Math Is Fun Forum

paulb203

Member

Registered: 2023-02-24

Posts: 317

Dividing powers of 10

10^6/(2)
=1,000,000/2
=500,000
*
Is there a way of doing this without converting 10^6 to 1,000,000?
For example, in the way we would do;
10^6/(10^2)=10^6-2
10^6-2=10^4

Can I express 2 in terms of 10^y?
2=10/5
10/5= what, in terms of 10^y?
Is it possible to express 10/5 in terms of 10^y?

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KerimF

Member

From: Aleppo-Syria

Registered: 2018-08-10

Posts: 240

Re: Dividing powers of 10

This came to mind (though not exactly what you have in mind):
10^6/(2) = 10/2*10^(6-1) = 5*10^5 = 500,000

Last edited by KerimF (2024-10-28 03:38:04)

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paulb203

Member

Registered: 2023-02-24

Posts: 317

Re: Dividing powers of 10

Thanks, Kerim F

I managed to follow that, although I did need pen and paper

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Prioritise. Persevere. No pain, no gain.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,623

Re: Dividing powers of 10

We are into the realms of logarithms:

So log is the inverse function of 'to the power'

a is called the base and can be anything. Most common are logs in base 10 and logs in the natural log base, e.  Best to have some calculus to appreciate the latter.

On a (scientific) calculator the natural log base button is marked ln, and the base ten button log.

So back to the question

Can I express 2 in terms of 10^y?

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

paulb203

Member

Registered: 2023-02-24

Posts: 317

Re: Dividing powers of 10

Thanks, Bob.

Logarithms are on my to-try-list, but further down the line. Looking forward to them.

I did try out 10^0.3010 and got ≈ 2

Then I tried 10^6-0.3010 and got ≈ 500,000

Q. Should that 6-0.3010 be in brackets?

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Prioritise. Persevere. No pain, no gain.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,623

Re: Dividing powers of 10

Yes as it's 10 to the whole expression.

I'm of an age where there were no calculators to use for calculations. So logs were taught early on as you can make use of this property:

This converts a multiplication into an addition. Similarly divisions and roots.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

paulb203

Member

Registered: 2023-02-24

Posts: 317

Re: Dividing powers of 10

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Prioritise. Persevere. No pain, no gain.