranda Reply
matter simply converts to pure energy
that's nice
Meshach
explain how to distinguish ethanol from a sample of ethanoic acid by chemical test
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explain how ethanol can be distinguished from ethanoic acid by chemical test
Alice
Using a suitable experiment, describe how diffusion occurs in gases.
Melody Reply
when the excited energy which are in gaseous state collides with another to liberate from one place to another
Meshach
Practice Key Terms 6

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Source:  OpenStax, Chemistry. OpenStax CNX. May 20, 2015 Download for free at http://legacy.cnx.org/content/col11760/1.9
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