Why do we see these appearing in Science? Some measurements in Science are either very very big or very very small. Thus for certain things you will get measurements such as 70000000000000000 light years or 0.0000000000000000576mm for things such as distance between planets or size of atoms respectively (not exact measurements, just examples). However adding lots of zeros may result in errors because having 100 zeros and 101 zeros is a BIG difference in reality but in writing it is only one extra zero which some careless people might not notice. Secondly it is extremely tedious to write, again possibly resulting in error as well as wasting time. Can you imagine writing 100 zeros in each number sentence you write? Thus people have started to use powers of 10 to express the numbers in standard form.
10^0=1
10^1=10
10^2=100
10^3=1000
These are examples of powers of 10 (which if you do not already know) are numbers whereby 10 multiplies itself a few times such as 10^3 means 10 multiplied by itself 2 more times which is 1000. This also works for other numbers besides 10. Fortunately for powers of 10 whenever you multiply by 10 you just need to add a zero onto the original value making multiplying by 10 very east; to find ten to the power of x you just take a 1 and put x number of zeros behind it.
An example of a number in standard form: 1.287*10^6. A number in standard form is always a value from 1 to 9.999999999999... multiplied by a power of 10. The exponent can be positive or negative (but not a decimal or fraction). For example, 5678350000000=5.67835*10^12.
In this way, doing multiplication and division is also easier; even addition and subtraction.
Examples:
For multiplication:
(5.67*10^4)(3.91*10^7)
=(5.67*3.91)(10^4*10^7)
=22.1697*10^11---------4+7=11 so 11 is the exponent for the result; only works for powers of 10
=2.21697*10^11---------remember to convert the coefficient to a single digit number (not including dp)
For division:
(5.67*10^7)/(3.91*10^4)
~1.45*10^3--------------note how similarly the exponents can be subtracted to get the resultant exponent
For addition:
(5.67*10^7)+(3.91*10^4)
=(5.67*10^7)+(0.00391*10^7)-----raise smaller exponent to larger one and change coefficient accordingly
=5.67391*10^7
For subtraction:
(5.67*10^7)-(3.91*10^4)
=(5.67*10^7)-(0.00391*10^7)
=5.66609*10^7
Remember that all these operations can also be done for negative exponents.
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However, to some people these numbers are meaningless. They don't really see much difference between 10^10 and 10^11. Thus we have prefixes.
Prefixes in English are phrases that can be added to the front of certain words that always change the meaning a certain way. Prefixes in Science work the same way, in a way multiplying the current value of that number by a certain power of 10. Some prefixes-kilo=10^3, mega=10^6, giga=10^9, milli=10^-3, nano=10^-9... the list goes on. The distance between most prefixes are multiples of 10^3 except hecto, deka, deci and centi, which are near one. Each of these prefixes has its own symbol.
58400000 grams (g)
=5.84*10^7 grams (g)
=58.4 Megagrams
0.00000764 metres (m)
=7.64*10^-6 metres (m)
=7.64 micrometres
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The next lesson, we went to the Science lab. We did an experiment, but a rather unexciting one-timing pendulums.
We took a retort stand, tied a string to a weight then clamped the string tightly. We then displaced the weight at an angle then let it swing freely for a minute while counting the number of oscillations. Finally we divide the time by the number of oscillations to find the period, or the time for one oscillation. We then repeated the steps for different lengths of string.
After the experiment, our teacher Mr Tan explained to us A LOT of things that we had to take note during the experiment.
Firstly, the angle could not be too big. Otherwise the swinging could get rather erratic.
Secondly, we had to look at the pendulum from in front not from the side. Basically you couldn't observe it from the angle whereby it swings towards you. This is because the period is defined by the time between every two times it crosses the fudicial line which is basically the centre point of the swing. If you view it from the side then you couldn't really see when it actually crossed the fudicial line.
Thirdly you couldn't start the timer immediately after the pendulum first crossed the fudicial line! You had to wait a few swings before starting the timer so as to let the pendulum stabilise.
The hardest part of the experiment was probably to measure and tie the weight to the string. We had to either let more string or tie more string around the weight to increase and decrease the length of string respectively. However at times it would be not tight enough making the weight almost fall out! Thus we would have to retie the whole thing making it quite a tedious process. It also pretty hard to measure the string properly with the ruler, and we did not know where to start measuring because part of the string was inside the clamp!
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That week, we had home-based learning, where we had to sit at home and use iVLE (our school e-learning platform) to listen to tutorials. Not as fun as learning in school...
Anyway, we learnt about mass, weight and density. (And a bit about gravity)
First, some definitions:
Mass-amount of substance in an object-measured in grams
Weight-force exerted by one object onto another due to gravity-measured in Newtons
*Note the difference between mass and weight-they are often confused
Density=mass/volume-can be considered as the concentration of substance inside the object for any specific volume
Gravitational field=a region whereby an object is affected by the force of gravity
(I can't define gravity yet though, sorry)
We also learnt that human reaction error time is from 0.2 to 0.3 seconds. I was thinking "so much?" Our NAPFA can change from a gold to a silver just because of a few milliseconds! It shocked me! Sadly there is no fixed error time so you can't like subtract a certain amount from your timing to get the real amount... if only there were some affordable equipment that can be more accurate...
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