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What are significant figures (sig figs)?
Digits in a measurement that show its precision, including certain zeros.
What is the rule for nonzero digits?
All nonzero digits (1–9) are significant.
What is the rule for zeros between nonzero digits?
Zeros between nonzero digits are significant.
What are leading zeros?
Zeros before the first nonzero digit; they are NOT significant.
What is the rule for trailing zeros after a decimal point?
They ARE significant.
What is the rule for trailing zeros in a whole number without a decimal point?
They are usually not significant unless otherwise indicated.
How many significant figures are in 0.048?
2 significant figures.
How many significant figures are in 28.09200?
7 significant figures.
How many significant figures are in 289000?
Usually 3 significant figures.
How many significant figures are in 25.000?
5 significant figures.
How many significant figures are in 0.00672000?
6 significant figures.
How many significant figures are in 20500?
Usually 3 significant figures.
How many significant figures are in 0.3001?
4 significant figures.
How many significant figures are in 6000?
Usually 1 significant figure.
How do you round to a certain number of significant figures?
Start at the first nonzero digit, count the required digits, and use the next digit to decide whether to round.
Round 3.682417 to 3 significant figures.
3.68
Round 21.860051 to 3 significant figures.
21.9
What sig fig rule is used for addition and subtraction?
Round the final answer to the same number of decimal places as the measurement with the fewest decimal places.
What sig fig rule is used for multiplication and division?
Round the final answer to the same number of significant figures as the measurement with the fewest significant figures.
Calculate 6.201 + 7.4 + 0.68 + 12.0 using sig fig rules.
26.3
Calculate 1.31 × 2.3 using sig fig rules.
3.0
Why are significant figures important?
They show the precision of measurements and prevent answers from implying more precision than the data supports.
What is a measurement?
A value that describes a quantity using a number and a unit, with some degree of uncertainty.
What are the three parts of a measurement?
Magnitude, unit, and uncertainty/error.
What is magnitude?
The numerical value of a measurement.
What is a unit?
A standard used to describe or measure a quantity.
What is uncertainty in a measurement?
The estimated range within which the actual value may lie.
What does HAV stand for?
Highest Acceptable Value.
How do you calculate HAV?
Measured value + error.
What does LAV stand for?
Lowest Acceptable Value.
How do you calculate LAV?
Measured value − error.
What does RAV mean in these notes?
The range of acceptable values between the LAV and HAV.
A measurement is 34.56 m ± 0.02 m. What is the HAV?
34.58 m.
A measurement is 34.56 m ± 0.02 m. What is the LAV?
34.54 m.
A measurement is 34.56 m ± 0.02 m. What is the acceptable range?
34.54 m to 34.58 m.
What is the SI base unit for length?
Meter (m).
What is the SI base unit for mass?
Kilogram (kg).
What is the SI base unit for time?
Second (s).
What is the SI base unit for temperature?
Kelvin (K).
What is the SI base unit for amount of substance?
Mole (mol).
What is the SI base unit for luminous intensity?
Candela (cd).
What is the SI base unit for electric current?
Ampere (A).
What are derived units?
Units made by combining base units.
What is an example of a derived unit for speed?
Meters per second (m/s).
What is an example of a derived unit for area?
Square meters (m²).
What is an example of a derived unit for acceleration?
Meters per second squared (m/s²).
What is an example of a derived unit for density?
Kilograms per cubic meter (kg/m³).
What does kilo- mean?
1,000 or 10³.
What does mega- mean?
1,000,000 or 10⁶.
What does giga- mean?
1,000,000,000 or 10⁹.
What does deci- mean?
0.1 or 10⁻¹.
What is scientific notation?
A way to write numbers as a value from 1 up to, but not including, 10 multiplied by a power of 10.
Write 300,000 in scientific notation.
3.0 × 10⁵.
Write 0.0004 in scientific notation.
4 × 10⁻⁴.
What happens to exponents when multiplying powers of 10?
Add the exponents.
What happens to exponents when dividing powers of 10?
Subtract the denominator's exponent from the numerator's exponent.
How do you add or subtract numbers in scientific notation?
Write them with the same power of 10, then add or subtract the coefficients.
What is matter?
Anything that has mass and takes up space.
What are examples of things that are not matter?
Sound, light, heat, shadows, and energy.
What is a physical property?
A characteristic that can be observed or measured without changing a substance into a different substance.
What is a chemical property?
A characteristic describing a substance's ability to undergo a chemical change.
What is a physical change?
A change in form or state that does not create a new substance.
What is a chemical change?
A change that produces one or more new substances.
Is melting ice a physical or chemical change?
Physical change.
Is rusting iron a physical or chemical change?
Chemical change.
What are the four states of matter covered in these notes?
Solid, liquid, gas, and plasma.
What is a solid?
A state of matter with a definite shape and definite volume.
What is a liquid?
A state of matter with a definite volume but no definite shape.
What is a gas?
A state of matter with no definite shape or definite volume.
What is plasma?
An energized state of matter containing charged particles.
What is an intensive property?
A property that does not depend on the amount of substance.
What are examples of intensive properties?
Density, temperature, color, and melting point.
What is an extensive property?
A property that depends on the amount of substance.
What are examples of extensive properties?
Mass, volume, and total amount of matter.
What can affect the state of matter?
Changes in temperature and pressure.
At what temperature does water boil at 1 atmosphere of pressure?
100°C.
What does STP stand for?
Standard Temperature and Pressure.
What is solubility?
The ability of a substance to dissolve in another substance.
Which substances can dissolve in water: salt, sugar, or sand?
Salt and sugar dissolve; sand does not appreciably dissolve.
What is a pure substance?
Matter with a fixed composition and characteristic properties.
What are examples of pure substances?
Water (H₂O), oxygen (O₂), and iron (Fe).
What is a mixture?
A combination of substances that are physically combined rather than chemically bonded into one pure substance.
What is a homogeneous mixture?
A mixture with a uniform composition throughout.
What are examples of homogeneous mixtures?
Saltwater, air, vinegar, and brass.
What is a heterogeneous mixture?
A mixture that does not have a uniform composition throughout.
What are examples of heterogeneous mixtures?
Salad, oil and water, and sand in water.
What is an element?
A pure substance made of one type of atom.
What is a compound?
A substance made of two or more different elements chemically bonded in a fixed ratio.
What is the difference between an element and a compound?
An element contains one type of atom; a compound contains different elements chemically bonded together.
What is density?
Mass per unit of volume.
What is the formula for density?
D = m ÷ V.
What does D stand for in the density formula?
Density.
What does m stand for in the density formula?
Mass.
What does V stand for in the density formula?
Volume.
What are common units for density?
g/mL, g/cm³, and kg/m³.
How do you calculate volume of a rectangular object?
Length × width × height.
How do you calculate volume using water displacement?
Final water volume − initial water volume.
What is water displacement used for?
Finding the volume of an object by measuring how much the water level rises.
An object has a mass of 20 g and a volume of 5 mL. What is its density?
4 g/mL.
The water level rises from 56.9 mL to 67.8 mL. What is the object's volume?
10.9 mL.