Hi Everyone, i’m having difficulty grasping the concept of decimals and fractions in maths. Can someone please explain it in simple terms.
In:
You can represent a whole as 100%. That means you can represent half as 50%, a quarter as 25%, and so on.
You can represent 100% as 1. That means you can represent 50% as 0.5, 25% as 0.25 etc. The corollary is that you can also represent half as 0.5, quarter as 0.25 and so on.
The basic problem we’re trying to solve is how to express partial amounts. Hopefully whole numbers (1, 2, 245) make sense, but what if you’ve got an apple with a chunk missing? Clearly you’ve got less than 1 apple but more than 0. We need a way to accurately document that.
Decimals and fractions use the same concept, they just write it down differently. The concept is “Divide the whole thing I want to measure into some number of identical slices, then count how many slices worth I have in my partial thing.” So, for example, I could slice an apple up into 100 identical pieces, slice my partial apple into pieces of the same size, count the number of pieces I’ve got, and if I compare that to 100 I get a good measurement of how much partial apple I have.
Now we want to write that down in a way that’s way more compact than that long sentence. One way is to write down both number…the number of slices I chose to use for a whole apple, and the number I found in my partial apple. That’s a fraction. 42 / 100 means I sliced a whole apple into 100, counted how many slices that size I have in my partial apple, and had 42.
I could also tell you “I only slice apples up into tens, or tens of tens…could be 10, 100, 1000, 10000000, etc.” and then just tell you how many slices I found. That’s a decimal. 0.42 means I sliced it into 100 (two digits past the decimal) and I found 42 of them. 0.420 means I sliced it into 1000 (three digits past the decimal) and found 420 of them. 0.042 means I still sliced it into 1000 (three digits past the decimal) but only found 42 of them. I could just as easily write it as fractions: 42/100, 420/1000, and 42/1000 respectively.
% is a special case where the symbol says “I sliced it into 100” and I just tell you how many I have. It’s just a convenience because, most of the time, figuring out partial things down to the hundredths in everyday life is good enough. You can convert % to decimal just by sticking those two digits to the right of the decimal point (since we know it’s 100 slices) or putting it over 100 (for the same reason). 42% = 0.42 = 42/100
One concept, several ways of writing it down.
the concept behind decimals and fractions is “dividing something into pieces”.
think a pizza.
you can cut your pizza into 8 slices. each slice is 1/8th of a pizza now.
4 slices are 4/8ths or 1/2 (one half) of a pizza.
generally you try to simplify fractions (4/8 -> 1/2; 6/18 -> 1/3; 14/10 -> 7/5) to make them easier to handle, you do this by finding a number that divides both the number above and the number below the line without issues.
the idea of the way we write fractions is the number above the line is how many pieces you have, the number below the line is “how many pieces make one whole thing”.
in my pizza example: 1 slice is 1 eigth of a pizza, so 1/8 pizza.
12 slices would be one and a half pizzas so 12/8 pizza (or simplified 3/2).
sometimes you dont care about the exact value or so and then you use decimals.
you get the decimals by doing what our notation already suggests:
you divide the upper number by the lower number:
– 12:8 is 1 rest 4, then long division -> 40:8 is 5, so you get 1.5 as the result. meaning 12/8 = 3/2 = 1.5
– 1:8 is 0, then 1, then 2, then 5 if you do the division and in the end you get 1/8 = 0.125
we can easily verify this: 1= 8* 1/8 = 8 * 0.125 = 1 (one pizza is 8 slices, 8 slices is one pizza)
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