1.4 Measurements

The periodic table shows how elements are grouped.

The background color indicates whether an element is a metal, metalloid, or nonmetal, while the element symbol color indicates whether it is a solid, liquid, or gas.

You will be able to describe the process of measurement, identify the three basic parts of a quantity, and perform basic unit calculations by the end of this section.

The size or magnitude of the measurement, a standard of comparison for the measurement, and an indication of the uncertainty of the measurement are provided by every measurement.
Uncertainty is an aspect of the measurement result that is more implicit and will be discussed later.

The number can be represented in a variety of ways.

The maximum takeoff weight of a plane is 298,000 kilograms, which can be written as 2.98 x 105 kilograms.

The average mosquito has a mass of about 25 kilograms.

When we buy a bottle of soft drink, we expect it to be two times larger than the one that everyone agrees to be 1 liter.

A 0.25-pound hamburger weighs onefourth as much as 1 pound because it is measured.
Without units, a number can be meaningless.

Suppose a doctor prescribes phenobarbital to control a patient's seizures and states a dosage of 100 without specifying units.

A single dose of 100 g is more than 10 times the lethal amount and will be confusing to the medical professional who is giving it.

The units listed in Other units can be used to derive the results of scientific measurements in SI units, an updated version of the metric system.

The United States National Institute of Standards and Technology has used SI units since 1964.

Some units are fractions or multiples of a base unit.

quarts, pints, or gallons are the base units for ice cream.
The SI system uses fractions or multiples of units, but they are always powers of 10.
The base unit is used to name Fractional or multiple SI units.
The powers to which 10 are raised are listed in Table 1.3.

This is where you can learn the basics of scientific notation.

The initial units of the metric system were established in France during the French Revolution.

The original standards for the kilogram and the meter were adopted by other countries.
The SI base units are commonly used in chemistry.
In the future, other SI units will be introduced.

The distance from the North Pole to the equator was originally specified as one millionth of a mile.

The distance light in a vacuum travels in less than one second.
A meter is about 3 inches longer than a yard.
Longer distances can be reported in kilometers, while shorter distances can be reported in centimeters or millimeters.

The original definition of a kilogram was a cube of water with an edge length of 0.1 meters.

Any object with the same mass as this cylinder is said to have a mass of 1 kilogram.
A kilogram is 2.2 pounds.
The gram is the same as the mass of the kilogram.

The National Institute of Standards and Technology in Maryland houses a replica prototype kilogram.

It is an intensive property.

The word kelvin is used for the word, K for the unit symbol, and the degree symbol is not used.
The two scales place their zeros in different places, but Celsius degrees are the same magnitude as kelvin.
The normal human body temperature is approximately 310 K (37 degC), and water and boil at 373.15 K (100 degC) by definition.
The conversion between these two units and This OpenStax book is free at http://cnx.org/content/col11760/1.9 the Fahrenheit scale will be discussed later in this chapter.

3 microseconds is 0.000003 s, 10 megaseconds is 5,000,000 s, and 5 megaseconds is 106 s.

Hours, days, and years can be used.

The seven SI base units can be used to derive many units.

The base units of mass and length can be used to define a unit of density.

We could build a box with the edge lengths of a single meter.

The box would hold a meter of water.

The decimeter is used to derive a unit of volume.

A cube with edge lengths of exactly one decimeter has a volume of one decimeter.
A liter is about 1.06 quarts.

Mass and volume are used to determine density.

The units of density are determined by the base units of mass and length.

The kilogram per m3 is the SI unit for density.

We often use grams per cm3 for densities of liquids and gases, and grams per liter for gases, because this is an inconvenient unit.

The density of gasoline is 0.7 g/ cm3 and the density of gold is 19 g/ cm3.

The air density is 1.2 g/L.
The densities of some substances are shown in the table.

The most straightforward way to determine the density of an object is to separate the mass and volume of the object and then divide it by the volume.

The mass is found directly by weighing, but the volume is found indirectly through length measurements.

For hundreds of years gold has been a form of currency.

People have considered filling the centers of hollow gold bricks with lead to fool buyers into thinking that the entire brick is gold.
Lead is a dense substance, but it is not as dense as gold.

The density of a substance can be determined by dividing its mass by its volume.

The edge length is used to calculate the cube's volume.

The density of wood, ice, brick, and aluminum can be explored by using the interactive simulator.

