Scientific Notation question

[poopy]

Evaluate the following giving answers in scientific notation:

400 x (2.0 x 10-�)

&

(4.5 x 10small4) � (5.0 x 10-�)

[Suzyboo]

0.8 = 8 * 10 ^ -1

900000 = 9 * 10^5

[Muppit]

Maths homework is much easier these days! I started to think that it would have been handy to have had answer bank when I was at school... but then realised that if I had cheated then I probably wouldn't be able to do it now and wouldn't be one of the country's greatest engineers.

Poopy... if you can't do your homework, as for help, not the answers - you are only cheating yourself! (And everyone else should only be giving guidance too!)

[poopy]

This is not my homework, this is way above me as i was at school 20 years ago! It has been given to my son, he is having trouble understanding it and knows nothing about Answerbank, so i was askin for people to explain for me so i could inturn teach him a simple way of understanding it. Thank you.

[poopy]

Sorry Suzyboo, i didnt mean to ask for the answer i just wanted to know & understand how you did it. Im trying to find an easier way of doing it to explain to my son who is having difficulties understanding.

[mibn2cweus]

poopy, I don't think Suzyboo was offering an answer to the problem; only comparative samples of exponential notation.

Click your mouse here for a more thorough explanation of how to work with exponents. Especially look (scroll about half way down the page) at ~ "Simplify and express in scientific notation:"

[mibn2cweus]

D'oh! . . . on further examination, those were the answers!

[Buenchico]

Because of the difficulties of typing mathematical terms, I've used the ^ notation for what follows. e.g. 10 squared is typed as 10^2, 10 cubed is 10^3 etc:

'Standard index notation' (as it's properly called) requires that a number is written as a term (which must be 1 or greater, and less than 10) multiplied by a power of ten.

So, for example 400 = 4.00 x 10^2

So your first question can be rewritten as
4.00 x 10^2 x 2.0 x 10^-3

4.00 x 2.00 shouldn't present many difficulties! (8, or for a pedantically correct answer, 8.0000)

When multiplying powers of ten, the indices are added, rather than multiplied. (If we were dividing, the second power would be subtracted). So 10^2 x 10^-3 = 10^-1.

So, starting from the beginning, we've got:

400 x (2 x 10^-3)

= 4.00 x 10^2 x 2 x 10^-3

= 8.00 x 10^-1

==========================================

Here's the second question:

(4.5 x 10^4) � (5.0 x 10^-2)

= (4.5 � 5.0) x (10^4 � 10^-2) {I've simply rearranged the terms there, to make things easier}

= 0.9 x 10^6 {It's tempting to think that we've found the answer but the first term isn't in the required range, so we need another stage}

= 9 x 10^-1 x 10^6

= 9 x 10^5

Chris

[factor-fiction]

Oh-No-NoKnow- 3! would be factorial which is 6.

Buenchico- great answer

[Muppit]

My bad. Sorry.