10 to the power of .......

[Jay 1987]

starting to get my head around the maths, but I have a question in the example equation 10 to the power of 6 has turned to 10 to the negative 6 why is this the case ?

 

[SparkyChick]

Because the 10 ^ 6 is on the bottom.

400
-----
2 x 10^6

Is the same as

400 x 10^-6
-----
2


Just in case you're not familiar with the notation.... x ^ y is x to the power y.

 

[SparkyChick]

I should add, basically when you flip a number to a power like that between the top and bottom of a division, you negate it's power.

So... 1 / 2^2 = 1 x 2^-2.

 

[Jay 1987]

So 10 ^6 when on the bottom is positive
And when on the top is negative ?

Is this the correct principle in all situations?

Or does it vary ?

 

[SparkyChick]

10^6 = 1 million.

So, if you divide 1 by 1000000 you'll get 0.000001, which is 10^-6.

1/10^6 = 10^-6
1/10^-6 = 10^6

You change the sign when you move the number from the numerator (top of the fraction/division) to the denominator (bottom of the fraction/division) or vice versa.

 

[Jay 1987]

I should add, basically when you flip a number to a power like that between the top and bottom of a division, you negate it's power.

So... 1 / 2^2 = 1 x 2^-2.

This one you used the example of division turning into multiplication with the positive turning to minus. I get this one

 

[Jay 1987]

10^6 = 1 million.

So, if you divide 1 by 1000000 you'll get 0.000001, which is 10^-6.

1/10^6 = 10^-6
1/10^-6 = 10^6

You change the sign when you move the number from the numerator (top of the fraction/division) to the denominator (bottom of the fraction/division) or vice versa.

This one there both fractions. I don’t get this one ?

 

[westward10]

It is called transposition.

 

[SparkyChick]

So let's take the first one...

1
-----
10^6

This is the same as writing

1
-----
1 x 10^6

Which is the same as writing

1
-----
1000000

Which equals 0.0000001 or 1 x 10^-6.

Which is the same as writing

1 x 10^-6
----
1

As @westward10 says, the mathematical terminology is transposition.

 

[Jay 1987]

So let's take the first one...

1
-----
10^6

This is the same as writing

1
-----
1 x 10^6

Which is the same as writing

1
-----
1000000

Which equals 0.0000001 or 1 x 10^-6.

Which is the same as writing

1 x 10^-6
----
1

As @westward10 says, the mathematical terminology is transposition.

Thanks for this, I’m going to go away and internalise it!

Very helpful !

 

[Jay 1987]

Ok so I’m back!

I = V
————. Work out I = current
R

400 v
————
2 x 10 ^6 ohms Is the same as


400
———-
2,000,000.

As 2 mega ohms is 2,000,000 ohms

Is this part correct, I need to do it in stages


If I divide. 400. I get
————. = 0.002
2,000,000


What am I doing wrong ?

 

[SparkyChick]

It is slightly wrong, but I suspect it's a typo... the correct answer is 0.0002 Amps, 0.2mA (milli-amps) or 200uA (micro-amps).

Why do you think you're doing it wrong?

1v across a resistance of 1 ohm is 1 amp. 100v across 1 ohm is 100 amps. 1v across 100 ohm is 0.01 amp.

So as voltage increases, current increases, as resistance increases, current decreases.

 

[Jay 1987]

Getting ready for college, be back later