Scientific Notation

PurpleBTae

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Sep 6, 2021
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If I am going from standard form to scientific notation, and I am moving the decimal to the right, will I ADD 1 to the exponent or SUBTRACT 1 from the exponent??
 

PurpleBTae

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Sep 6, 2021
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Oh wait a minute... It would be ADDING wouldn't it? Okay NVM. I will delete this question.
 

Subhotosh Khan

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If I am going from standard form to scientific notation, and I am moving the decimal to the right, will I ADD 1 to the exponent or SUBTRACT 1 from the exponent??
According to your textbook, what is the form of "standard form"?

Please post some example problem where you need to convert from 'standard form to scientific notation'.
 

HallsofIvy

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"Moving the decimal to the right" is equivalent to multiplying that number by a power of 10 but when you are writing a number in "Scientific notation" you want to keep the number the same, NOT change it. so if you multiply one part by a power of 10 you need to divide the other part: 300.97 x 10^8 is the same as 3009.7 x 10^(8-1)= 3009.7 x 10^7.

You can see that if you write the numbers in "regular" notation:
300.97 x 10^8 we need to move the decimal point 8 places so add 6 zeros- 30097000000.
3009.7 x 10^7we need to move the decimal point 7 places so add 6 zeros- 30097000000.
 

Jomo

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If you have a product, you can multiply one number by any non-zero value you want as long as you divide the other number by that same value.

I can easily compute 25*28 in my head (and so can you!). I multiply 25 by 4 to get 100 and I divide 28 by 4 to get 7. So 25*28 = 100*7 which is easily seen to be 700.

Now if you have 300.97*10^7 (and you want this in Scientific Notation) you can divide 300.97 by 100 (or 10^2) to get 3.0097 and multiply 10^7 by 100 or 10^2 to get 10^9. So 300.97*10^7 = 3.0097*10^9.

This is a very powerful tool to have!
 
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