Chapter 2 Measurements and Calculations (Video) - Practice Flashcards

50 practice flashcards covering key concepts from Sections 2.1–2.8 (Scientific Notation, SI Units, Length/Volume/Mass, Uncertainty and Significant Figures, Dimensional Analysis, Temperature Conversions, Density).

What is measurement?

Measurement is a quantitative observation that involves using numbers and units to describe the attributes of an object or event. For example, stating that a table is 2 meters long is a measurement.

In a measurement, what does the number tell you?

In a measurement, the number indicates the magnitude or quantity of what is being measured, providing a numerical value to the observation. For instance, in the measurement '5 kg,' the number '5' quantifies the mass.

In a measurement, what does the unit tell you?

In a measurement, the unit specifies the standard scale used for measuring a quantity, providing context and meaning to the numerical value. For example, 'meters' in '10 meters' indicates that length is measured against the standard meter.

What is scientific notation?

Scientific notation is a method of expressing very large or very small numbers as a product of a number between 1 and 10 and a power of 10, making it easier to handle and compare such numbers. For example, 0.000003 can be written as 3 × 10^{-6}.

How is the power of 10 determined in scientific notation?

The power of 10 in scientific notation is determined by the number of places the decimal point must be moved to convert the number into a form where only one non-zero digit is to the left of the decimal point. Moving the decimal to the left results in a positive exponent, while moving it to the right results in a negative exponent.

If the decimal point is moved to the left in scientific notation, what is the exponent sign?

When expressing a number in scientific notation, if the decimal point is moved to the left, the exponent of 10 is positive. This indicates that the original number was larger than the coefficient (the number between 1 and 10) and was divided by a power of 10 to get the coefficient.

If the decimal point is moved to the right, what is the exponent sign?

In scientific notation, if the decimal point is moved to the right, the exponent of 10 is negative, indicating the number is less than 1. This means that the original number was smaller than the coefficient and was multiplied by a power of 10 to get the coefficient.

Express 345 in scientific notation.

To express 345 in scientific notation, you move the decimal point two places to the left, resulting in 3.45 × 10^2.

Express 0.0671 in scientific notation.

To express 0.0671 in scientific notation, you move the decimal point two places to the right, resulting in 6.71 × 10^{-2}.

Which expression correctly expresses 7,882 in scientific notation?

The correct expression of 7,882 in scientific notation is 7.882 × 10^3, showing that the decimal point is moved three places to the left.

Which expression correctly expresses 0.0000496 in scientific notation?

The correct expression of 0.0000496 in scientific notation is 4.96 × 10^{-5}, achieved by moving the decimal point five places to the right.

What is the SI base unit for mass?

The kilogram (kg) is the SI base unit for mass, defined as the mass of the international prototype kept at the Bureau International des Poids et Mesures (BIPM).

What is the SI base unit for length?

The meter (m) is the SI base unit for length, defined as the distance light travels in a vacuum in 1/299,792,458 of a second.

What is the SI base unit for time?

The second (s) is the SI base unit for time, defined based on the cesium-133 atom's radiation period.

What is the SI base unit for temperature?

The kelvin (K) is the SI base unit for temperature, where zero kelvin is defined as absolute zero, and the size of one kelvin is the same as one degree Celsius.

What is the SI base unit for electric current?

The ampere (A) is the SI base unit for electric current, defined by the force between electrical conductors.

What is the SI base unit for amount of substance?

The mole (mol) is the SI base unit for the amount of substance, defined as containing exactly 6.02214076 × 10^{23} elementary entities.

What is the fundamental SI unit for length?

The meter is the fundamental SI unit for measuring length, serving as the basis for deriving other units such as square meters for area and cubic meters for volume.

What is the SI unit for volume in the metric system?

In the metric system, the SI unit for volume is the cubic meter (m^3), but it is commonly measured in liters (L), where 1 L is defined as the volume of 1 kilogram of water at its maximum density and 1 mL equals 1 cm^3.

Is 1 L equal to 1 dm^3?

Yes, 1 liter (L) is equal to 1 cubic decimeter (dm^3), both representing the same volume in the metric system. This equivalence simplifies calculations involving volumes in chemistry and physics.

Is 1 mL equal to 1 cm^3?

Yes, 1 milliliter (mL) is equal to 1 cubic centimeter (cm^3); this identity is frequently used in scientific measurements, especially when dispensing small volumes of liquids.

What is the purpose of prefixes in the metric system?

Prefixes in the metric system are used to scale the base units by powers of ten, making it easier to express quantities that are much larger or smaller than the base unit. For example, 'kilo-' means 1000, so 1 kilometer is 1000 meters.

What is an example of an exact number?

An exact number is a value that is known with complete certainty because it is defined or counted rather than measured. For example, there are exactly 12 inches in a foot, so '1 foot = 12 inches' is an exact relationship.

What is the mass in pounds of 1 kilogram?

1 kilogram is approximately equal to 2.2046 pounds. This conversion factor is commonly used when converting mass from the metric system to the imperial system.

What is the mass in grams of 1 pound?

One pound is approximately equal to 453.59 grams. This conversion factor is useful for converting weights from the imperial system to the metric system.

Are leading zeros in a number always significant?

No, leading zeros, which appear to the left of the first non-zero digit in a number, are not considered significant because they only serve to indicate the position of the decimal point and do not add to the precision of the measurement. For instance, in 0.0025, the leading zeros are not significant.

Are captive zeros significant?

Yes, captive zeros, which are zeros located between nonzero digits, are always significant because they indicate that the quantity has been measured to that decimal place. For example, in the number 2005, both zeros are significant.