This simulation shows how to determine density using displacement of water.

Determine the density of the blocks.

When you open the density simulation and select Same Mass, you can choose from several colored blocks that you can drop into a tank of water.

The yellow block floats and the water level goes up to 105.00 L. The water level goes up to 101.25 L when the red block sinks because it is more dense than water.

Since the yellow block is not completely submerged, you cannot determine the density of the red block.

Put the green block in the middle of the tank after removing the blocks from the water.

Determine the density of the block.

By the end of this section, you will be able to define accuracy and precision, Distinguish exact and uncertain numbers, Correctly represent uncertainty in quantities using significant figures, and apply proper rounding rules to computed quantities.

The numbers are exact.
By definition, 1 foot is exactly 12 inches, 1 inch is 2.54 centimeters, and 1 gram is zero grams.
Due to practical limitations of the measurement process used, the quantities derived from measurements other than counting are uncertain to varying extents.

The numbers of measured quantities are not exact.

The lowest point on the curved surface of the liquid should be read to measure the volume of liquid in a graduated cylinder.

If you want to measure the volume of liquid in this graduated cylinder, you have to divide the distance between the 21 and 22 marks into tenths of a liter.

A reasonable estimate of the liquid's volume is possible with the help of the OpenStax book at http://cnx.org/content/col11760/1.9 be 21.6 The digits 2 and 1 are certain, but the 6 is an estimate.

Some people think the tenth-place digit is 5, while others think it's 7 and think it's closer to the 22-mL mark.
It would be pointless to estimate a digit for the hundredths place, since the tenths-place digit is uncertain.
Measurement to one-tenth of the smallest scale division is possible with numerical scales such as the one on this graduated cylinder.
The scale has 1mL divisions, so volumes can be measured to the nearest 0.1 mL.

Even if you don't make an estimate, this concept still holds true.

You can get a reading of 6.72 g if you put a quarter on a balance.
The quarter's mass may be between 6.722 and 6.724 grams.
If you stand on a scale that shows weight to the nearest pound, the 1 (hundreds), 2 (tens) and 0 (ones) are all significant values.

All the digits in the result are significant when you make a measurement.

All nonzero digits are significant, and only zeros require some thought.
We will use the terms "leading," "trailing," and "captive" for the zeros and will consider how to deal with them.

The first nonzero digit on the left should be counted along with the rest of the digits.

Unless the last digit is a trailing zero, this is the number of significant figures in the measurement.

Captive zeros are always significant because of their measurement.

The leading zeros tell us where the decimal point is.

The leading zeros are not significant.

We could express the number as 8.32407 x 10-3 and then use 10-3 to locate the decimal point, as described in Appendix B.

There is a zero to the left of the decimal point location in a number that ends with significant figures.

The essential ideas decimal point is located in the first chapter.

The ambiguity can be solved with the use of exponential notation: 1.3 x 103, 1.30 x 103, or 1.300 x 103.
If only the decimal-formatted number is available, it is wise to assume that all trailing zeros are insignificant.

When determining significant figures, be sure to pay attention to reported values and think about the measurement and significant figures in terms of what is reasonable or likely.

The resident population of the US was reported in the January census.
People are constantly being born, dying, or moving into or out of the country, and assumptions are made to account for the large number of people who are not actually counted.
It's reasonable to think that we know the population to within a million or so, in which case the population should be reported as 3.17 x108 people.

Results from a measurement are at least as uncertain as the measurement itself.

We have to take the uncertainty in our measurements into account.

When we add or subtract numbers, we should round the result to the same number of decimal places as the number with the least number of decimal places.

We should round the result to the same number of digits as the number with the least significant figures in terms of multiplication and division.

If we round up or down, we get an even value for the retained digit.

Let's work through the rules with a few examples.

When we add or subtract numbers, we should round the result to the same number of decimal places as the number with the least number of decimal places.

The rule is that we should round the result to the same number of digits as the number with the least significant figures.

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 bathtub is long, wide, and deep.

If the tub is rectangular, you can calculate its volume in liters.

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

The density of iron is close to that of rebar, which supports the fact that it is mostly iron.

An irregularly shaped piece of a shiny yellowish material is weighed and submerged in a graduated cylinder.

If the same results are repeated in the same manner, they are said to be precise.

A measurement that is very close to the true or accepted value is considered accurate.
Accurate values agree with a true value.
The results of an archery competition can be extended to other contexts.