How do you write #0.000000001# in scientific notation?

2 Answers
smendyka
Jan 3, 2017

#1.0 xx 10^-9#

Explanation:

Because we need to move the decimal point 9 places to the right, the exponent for the #10#s term will be negative:

#0.000000001 = 1.0 xx 10^-9#

Tony B
Jan 3, 2017

#1.0xx10^(-9)#

Explanation:

#color(blue)("Perhaps 'splitting hairs'")#

Some people state "move the decimal point"

I state "fix the decimal point and move the numbers".

Reason:

Consider the value 1.0
Now consider the modification #1.0xx10# you have changed from counting in units to counting in tens. Consequently the number shifts to the left by 1 place and you insert the place keeper of 0 giving #10.0 larr" movement of numbers is 1 place"#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Answering the question")#

The target for this number is to end up with #1.0#

But 1.0 is not the same value we started with. So we need to include (without applying it) a correction so that the actual overall value becomes the same.

So we have #1.0/10^9 = 0.000000001#

But another way of writing #1/10^9" is "10^(-9)# so we end up with the form:

#1.0xx1/10^9=1.0xx10^(-9)#

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