8.9 x 10^-3
8.90 x 10^-3
It has to be 10^-3 (ten to the negative three) because when you move the decimal back to it’s proper place you are moving it to the left.
and it has to be 8.90 because you have to observe correct sig figs. The 0 at the end of the number is significant because it is at the end of the number AND to the right of the decimal point.
8.90 x 10^3
you need to keep all the sig figs
How do you express a number in scientific notation?
A scientific notation is a way to represent very large or very small numbers concisely, where a number is written in the form of power of 10, following the formula below:
m × 10n
- m, the mantissa, must be between 0 and 9.999 …
- n, the exponent, is a positive or a negative integer, including 0
To convert any number to scientific notation, we must follow these two rules:
- The decimal will be shifted to the left whenever the given number is 10 or greater and the power of 10 is positive.
- The decimal will be shifted to the right whenever the given number is smaller than 1 and the power of 10 is negative.
Let’s learn through examples:
Example 1: How do you express 0.0005 in scientific notation?
This number 0.0005 can be written as 0.0005 × 100 in powers of 10.
So, according to the first rule, to convert 0.0005 × 100 to scientific notation, we will shift the decimal to right and multiply with negative powers of 10 until the number comes between 1 and 10.
Thus, the scientific notation for 0.0005 is 5 × 10-4
Example 2: How do you write 427,000 in scientific notation?
This number 427000 can be written as 427000 × 100 in powers of 10.
So, according to the first rule, to convert 427000 × 100 into scientific notation, we will shift the decimal to right and multiply with positive powers of 10 until the number comes between 1 and 10.
So, the scientific notation for 427000 is 4.27000 × 10-4