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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

who are the alchemist?
Victor Reply
alchemy science of transmutation. typically it is aim at tranforming lead to or other base metals to gold and the creation of the philosophers stone which in reality isn't a stone it's something priceless something we all need for coming times. don't be fooled
Kendrick
read Corinthians 5 verses 50 to the end of the chapter then read revelations chapter 2 verse 17
Kendrick
The word "Alchemy" comes from the forgotten name for Ancient Egypt, Khemmet. Khem was the name for the Egyptian Empire, but the actual land of Egypt was called Khemmet because the "T" on the end of a word denoted a physical location on Earth and not just an idea.
Michael
What's the mass number of carbon
Charlie Reply
first Faraday's law
Akinbola
mass number of carbon is 12.
Nnenna
wat d atomic number of oxygen
safiya
atomic number of oxygen is 8
Nnenna
which quantum number divides shell into orbitals?
Tomiwa Reply
azimuthal
Emmanuel
hi
Charlie
azimuthal
reinhard
azimuthal
Charlie
what is atom
Desmond Reply
an atom is a smallest indivisible part of an element
Henry
an atom is the smallest part of an element that takes part in a chemical reaction
Nana
wat is neutralization
Dubem Reply
when any acid reacts with base to decrease it's acidity or vice-versa to form salt and solvent.. which is called neutralization
Santosh
explain buffer
Organic
buffer is a solution which resists changes in pH when acid or alkali added to it..
Santosh
hello, who is online
UTHMAN
buffer is the solution which resist the change in pH by addition of small amount of acid or alkali to it
KAUSIK
neutralisation is the process of mixing of a acid and a base to form water and corresponding salt
KAUSIK
how to solve equation on this
Princewill Reply
what are the elent of ionic and covalent bonding
Princewill
what is gases
Wesike Reply
Its one of the fundamental sate of matter alone side with liquid, solid and plasma
John
What is chemical bonding
John
To my own definitions. It's a unit of measurement to express the amount of a chemical substance.
Ozoaniehe Reply
What is mole
TAMIL Reply
It's the unit of measurements used to express the amount of chemical substance.
Ozoaniehe
What is pressure
Stellamaris Reply
force over area
Jake
force applied per unit area
john
force applied per unit area
Prajapati
Why does carbonic acid don't react with metals
Aditya Reply
Why does carbonic acid don't react with metal
Aditya
Some metals will react depending on their Standard Electrode Potential. Carbonic acid is a very weak acid (i.e. a low hydrogen ion concentration) so the rate of reaction is very low.
Paul
sample of carbon-12 has a mass of 6.00g. How many atoms of carbon-12 are in the sample
Emokiniovo Reply
a sample of carbon-12 has a mass of 6.00g. How many atoms of carbon-12 are in the sample
Sharmin Reply
an object of weight 10N immersed in a liquid displaces a quantity of d liquid.if d liquid displaced weights 6N.determine d up thrust of the object
ugonna Reply
how human discover earth is not flat
Jason Reply
We don't fall off. If set off in any direction in a straight line and keep going. You'll end up back where you started.
Adelle
earth is spherical
Unique
Also, every other planet is spherical as that is the most energy efficient shape. gravity pulls equally on all areas. Sphere.
Adelle
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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