Question

How would you write 90cm in scientific notation?

Answer 1

The goal of writing a number in scientific notation is to have a decimal number, with one digit to theleft of the decmial point, followed by a × 10to some power.
To format your number in this way, we'll divide the 90cm by 10, 1 time(s), making it a 9.
We do this, because each division by 10 moves the decimal point to the left one digit.
But in order to keep our number the same number, we must have a × 101 next to the 9.


So, the final answer is 9 × 101

Answer 2

I forgot to mention it is to be expressed in meters, using powers of 10. I don't know if that will change the answer.

Answer 3

Yes, by converting to metres,
90 cm = 0.1 m.
So
0.1 m = 1.*10^-1
Note that I did not put 1.0 because the original number is 90, which does not guarantee the accuracy of the second digit. A trailing zero can be indicated significant by overlining or underlining the number.

Answer 4

Yes, by converting to metres,
90 cm = 0.9 m.
So
0.9 m = 9.*10-1
Note that I did not put 9.0 because the original number is 90, which does not guarantee the accuracy of the second digit. A trailing zero of a whole number can be made significant by overlining or underlining the last significant zero.

Answer 5

Another way to indicate that the zero of 90 is a significant figure is to place a decimal after the zero, (as in 90.). So 9 x 10^1 means you have only one s.f. and 90. would be that both the 9 and the zero were s.f. A problem is created, however, when the 90 comes at the end of a sentence which ends with a period; we don't know if the . is telling us its the end of a sentence or that the number has two s.f. (or both). I hope this doesn't violate any math rules; I use this in chemistry.

Answer 6

Very true!
I do the same in maths and physics, namely put the decimal point to indicate significance of trailing zeroes where appropriate.

Answer 7

Thanks for the reply, Mathmate.

Answer 8

Thanks for helping out!