Help with indices

[neddyw]

Can someone please help with this question.
(2.5x10^2) x (4.5x10^-3) = 1.125x10^0
I thought if you multiplied numbers with indices you timesed the numbers then added the indices but 2+ -3 doesnt equal 0?

[mollykins]

you have (2.5x100) x (4.5 x (10/3)) = 1.125 (the final 10 is to the power of 0 which always equals 1)

[mollykins]

Hangon i think i got the 10/3 bit wrong sorry.

anything to the power of 0 is 1.

'a' to the power of 1 = 'a'

'a' to the power of '-b' equals 1/ 'a' to the power of 'b'

so the second brackets would be (4.5 x (1/10 to the power of 3)

[mollykins]

So you have (2.5x100) X (4.5x (1/ 10 to the power of 3) = 1.125

[Prudie]

You are nearly there and correct

2.5 x10^2 x 4.5 x 10^-3 = 2.5 x 4.5 x 10^(2 + -3) =11.25 x 10^ -1 = 1.25 x 10^0

As Molly said they are making the answer multiply by 1
Suggest it was expected in standard form ( a number expressed as >0<10 raised to a power of 10)

[Prudie]

sorry typo
= 1.125 x 10^0

[mollykins]

where did you get the 2+-3 from?

[Prudie]

adding the powers of 10 in the question 2 and -3 (gives 10 to the -1)

[neddyw]

Thanks for responses guys. The bit I was struggling with was where the 10^0 came from. Like I sais in my question I thought you added the indices together. Do you do that for something else??

[Prudie]

you are right neddy, you do add the indices. As I tried to explain at the end of my post the answer comes out to 11.25 x 10^ -1 which you get from adding the indices.
They've gone one step further though and instead of 11.25 as the numerical bit they have divided by 10 to give 1.125. To keep the equality then the power has to be multiplied by 10:-
10^-1 x 10^1 = 10^0 = 1
It's just a different way of expressing the answer but is the same value

[neddyw]

Many thanks Prudie. I'm ok at maths if you use words of 1 syllabel!!

[bibblebub]

you mean 10^0 syllables

[Buenchico]

Just to add to what's been written above:

A number is only said to be expressed in 'standard index form' (a x 10^b) when a is between 1 and 10. (a can be exactly equal to 1, but not to 10).

So, if you simply write the answer to your multiplication as 11.25 x 10^-1 you have failed to produce an answer in standard index form.

So it's necessary to write 11.25 in standard index form itself, and then to multiply it by 10^-1:
11.25 x 10^-1 = 1.125 x 10^1 x 10^-1 = 1.125 x 10^0

Simply keep it in mind that the first term must be between 1 and 10, then you won't go wrong ;-)

Chris

[factor-fiction]

Drat- I missed this thread, although I couldn't have improved on those excellent answers from Prudie and Buenchico.