Understanding ratios between exponents, me understand.

In summary: This shows that the exponent of 0.23 leads to different results for different units of mass. But you can still use the formula as long as you consistently use the same units for the masses and for the constant. This is because the units of the constant are chosen so that the formula works correctly.
  • #1
christian0710
409
9
1. I need some help understanding ratios between 2 numbers/quantities og exponents:

2.Here is the problem, When you take the ratio between 100grams and 1000grams it is 100g/1000g = 0,10 and you can convert this to kilos 0,1kg/1kg = 0,10 and the ratio stays intact, that makes sense. But let's say the relationship between the mass of the egg a bird lays and the mass of the bird is given by M_egg = c*M_bird^(0.77). Then the constant c is a ratio betwen M_egg/M_bird^0,77. If the bird weighs 1.5kg and the egg weighs 0,070kg, then I get two completely different results if I first calculate the ratio in grams and efter that in kg. Why is that? And how do you work around it?

In grams M_egg/M_bird^077 = 0,070kg/1.5^(0,77)kg = 0.051
in kg M_egg/M_bird^077 = 70g/1500^(0,77)5 = 0.025

Is there some fundamental theory i need to understand about exponents that i missed out on?
 
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  • #2
christian0710 said:
1. I need some help understanding ratios between 2 numbers/quantities og exponents:

2.Here is the problem, When you take the ratio between 100grams and 1000grams it is 100g/1000g = 0,10 and you can convert this to kilos 0,1kg/1kg = 0,10 and the ratio stays intact, that makes sense. But let's say the relationship between the mass of the egg a bird lays and the mass of the bird is given by M_egg = c*M_bird^(0.77). Then the constant c is a ratio betwen M_egg/M_bird^0,77. If the bird weighs 1.5kg and the egg weighs 0,070kg, then I get two completely different results if I first calculate the ratio in grams and efter that in kg. Why is that? And how do you work around it?

In grams M_egg/M_bird^077 = 0,070kg/1.5^(0,77)kg = 0.051
in kg M_egg/M_bird^077 = 70g/1500^(0,77)5 = 0.025

Is there some fundamental theory i need to understand about exponents that i missed out on?


Not really. But since the masses of the egg and the bird can be expressed in different units, this implies that the constant 'c' also has some units, which may not be stated. As long as you use the proper units for the masses of the egg and bird with a particular value of 'c', the formula will work. Otherwise, ...
 
  • #3
SteamKing said:
As long as you use the proper units for the masses of the egg and bird with a particular value of 'c', the formula will work. Otherwise, ...
... it will also work if you include the units for the given value of c. In the present case, the units would be something like kg0.23 or gm0.23, etc. E.g. 0.22 gm0.23 = 0.045 kg0.23.
 

FAQ: Understanding ratios between exponents, me understand.

1. What are exponents and how do they work?

Exponents are a way of representing repeated multiplication of a number by itself. They are written as a superscript number after the base number, and indicate how many times the base number should be multiplied by itself. For example, 23 would be read as "2 to the power of 3" and means 2 multiplied by itself 3 times (2 x 2 x 2 = 8).

2. How do I calculate the ratio between two exponents?

To calculate the ratio between two exponents, you can use the quotient rule for exponents, which states that when dividing two powers with the same base, you subtract the exponents. For example, if you wanted to find the ratio between 25 and 23, you would calculate 5-3=2, and the ratio would be 2:1.

3. How can understanding ratios between exponents be useful in real life?

Understanding ratios between exponents can be useful in many areas of science and mathematics, such as engineering, physics, and finance. For example, in physics, ratios between exponents are used to calculate the half-life of radioactive elements, and in finance, they are used to calculate compound interest.

4. What are some common mistakes to avoid when working with ratios between exponents?

One common mistake to avoid when working with ratios between exponents is forgetting to use the quotient rule when dividing powers with the same base. Another mistake is confusing the base number with the exponent, as this can change the value of the ratio significantly.

5. How can I practice and improve my understanding of ratios between exponents?

One way to practice and improve your understanding of ratios between exponents is to work through practice problems and exercises. You could also try creating your own problems and solving them, or teaching the concept to someone else. Additionally, there are many online resources and tutorials available for further practice and review.

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