To convert the number 123 [tex]\(\times\)[/tex] 10[tex]\(^-8\)[/tex] into the correct scientific notation, follow these steps:
1. Understand the form of scientific notation: Scientific notation expresses a number as [tex]\(a \times 10^b\)[/tex], where [tex]\(1 \leq a < 10\)[/tex] and [tex]\(b\)[/tex] is an integer.
2. Adjust the given number: The number we have is 123. To convert 123 into a value between 1 and 10, we need to move the decimal point two places to the left.
- Move the decimal point two places to the left in 123:
[tex]\[
123 \rightarrow 1.23 \times 10^2
\][/tex]
3. Combine the new base value with the original power of 10: We initially had 123 [tex]\(\times\)[/tex] 10[tex]\(^-8\)[/tex]. Now we represent 123 as [tex]\(1.23 \times 10^2\)[/tex]. Therefore, we need to combine the exponents from the conversion:
- The 2 in [tex]\(10^2\)[/tex] comes from moving the decimal point.
- The original exponent is [tex]\(-8\)[/tex].
Now, add these exponents together:
[tex]\[
2 + (-8) = -6
\][/tex]
4. Write the final scientific notation: Now combine the coefficient [tex]\(1.23\)[/tex] with the new exponent of 10:
[tex]\[
1.23 \times 10^{-6}
\][/tex]
So the correct scientific notation for [tex]\(123 \times 10^{-8}\)[/tex] is:
[tex]\[1.23 \times 10^{-6}\][/tex]
