Sure! Let's convert the given number [tex]\( 0.065 \times 10^8 \)[/tex] into proper scientific notation step-by-step.
1. Understand the format of scientific notation:
Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form. It is generally written as:
[tex]\[
a \times 10^b
\][/tex]
where [tex]\( 1 \leq a < 10 \)[/tex] and [tex]\( b \)[/tex] is an integer.
2. Identify the number and its base:
The given number is [tex]\( 0.065 \times 10^8 \)[/tex].
3. Adjust the decimal place:
We need to convert [tex]\( 0.065 \)[/tex] into a number between 1 and 10. To do this, we move the decimal point one place to the right:
[tex]\[
0.065 \rightarrow 6.5
\][/tex]
4. Adjust the exponent:
Since we moved the decimal one place to the right to convert [tex]\( 0.065 \)[/tex] to [tex]\( 6.5 \)[/tex], we counterbalance this by decreasing the exponent by the same amount (from [tex]\( 8 \)[/tex] to [tex]\( 7 \)[/tex]).
5. Combine the coefficient and the adjusted exponent:
Thus, the number in proper scientific notation is:
[tex]\[
6.5 \times 10^6
\][/tex]
So, the coefficient [tex]\( a \)[/tex] is [tex]\( 6.5 \)[/tex] (this goes into the green box) and the exponent [tex]\( b \)[/tex] is [tex]\( 6 \)[/tex] (this goes into the yellow box).