When are trailing zeros significant?

Trailing zeros are significant only if the number contains a decimal point. If there is no decimal point, trailing zeros are generally assumed not to be significant. For example, 25.00 implies that the measurement was precise to the hundredths place, making the zeros significant.

What is the advantage of using exponential notation?

Exponential notation provides a clear way to express the number of significant figures in a number and simplifies the expression of very large or very small numbers, preventing confusion about the precision of the measurement.

What is an example of a number written in exponential notation and its significant figures?

For example, writing the number 300 as 3.00 × 10^2 explicitly indicates that there are three significant figures. Without the exponential notation, it would be unclear whether the trailing zeros are significant.

What is Rule 1 for rounding off?

Rule 1 for rounding states that if the digit immediately following the last significant digit is less than 5, the last significant digit remains the same. However, if the digit is 5 or greater, the last significant digit is increased by 1.

Give examples of Rule 1 rounding.

As an example of Rule 1 rounding, 5.64 rounds to 5.6 because the 4 is less than 5, and 5.68 rounds to 5.7 because the 8 is greater than 5.

What is Rule 2 for rounding off?

Rule 2 for rounding states that in a series of calculations, carry extra digits through to the final result and then round off the final answer. This avoids the accumulation of rounding errors that can occur if you round off intermediate results.

In multiplication or division, how many significant figures determine the result?

In multiplication or division, the result should be rounded to the same number of significant figures as the factor with the fewest significant figures. This ensures that the answer does not imply a precision greater than that of the least precise measurement used in the calculation.

In addition or subtraction, what determines the precision of the result?

In addition or subtraction, the precision of the result is determined by the term with the smallest number of decimal places. The final answer should be rounded to the same number of decimal places as the number with the fewest decimal places.

What is the result of 1.342 × 5.5 when rounded to two significant figures?

The multiplication of 1.342 by 5.5 yields 7.381. When this result is rounded to two significant figures, it becomes 7.4.

How do you measure the volume of a solid by water displacement?

To measure the volume of a solid by water displacement, you record the initial volume of water in a graduated cylinder, carefully submerge the solid, and then measure the new volume. The volume of the solid is the difference between the final and initial volumes.

What is density?

Density is defined as mass per unit volume, which describes how much mass is contained in a given volume. It is commonly expressed in grams per cubic centimeter (g/cm³) or grams per milliliter (g/mL).

What units are commonly used for density?

Common units used for density include grams per cubic centimeter (g/cm^3) for solids, grams per milliliter (g/mL) for liquids, and grams per liter (g/L) for gases. These units help express density in appropriate scales relative to the substance being measured.

What density would a mineral have if it has mass 17.8 g and volume 2.35 cm^3?

If a mineral has a mass of 17.8 g and a volume of 2.35 cm^3, its density would be 7.57 g/cm³, calculated by dividing the mass by the volume: \frac{17.8 g}{2.35 cm^3}.

What is the mass of a 49.6 mL sample with density 0.85 g/mL?

If a sample has a volume of 49.6 mL and a density of 0.85 g/mL, its mass would be 42.16 g, determined by multiplying the volume by the density: 49.6 mL × 0.85 g/mL.

If an object has a mass of 243.8 g and a volume of 0.125 L, what is its density in g/cm^3?

If an object has a mass of 243.8 g and a volume of 0.125 L, to find its density in g/cm³, first convert liters to cubic centimeters (1 L = 1000 cm³), then divide the mass by the volume. The density is 1.95 g/cm^3.

When 75.0 g of copper is added to 50.0 mL of water, what is the volume reading after displacement?

Since copper has a density of approximately 8.96 g/mL, adding 75.0 g of copper to 50.0 mL of water will displace ~8.4 mL of water (75.0 g/8.96 g/mL). Therefore, the new volume reading will be approximately 58.4 mL.

What are the steps in dimensional analysis?

Dimensional analysis involves using conversion factors to convert from one unit to another. The steps include identifying the given units and the desired units, setting up the conversion factors, canceling out units that appear in both the numerator and denominator, and performing the calculations to obtain the result in the desired units.

What is a typical conversion factor used to convert feet to inches?

A conversion factor used to convert feet to inches is 1 foot = 12 inches. This relationship allows you to easily convert measurements in feet to inches by multiplying the number of feet by 12.

What are the three temperature scales mentioned?

The three temperature scales commonly used are Fahrenheit, Celsius, and Kelvin. Fahrenheit and Celsius are relative scales, while Kelvin is an absolute scale with its zero point at absolute zero.

What is the Kelvin equivalent of 102°F (dog body temperature)?

The Kelvin equivalent of 102°F, a typical body temperature for dogs, is approximately 312 K. This is calculated by first converting Fahrenheit to Celsius and then Celsius to Kelvin, using the formulas °C = \frac{5}{9}(°F - 32) and K = °C + 273.15.

What temperature corresponds to the point where °C equals °F?

-40°C is equal to -40°F, which is based on the conversion formula linking the Celsius and Fahrenheit scales: °F = \frac{9}{5}°C + 32.

What is the density formula?

The density formula is Density = \frac{mass}{volume}, illustrating that density is calculated by dividing the mass of a substance by its volume. This formula is fundamental in physics and chemistry for characterizing substances.

What is the main purpose of measurement units in science?

Measurement units in science standardize quantities, allowing scientists around the world to communicate results effectively and ensuring that findings can be replicated accurately. Standardization is crucial for the integrity and reliability of scientific research.