Search for:. Exact Numbers. Learning Objective Recognize exact and measured numbers. Key Points An exact number has absolutely no uncertainty in it. Exact numbers cannot be simplified and have an infinite number of significant figures.
A stopwatch can be used to measure the time in seconds. Though we are aware of the basic defined metric systems for length, mass, volume, but there are numerous other quantities in the physical world, for which we need to define the base unit. Quantities like, force, power, area, magnetic intensity, have their own individual units, which have been derived from the basic 7 quantities of the metric system of measurement.
Such quantities of the basic system are sometimes not sufficient to overcome the challenges of studying and measuring other higher quantities existing in physics.
Here we shall look at some of the other important physical quantities and their units. Area: The area is the space occupied by a two-dimensional shape or figure. The area is measured in square units like sq. Let us look at the below example. If the area of each square is 1 cm 2. Volume: Volume is the space enclosed or occupied by any three-dimensional object or solid shape. It has length, width, and height. It is measured in cubic units like cm 3 , m 3 , etc.
Let us look at a simple example. The initial volume of water in the container is 20 units. The volume of water when the object is placed inside the container 30 is units. Finding the Volume of an object can help us determine the amount required to fill that object, for example, the amount of water in a bottle.
Time: Time is the ongoing sequence of events taking place. It also helps us set the start time or the end time of events. One of the very first experiences we have with mathematics is learning how to measure time. You may already know that the measurement of time is done using a watch and a calendar. Now, let's learn how to read and represent time along with how to read a calendar. Speed: Speed is the change in position of the object with respect to time.
It is the ratio of distance traveled by the object to the time taken to travel that distance. In vehicles, we have a speedometer that records the speed at which the vehicle is traveling.
Acceleration: Acceleration is the rate of change of velocity with respect to time. It is a vector quantity. It has magnitude and direction. Force: Force is a push or a pull. When two objects interact with each other, the object changes its position based on the force acting on it. You apply force to move an object from its place and you also apply force to stop a moving object.
The SI unit of force is Newton named after the scientist named Newton. The basic 7 measurable quantities are standardized, and they use the units listed below in the table. There are the basic 7 units of measurement, and the rest other units are derived from here like the area, volume, force, acceleration, etc we just discussed above.
Please find below the seven different quantities and their units of measurements. Just like the metrics system, the US follows the imperial system of units, also called the U. S customary units. Here things are measured in feet, inches, pounds, ounces, etc. Let us explore them in detail in the following sections. Length: The four most commonly used measures of lengths are inch, feet, yards, miles.
Let us look at the conversions from one unit to another. Area: An area is a two-dimensional unit. It is the amount of space occupied by the object. We use inches, feet, yards, miles to measure the length and thus area too. The area is measured in square units such as square inch, square foot, square yard, square mile, acre. Another scale was discovered when a bronze rod was found to have marks in lengths of 0.
It is certainly surprising the accuracy with which these scales are marked. Now units of this measure is Measurements of the ruins of the buildings which have been excavated show that these units of length were accurately used by the Harappans in their construction. European systems of measurement were originally based on Roman measures, which in turn were based on those of Greece.
The Greeks used as their basic measure of length the breadth of a finger about These units of length, as were the Greek units of weight and volume, were derived from the Egyptian and Babylonian units. Trade, of course, was the main reason why units of measurement were spread more widely than their local areas. In around BC Athens was a centre of trade from a wide area.
The Agora was the commercial centre of the city and we know from the plays of Aristophanes the type of noisy dealing which went on there. Most disputes would arise over the weights and measures of the goods being traded, and there a standard set of measures kept in order that such disputes might be settled fairly.
The size of a container to measure nuts, dates, beans, and other such items, had been laid down by law and if a container were found which did not conform to the standard, its contents were confiscated and the container destroyed.
The Romans adapted the Greek system. They had as a basis the foot which was divided into 12 inches or ounces for the words are in fact the same. The Romans did not use the cubit but, perhaps because most of the longer measurements were derived from marching, they had five feet equal to one pace which was a double step, that is the distance between two consecutive positions of where the right foot lands as one walks.
Then 1 , paces measured a Roman mile which is reasonably close to the British mile as used today. This Roman system was adopted, with local variations, throughout Europe as the Roman Empire spread. However, if one looks at a country like England, it was invaded at different times by many peoples bringing their own measures. The Angles, Saxons, and Jutes brought measures such as the perch, rod and furlong.
The fathom has a Danish origin, and was the distance from fingertip to fingertip of outstretched arms while the ell was originally a German measure of woollen cloth. In England and France measures developed in rather different ways. We have seen above how the problem of standardisation of measures always presented problems, and in early 13 th century England a royal ordinance Assize of Weights and Measures gave a long list of definitions of measurement to be used.
On one hand it was an extremely successfully attempt at standardisation for its definitions lasted for nearly years. The Act of Union between England and Scotland decreed that these standards would hold across the whole of Great Britain. Locally, however, these standards were not always adhered to and districts still retained their own measures.
Of course, although an attempt had been made to standardise measures, no attempt had been made to rationalise them and Great Britain retained a bewildering array of measures which were defined by the ordinance as rather strange subdivisions of each other. Scientists had long seen the benefits of rationalising measures and those such as Wren had proposed a new system based on the yard defined as the length of a pendulum beating at the rate of one second in the Tower of London.
In France, on the other hand, there was no standardisation and as late as Arthur Young wrote in " Travels during the years , , " published in :- In France the infinite perplexity of the measures exceeds all comprehension. They differ not only in every province, but in every district and almost every town. In fact it has been estimated that France had about different names for measures at this time, and taking into account their different values in different towns, around , differently sized units.
To a certain extent this reflected the powers which resided in the hands of local nobles who had resisted all attempts by the French King over centuries to standardise measures. The numbers of defined quantities are also exact. By definition, 1 foot is exactly 12 inches, 1 inch is exactly 2. Quantities derived from measurements other than counting, however, are uncertain to varying extents due to practical limitations of the measurement process used.
The numbers of measured quantities, unlike defined or directly counted quantities, are not exact. To measure the volume of liquid in a graduated cylinder, you should make a reading at the bottom of the meniscus, the lowest point on the curved surface of the liquid. Refer to the illustration in Figure 1. The bottom of the meniscus in this case clearly lies between the 21 and 22 markings, meaning the liquid volume is certainly greater than 21 mL but less than 22 mL.
In the number Some people might estimate the meniscus position to be equally distant from each of the markings and estimate the tenth-place digit as 5, while others may think it to be even closer to the mL mark and estimate this digit to be 7.
Note that it would be pointless to attempt to estimate a digit for the hundredths place, given that the tenths-place digit is uncertain. In general, numerical scales such as the one on this graduated cylinder will permit measurements to one-tenth of the smallest scale division. The scale in this case has 1-mL divisions, and so volumes may be measured to the nearest 0.
This concept holds true for all measurements, even if you do not actively make an estimate. If you place a quarter on a standard electronic balance, you may obtain a reading of 6. The digits 6 and 7 are certain, and the 2 indicates that the mass of the quarter is likely between 6. The quarter weighs about 6. If we weigh the quarter on a more sensitive balance, we may find that its mass is 6.
This means its mass lies between 6. All of the digits in a measurement, including the uncertain last digit, are called significant figures or significant digits. Whenever you make a measurement properly, all the digits in the result are significant. But what if you were analyzing a reported value and trying to determine what is significant and what is not? Well, for starters, all nonzero digits are significant, and it is only zeros that require some thought.
Starting with the first nonzero digit on the left, count this digit and all remaining digits to the right.
0コメント