Multiplying mass as kg and grams= 2 different results?

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In summary, when multiplying two quantities, it is important to also multiply their units. In the given example, multiplying 1kg and 0.5kg gives a result of 0.5 kg2, but converting the units to grams and then performing the multiplication gives a result of 500 000 g2, which is equivalent to 0.5 kg2. This problem can be avoided by always considering the units when performing calculations.
  • #1
christian0710
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Hi, I'm just wondering. If you mulitiply 1kg with 0.5kg you get 0.5kg

But if you do the multiplication in grams you get
1000g *500g = 500.000g = 500kg. a dompletely different result.

Why is that? How do you avoid this problem?
 
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  • #2
christian0710 said:
Hi, I'm just wondering. If you mulitiply 1kg with 0.5kg you get 0.5kg

But if you do the multiplication in grams you get
1000g *500g = 500.000g = 500kg. a dompletely different result.

Why is that? How do you avoid this problem?

No, when you multiply 1kg with 0.5 kg you get 0.5 kg2 - square kilograms. You must also multiply the units!

1000g *500g = 500 000 g2

Now, to convert square kilograms to square grams,

1kg * 1kg = 1000 g * 1000 g = 1 000 000 g2

So, now we take 500 000/ 1 000 000 g2 = 0.5 kg2. Precisely the same result.
 
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## 1 \ kg \ \times \ 0.5 \ kg=0.5 \ (kg)^2=0.5 \ \times \ 10^6 \ g^2 ##
## 1000 \ g \ \times \ 500 \ g=0.5 \ \times \ 10^6 \ g^2 ##
 
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  • #4
christian0710 said:
Hi, I'm just wondering. If you mulitiply 1kg with 0.5kg you get 0.5kg
Without any context, I can't think of any reason you would want to multiply two quantities in kilogram units.

As already posted, the units of the product would be kg2, which by itself isn't very meaningful.
christian0710 said:
But if you do the multiplication in grams you get
1000g *500g = 500.000g = 500kg. a dompletely different result.

Why is that? How do you avoid this problem?
 
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Related to Multiplying mass as kg and grams= 2 different results?

1. Why do we use different units (kg and grams) when measuring mass?

Different units of measurement are used to represent different ranges of values. Kilograms are used for larger masses, while grams are used for smaller masses. This allows for more precise and accurate measurements.

2. How do we convert between kilograms and grams?

To convert from kilograms to grams, you multiply by 1000. To convert from grams to kilograms, you divide by 1000. For example, 1 kg = 1000 g, and 500 g = 0.5 kg.

3. Why do multiplying mass as kg and grams result in two different answers?

This is because kilograms and grams are two different units of measurement for mass. When multiplying, the unit of measurement must also be multiplied. For example, if you have 2 kg and you multiply it by 2, the result is 4 kg. But if you have 2 kg and you multiply it by 2 g, the result is 4 kg * g, which is a different unit of measurement.

4. Can we add or subtract masses in different units (kg and grams)?

Yes, we can add or subtract masses in different units as long as we convert them to the same unit first. This ensures that we are working with the same unit of measurement and will result in an accurate answer.

5. Is there a preferred unit to use when measuring mass?

It depends on the context in which the mass is being measured. In scientific and mathematical calculations, it is often preferred to use the base unit of measurement, which is kilograms. However, for everyday use, using grams may be more practical and easier to understand.

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