In previous lesson, we have discussed the classification of physical quantities. In this lesson, we will continue our discussion on scientific notation and prefixes. Under prefixes, we will discuss how to use the scientific calculator to solve problems involving prefixes. We will also discuss the conversion of prefixes, including the conversion of the unit of area,volume, speed and density.
Scientific Notation
Scientific notation (also known as Standard form) is a convenient way to write very small or large numbers.
Let’s say we have a number. Let’s say it is 50,000,000,000. it can be written as 5 x 10,000,000,000 (Five times 10 billion). The number 10,000,000,000 million can be further expressed as 1010 (10 to the power of 10). Therefore 50,000,000,000 = 5 x 1010. This is much easier to be read. We can straight away tell its value just by a glance.
In this notation, numbers are separated into two parts, a real number with an absolute value between 1 and 10 and an order of magnitude value written as a power of 10. This method to write a number is called the scientific notation.
Prefixes
Prefixes is a letter or a few letters placed in front of a word to modify its meaning. The prefixes that we are going to discuss here is the SI prefixes, which is used in front of an SI unit. An SI unit used with prefixes indicate multiples or submultiples of a base unit. For example, kilometer – kilo is the prefix of the base unit, meter. The prefix act as a multiplier. In this case, kilo represents a multiple of 1000.
The below table shows the list of prefixes that you need to know in SPM syllabus. A more complete list can be found in wikipedia.
One of the question that student always ask is: “Do we need to memorise all of these prefixes?”, and the answer is, “YES”. You need to memorise all of these prefixes together with its standard form and symbol. If you really can’t memorise all, then you are advised to memorise at least the 6 most frequently use prefixes. They are Mega, kilo, deci, centi, milli and micro. If you own a Casio fx-570MS calculator, then I have a good news for you. Most of the prefixes in this table can be found in your calculator. We will discuss this in the later part of this presentation.
How to convert a number with prefix to a normal number?
We can convert a number with prefix to a normal number by multiplying the number by the value of the prefix.
For example, 23 MHz. The value of Mega is 1 million or 106. Therefore, we can rewrite the number as 23 x 106 Hz.
23 MHz = 23 x 106 = 23,000,000
In conclusion, we convert a number with prefix to a normal number by multiplying the number with the value of the prefix.
How to convert a normal number to a number with prefix?
We can convert a normal number to a number with prefix by dividing the number by the value of the prefix.
For example, 230,000 Hz is equal to how many MHz? The value of Mega is 1 million or 106. To write a normal number with a prefix, we divide the number by the value of the prefix and we get 0.23 . 230,000 Hz is equal to 0.23 MHz.
230,000 Hz = 230,000/106 MHz = 0.23MHz
In conclusion, we convert a normal number to a number with prefix through dividing the number by the power of the prefix.
If we want to convert a normal number to a number with prefix, we divide the number by the value of the prefix.
If we want to convert a number with prefix to a normal number, we multiply the number by the value of the prefix.
Using Calculator
If you own a casio fx-570MS calculator, you can do the conversion much easier. You can find the following prefixes in the calculator. Tera, Gega, Mega, kilo, mili, micro, nano, pico and fento. Take notes that deci and centi are not given. We are going to deal with this problem in the later slide.
We can key in the prefixes by pressing “shift” and the buttons representing the prefixes. For example, if we want to key in kilo, we press “shift” “6” and if we want to key in mili, we press “shift” “5”………
Let’s see how we can convert a number with prefix to a normal number by using a calculator. Let’s say we want to know 300km is equal to how many m. In the calculator, we press [3] [0] [0]. Kilo is at [button 6]. Therefore, we press [shift] [6]. You can see a small letter k shows on the screen here. To get the answer, we press [=]. The answer will immidiately shown on the screen. It is 300,000. 300km is equal to 300,000 metre.
We can also convert a normal number to a number with prefix easily. In previous slide, we have learned that if we want to convert a normal number to a number with prefix, we divide the number by the value of the prefix.
For example, if we want to know 0.0112m is equal to how many milimitres, we divide 0.0112 by the value of mili.
Let’s see how we can do this in a calculator. In our fx-570MS calculator, we press .0112 divided by ….. Take notes that if we want to key in zero point something, we can omit the first zero and straight away key in point something. For example, if we want to key in 0.0112, we can always omit the zero before the decimal point and just key in .0112. mili can be inserted by pressing [shift] [5]. We can then press [=] to get the answer. Opps! The screen tells us syntax ERROR.
