At the end of this lesson, you will be able to convert units from SI to English and vice versa, recall rounding off of numbers, designate multiples and subdivisions of any unit using prefixes, identify significant figures, and express numbers in scientific notation. We all know that physics is a branch of science, but physics is not just it, physics is an experimental science where physicists perform experiments to test hypotheses. And the conclusions in the experiments are derived from measurements.
Physicists use numbers to describe measurements. Such a number is called a physical quantity. However, a physical quantity would make sense to everyone when compared to a reference standard. So what are physical quantities?
Physical quantities are those quantities that can be measured. These are quantities that are used to describe the laws of physics. Here in this picture, we have length, mass, time, electric current, temperature, luminous intensity, and amount of substance. Yes, all of these are physical quantities.
Since 1960 the system of units used by scientists and engineers is the metric system, which is officially known as the international system or SI units. To make sure that scientists from different parts of the world understand the same thing when referring to a measurement, standards have been defined for measurements of length, time, and mass. Tilde it should be inches, feet.
Yard and pounds tilde. No, it's meters centimeters kilometers and kg In this lesson we will be focusing on these three physical quantities namely length mass and time length of one meter is defined as the distance traveled by light in a vacuum in one 299 million seven hundred ninety two thousand four hundred fifty eight second Based on the definition that the speed of light is exactly 299,792,458 meters per second, time of one second is defined as 9,192,631,770 cycles of the microwave radiation due to the transition between the two lowest energy states of the cesium atom. This is measured from an atomic clock using this transition. Mass of 1 kg is defined to be the mass of a cylinder of platinum-iridium alloy at the International Bureau of Weights and Measures. Today, few countries continue to use the British system of units like in the United States.
The conversion between the British system of units and SI units have been defined exactly on the left. We have English to metric conversions for both length and weight. Let us now try to convert some expressions. To convert 28 oz to grams, first, write down 28 oz, then multiply it by the conversion factor.
The conversion factor can be found in the table of conversions discussed earlier. For this problem, 1 oz is equals to 28.3 g. In writing the conversion factor, notice that the denominator must have the same unit with the number we are going to convert.
While the numerator must have the unit that we need to convert the given into. In this equation, we have oz and g. The given is an ounce, so our denominator must be an ounce.
Our numerator on the other hand is in grams because it is the unit we are converting into. After writing our equation, we need to cancel similar units. In this case, we need to cancel ounce, leaving us grams.
Now, multiplying 28 by 28.3 grams, we have 792.4 grams. Sounds easy. Let's try converting the remaining ones. To convert 3 feet to cm, Let us write the equation first. 1 foot is equals to 30.5 centimeters according to the table of conversion.
Our given is in feet so we write 1 foot as the denominator. On the other hand, we write 30.5 centimeters as the numerator because it is the unit we need to convert our given into. Canceling similar feet units, we are left with 3 multiplied by 30.5 centimeters and the answer is 91.5 centimeters.
Let's try another. To convert 2 kg to oz, let us look for the conversion factor on the given conversion table. Nothing is given to directly convert kg to oz, but worry not. We can use kg to g and g to oz.
Let us write 2 kg and use the conversion factor for kg to g as shown, then multiply it again by another conversion factor leading us to our design. Dired unit, the ounce. Canceling all similar units. Kilograms and grams, we now multiply 2 by 1000, and 0.0353 ounce.
2 kilograms is equals to 70.6 ounce. In certain cases, particularly in scientific usage, it becomes convenient to provide for multiples larger than 1000 and for subdivisions smaller than 1000. In the metric system of measurement, Designations of multiples and subdivision of any unit may be arrived at by combining with the name of the unit the prefixes on the table. So how do I use the prefixes? To use prefixes, for example, 12 times 10 raised to the sixth power, we need to look at the table of prefixes, and find the factor 10 raised to the sixth power. Here 10 raised to the sixth power is equal to the prefix mega, with the symbol m.
Replacing 10 raised to the sixth power with our prefix, we write 12. capital M, followed by a small m. We read this as 12 megameters. Significant figures also known as the significant digits or precision of a number written in positional notation are digits that carry meaningful contributions to its measurement resolution.
We have rules in determining the number of significant figures. First, all non-zero digits do count. 24 has two significant figures, while 3.56 has three significant figures.
Second, leading zeros don't count. For example, zeros in front of numbers, and in 0.0025 we only have two significant figures. Third, captive zeros do count. Captive zeros are zeros between non-zero numbers.
For example, 1502 has zero between 5 and 2, thus, it has four significant figures. Also, 1.008 has zeros between 1 and 8, thus, it has four significant figures. Fourth, trailing zeros do count if the number contains a decimal. For example, zeros at the end of numbers. 100 has only one significant figure because it does not have a decimal point.
2,306.0 has five significant figures because it has a decimal. And 1.00 times 10 raised to the power of 3 has three significant figures. Scientific notation is a way of expressing real numbers that are too large or too small to be conveniently written in decimal form.
