Calculating the area of a circle or square using decimals

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I came across something that is completely counter-intuitive, and I'm wondering if I'm correct or not. If a square has a side that is .8m someone would do .8 time .8 which is .64. How can an area be smaller than a side I thought and so I looked it up and found only one site that said something that made sense. They said that if it was smaller than 1 then you should scale down the measurement so that it would be a whole number. So I tried 80cm by 80cm which came out to 6400cm which is 64m. When you multiply .8 meters by .8 meters it comes out to .64 meters. Am I correct, and if so, why isn't this taught in schools?
 

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  • #2
Nidum
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So I tried 80cm by 80cm which came out to 6400cm which is 64m
How many square centimetres are there in a square metre ?

What is the correct abbreviated way to write 'square metres' - is it m or is it m2 ?
 
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  • #3
DrClaude
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I came across something that is completely counter-intuitive, and I'm wondering if I'm correct or not. If a square has a side that is .8m someone would do .8 time .8 which is .64. How can an area be smaller than a side I thought and so I looked it up and found only one site that said something that made sense. They said that if it was smaller than 1 then you should scale down the measurement so that it would be a whole number. So I tried 80cm by 80cm which came out to 6400cm which is 64m. When you multiply .8 meters by .8 meters it comes out to .64 meters. Am I correct, and if so, why isn't this taught in schools?
Careful with the units! That's 0.8 m × 0.8 m = 0.64 m2. Likewise, 80 cm × 80 cm = 6400 cm2 = 0.64 m2.

To visualize it, draw a square of side 1 and another square of size 0.8 inside it (make one the corners to coincide). You will see how the resulting small square is about 64% the size of the big square.
 
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How many square centimetres are there in a square metre ?

What is the correct abbreviated way to write 'square metres' - is it m or is it m2 ?
I understand that I didn't use the correct way to show measurements, but that still doesn't help my question. Your answer is the equivalent of me asking "Are there things that shouldnt be an adverb." and you respond with "You forgot an apostrophe in 'shouldn't'."
 
  • #5
DrClaude
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I understand that I didn't use the correct way to show measurements, but that still doesn't help my question. Your answer is the equivalent of me asking "Are there things that shouldnt be an adverb." and you respond with "You forgot an apostrophe in 'shouldn't'."
Actually, it is crucial to your question. You wrote:
How can an area be smaller than a side
which you will figure out is not a valid question with the use of correct units.
 
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  • #6
phyzguy
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Since the units are different, as others have pointed out, they are different things. Your question of , "How can an area be smaller than a side?" is like asking, "How can my age be less than my height?" or "How can 1 tree be less than 100 apples when all of the apples are growing on the tree?"
 
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  • #7
Nidum
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Forget the area problem itself and just think about how numbers work .

Sketch a graph of y = x2 for x = 0 to 3 . What is different about the sections of the graph for where x is in the range 0 to 1 and for where x is in the range 1 to 3 ?
 
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  • #8
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Careful with the units! That's 0.8 m × 0.8 m = 0.64 m2. Likewise, 80 cm × 80 cm = 6400 cm2 = 0.64 m2.

To visualize it, draw a square of side 1 and another square of size 0.8 inside it (make one the corners to coincide). You will see how the resulting small square is about 64% the size of the big square.
Sorry for being rude, I fully understand now. When I visualized i thought of a square with .5cm sides and then a square that is 1cm^2. When I visualized putting the square in the .5 by .5 I realized the area only took up 1/4 of the square.
 
  • #9
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Forget the area problem itself and just think about how numbers work .

Sketch a graph of y = x2 for x = 0 to 3 . What is different about the sections of the graph for where x is in the range 0 to 1 and for where x is in the range 1 to 3 ?
Thank you for helping me understand the concept, it really helped.
 
  • #10
FactChecker
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A rectangle of dimensions 0.8 by 1.0 will have an area of 0.8. When the second dimension is reduced from 1.0 to 0.8, the area gets smaller.
 

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