Volume of a 0.200m Sided Square

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SUMMARY

The discussion clarifies that a square, defined by a side length of 0.200m, does not possess volume but rather area. The area of the square is calculated as 4.00 x 10-2 m2, reflecting three significant figures, consistent with the original measurement. The conversation emphasizes the importance of using scientific notation to accurately convey significant figures, particularly when precision is critical in calculations.

PREREQUISITES
  • Understanding of geometric shapes, specifically squares and cubes.
  • Knowledge of significant figures and their application in measurements.
  • Familiarity with scientific notation for expressing numbers.
  • Basic principles of area calculation for two-dimensional shapes.
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  • Research the concept of significant figures in scientific measurements.
  • Learn how to calculate the area of various geometric shapes.
  • Explore the differences between volume and area in geometry.
  • Study the application of scientific notation in engineering and physics contexts.
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Students, educators, and professionals in mathematics, engineering, and the sciences who require a clear understanding of area calculations and significant figures in measurements.

Mattofix
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if i have a sqaure of length 0.200m, is its volume 0.040 or 0.0400 mcubed?
 
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A square has no volume, only area. Do you mean a cube?
 
In determining "number of significant figures" there is always an ambiguity as to whether a "0" is "significant" or just a place holder. For that reason, if "significant figures" are important it is best to use "scientific notation". Here "0.200 m" would be best written "2.00 x 10-1 m", showing clearly that there are "3 significant figures".

If you really mean area rather than volume it would be best to write it as 4.00 x 10-2 m2, again showing clearly that there are "3 significant figures".
 
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sorry, i meant the area of a square, ok, so if 2.00 x 10-1 m is its length, would its area be 4.00 x 10-2 m2 or 4.0 x 10-2 m2?
 
Mattofix said:
sorry, i meant the area of a square, ok, so if 2.00 x 10-1 m is its length, would its area be 4.00 x 10-2 m2 or 4.0 x 10-2 m2?
The latter: 4.00 x 10-2 mp2. Since the orginal measurement had 2 three significant figures so must the answer.

It is better, by the way to talk about "significant figures" rather than "decimal places". The number of significant figures in the result of any calculation is the smallest number of significant figures in any number in the calculation. There is no such rule for "decimal places".
 

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