It may be referred to as scientific form or standard index form, or standard form in the UK. This base 10 notation is commonly used by scientists, mathematicians and engineers, in part because it can simplify certain arithmetic operations. The scientific notation is written as shown on the picture. It is composed of the coefficient which is a real number with an absolute value between 1 and 10, multiplied by, an order of magnitude value written as power of 10. To express numbers in scientific notation, the first thing we need to look at is the decimal point.
Remember that the direction of the movement of the decimal point will determine the magnitude and sign of the exponent. For the first example, 4567.89000 meters, the decimal point moves to the left and stops in the middle of 4 and 5. The decimal point passed 3 units to the left. giving us 4.56789. The left movement indicates a positive exponent, giving us 10 to the power of 3. For the second example, 0.004567 meters, the decimal point moved 3 units to the right.
A right movement of the decimal point indicates a negative exponent, giving us 4.567 times 10 to negative power of 3. Always remember, a movement to the left gives a positive exponent, while a movement to the right gives a negative exponent. Let's answer a sample problem. A snail moves 1 cm every 20 seconds.
What is this in inches per second? To answer this, first, we need to look at the given, 1 cm every 20 seconds then look at what is asked, we need to convert the given to inches per second. Let us now write the equation, 1 cm every 20 seconds is 1 cm over 20 seconds multiplied by our conversion factor, 1 inch equals 2.54 cm.
Canceling all similar units, we multiply 1 by 1 and divide with the product of 20 and 2.54. The result is 0.01968 inches per second. Expressing the result, 0.01968 inches per second to scientific notation, we can write it as 1.9 times 10 raised to negative 2 inches per second. By rounding off, we can get 2.0. For sample problem 2. a jeepney tried overtake a car the jeepney moves at 40 kilometers per hour convert this to the brita system feet per second 40 kilometers per hour is our given that we need to convert to feet per second multiplying are given with the conversion factors and cancelling the similar units kilometers and m for length an hour and minute For time, we get 36.444 feet per second.
Take note that in converting multiple units, we need to convert one at a time. In this problem, we first convert a kilometers into meter then into feet. Then, to convert hours, we write one hour on the numerator, which is equals to 60 minutes as written on the denominator, then convert it again to seconds.
Always remember, the key to converting multiple units is by writing the conversion factors one at a time. Now that you have learned how to convert units and express numbers in scientific notation, are you ready for a challenge? I have prepared five problems that we can solve together.
For the first problem, it takes about 8.0 minutes for light to travel from the sun to earth. How far is the sun for the earth in meters? Take note that the speed of light is 299,792,458 meters per second. First, right are given.
8 minutes. The question is how far, indicating that we are finding an answer with the unit of length. Looking at our given, we need to be able to cancel both units of time, so that only the unit of length is left. To do this, first, we need to convert minutes to seconds. 1 minute is equals to 60 seconds.
Multiplying 8 minutes by the conversion factor. 60 seconds equals 1 min. And by the speed of light, we get 143,900,379,840 meters.
Expressing this in scientific notation, we get 1.44 times 10 raised to 11 meters. For the second problem. Chloe made 1.5 liters of orange juice.
0.75 liters dropped out of the bottle. How many milliliters are left? The word dropped indicates that something is lost or been subtracted from the given. For this, we can write 1.5 liters where 0.75 is dropped, giving us 1.5 minus 0.75.
To determine what the remaining amount of juice is in milliliters, we can convert 0.75 liters to ml as shown. Multiplying 0.75 liters by the conversion factor 1000 ml over 1 liter, we get 750 ml. Now, Chloe has 750 ml of juice left. Sounds easy. Well, it really is just easy to solve conversion problems when you know the conversion factors and when you can easily convert verbal descriptions to an equation.
However, if up to this point you are still confused or just looking for more, let's proceed to the next problem. Peter planted 240 kg of potatoes and harvested 12 times more of them. How many tons of potatoes has he harvested?
Converting the verbal description, 12 times more of them or the 240 kilos of potatoes planted, we write 240 kilograms times 12. Now, proceeding to the main problem, how many tons of potatoes, meaning we need to convert the given unit to ton, we write, 2880 kilograms multiplied by our conversion factor for ton and kilogram, we get 3.175 ton. So, Peter harvested a total of 3.175 ton of potatoes. From 18.2 hectares, workers reaped 78.69 tons of grain.
What was the average yield per hectare of harvested grain? Converting the verbal description, average yield per hectare, we can write the equation as 78.69 tons of grains divided by 18.2 hectares. We get 4.32 tons of grain per hectare.
Ethan is trying to drink 1.9 liters of water every day. Given that Ethan drank 967 ml of water one morning, how many milliliters of water should he drink during the rest of the day? In this problem, we are only asked to subtract 967 ml of water from 1.9 liters.
But since they have dissimilar units, we need it to convert 1.9 liters to milliliters first, before deducting 967 ml from it. We write 1.9 liters multiplied by our conversion factor 1000 milliliters equals 1 liter minus 967 milliliters, we get 933 milliliters. This is all for today.
If you listened well and have understood everything that we have discussed, you can now solve the given problems on page 3 to 4 of your physics modules. Kindly write your solution for every problem, and don't forget to enclose your final answers in a box. That's it for today. Have a nice day.