Well, let’s check what’s the problem. I know for a lot of students when they did something wrong in the calculator, they will delete it by pressing the [on] button and redo everything again. This is a very bad habit. By pressing the [on] button, you are not only delete everything on the screen, you will also delete everything in the replay memory in your calculator as well. Your calculator is a very sophisticated machine. It can remember whatever you perform in the calculator previously up to 128 bytes of memory as long as you do not switch off the calculator or delete all the calculation by pressing the [on] button.
The correct way to delete only current calculation is using the [AC] button. You can delete everything on the screen by pressing the [AC] button. Pressing [AC] does not clear replay memory. You can always navigate to all the calculation you have performed by pressing the up or down arrow key. You can also move the cursor to the location you want by using the left or right arrow key. By doing so, you can check what is the mistake you have done and then fix it. If you press the [on] button, everything is gone, you don’t know what is your mistake and you have to redo everything again. So, make it a habit to use the [AC] button to delete but not the [on] button.
Let’s come back to our problem. We have a syntax error. To check what’s the mistake we have done, we press the left or right arrow key. You will find that the screen will immediately shows the last calculation we have performed. Well, I guess the problem is on the mili. Mili is a prefix. It is not a number. A prefix must attached to a number. It cannot stand alone. Which means, instead of putting mili, we need to put 1 mili.
To fix this problem, we insert “1” in front of mili to make it 1 mili. However, you will find that the “mili” will be deleted and replaced by 1. Of course we can key in the mili again by pressing [shift][5]. But this is not the correct way to solve the problem, because you will find that if you want to insert a number at the very front of the expression, you will need to retype everything again.
We can insert a number at any location by using the insert cursor. If you look closer at the calculator, you will notice that above the [delete] key, there is a 3 letters word INS. INS stands for insert. In order to convert to insert cursor, we press [shift] [DEL]. On the screen, you will notice a blinking box before mili. This is the insert cursor. Let’s key in [1]. You will find that this time the mili is not deleted. Let’s press [=] to perform the calculation. Yes, this is the answer. The answer is 11.2 . 0.0112 m is equal to 11.2 mm.
In conclusion, we can convert a normal number to a number with prefix by dividing the number by the prefix. As we mentioned before, the prefixes “deci” and “centi” are absent in the calculator. To solve this problem, we store this 2 values in the calculator’s long term memory. Let’s have a closer look at the calculator. In the calculator, there is a button label with [RCL]. This is the “recall” button. We can use this button to key in the value we have stored in our calculator. On top of it, there is a symbol “sto”, stands for “store”. This is the button that we use to store a number in the calculator. We can activate it by pressing [shift] [RCL] . In short, we use the [shift] [RCL] to store the value and the [RCL] button to recall the value.
The Casio fx-570MS calculator allows us to store up to 9 numbers in the long term memory of the calculator. In the calculator, we can see the 9 letters: A, B, C, D, E, F, X, Y and M which are red in colour. These are the buttons where we can store our numbers. For example, if we want to store 12345 in the calculator. We key in 12345, and then press [shift] [RCL]. [shift] [RCL] is to activate the “store” function. We then choose the location where we want to store the number. Let’s say we want to store it in A, hence we press [A]. The screen will shows an arrow pointing towards A. This shows that the number has already been stored in A. To recall the number, we press [RCL] [A] and the number will be displayed on the screen.
Now, let’s store desi and centi in the calculator. Before we start, of course we need to know the value of deci and centi. 1 deci = 0.1 and 1 centi = 0.01. I’ll suggest you to store “centi” in [C] and “deci” in [D].
To store desi in the calculator, we press 0.1, [shift], [RCL] [D]. The screen will show 0.1 -> D to indicate that the number is already stored in D. Again, the [shift][RCL] is to activate the store function.
To store centi in the calculator, we press 0.01, [shift], [RCL] [C]. The screen will show 0.01 -> C to indicate that the number is already stored in C.
These numbers will be stored permanently in the calculator, unless you press [shift] [mode] to clear the memory.
We have stored the value of centi and desi in our calculator where C = centi and D = desi. Now, let’s see how to make use of it.
For example, if we want to know 230 dm is equal to how many metres, in our calculator, we press 230. We have stored centi in C and desi in D. Therefore, to insert desi, we press [RCL] [D]. The screen will show 230D. We then press [=]. The screen shows that the answer is 23 . 230 dm is equal to 23m.