Rewrite this measurement with a simpler unit, if possible.
[tex]6.2 \frac{kg \cdot kg}{kg \cdot m \cdot m^2}[/tex]
Note: If you can simplify the unit at all, it may be possible to make more than one simplification. Be sure your final answer simplest possible unit.
Answer (2)
Simplify the unit by cancelling out common units.
k g \tildam \tildam 2 k g \tildakg = k g \tildam 3 k g 2
Cancel out one k g from the numerator and denominator: k g \tildam 3 k g 2 = m 3 k g
The simplified measurement is 6.2 m 3 k g
Explanation
Understanding the Problem We are given the measurement 6.2 k g \tildam \tildam 2 k g \tildakg and asked to simplify the unit.
The unit is k g \tildam \tildam 2 k g \tildakg . We can simplify this by cancelling out common units.
Simplifying the Unit We have k g \tildam \tildam 2 k g \tildakg = k g \tildam 3 k g 2 We can cancel out one k g from the numerator and denominator: k g \tildam 3 k g 2 = m 3 k g So the simplified unit is m 3 k g .
Final Answer Therefore, the simplified measurement is 6.2 m 3 k g .
Examples
Imagine you're describing the density of a material, like how much mass is packed into a certain volume. If you have a complex unit like k g \tildam \tildam 2 k g \tildakg , it's hard to grasp. Simplifying it to m 3 k g makes it much easier to understand and compare densities of different materials. For example, the density of water is approximately 1000 m 3 k g , while the density of air is about 1.2 m 3 k g . This concept is crucial in fields like physics, engineering, and material science.
The measurement 6.2 k g ⋅ m ⋅ m 2 k g ⋅ k g simplifies to 6.2 m 3 k g by canceling the common units. This final unit represents density, an important concept in physics. Simplifying measurements allows for clearer understanding and communication of quantities.
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