Scientific Notation question
Evaluate the following giving answers in scientific notation:
400 x (2.0 x 10-³)
&
(4.5 x 10small4) ÷ (5.0 x 10-²)
poopy Sat 06/09/08 10:17
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0.8 = 8 * 10 ^ -1
900000 = 9 * 10^5
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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!)
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Question Author
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.
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Question Author
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.
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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:"
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D'oh! . . . on further examination, those were the answers!
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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
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Oh-No-NoKnow- 3! would be factorial which is 6.
Buenchico- great answer
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