How would you write 90cm in scientific notation?
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
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.
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.
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.
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.
Very true!
I do the same in maths and physics, namely put the decimal point to indicate significance of trailing zeroes where appropriate.
Thanks for the reply, Mathmate.
Thanks for helping out!
To write 90 cm in scientific notation, we need to express it as a number between 1 and 10 multiplied by a power of 10. Here's how you can convert 90 cm to scientific notation:
1. Start by converting 90 cm to meters, since scientific notation typically uses meters as the base unit. Since 1 meter is equal to 100 centimeters, divide 90 cm by 100 to obtain 0.9 meters.
2. Next, express 0.9 meters in scientific notation form by moving the decimal point one place to the right. This gives 9.0 meters.
3. Finally, express 9.0 meters in scientific notation by multiplying it by a power of 10. Since we moved the decimal point one place to the right, the power of 10 will be 10^1. Therefore, we can write 9.0 meters (or 90 cm) in scientific notation as 9.0 x 10^1.
So, 90 cm can be written as 9.0 x 10^1 in scientific notation.