To convert [tex]\( 0.13 \times 10^5 \)[/tex] into correct scientific notation, follow these detailed steps:
1. Convert the Base Number to Scientific Notation:
- Start with the number 0.13.
- Convert 0.13 into a value between 1 and 10 by moving the decimal point one place to the right. This gives you 1.3.
- Since you moved the decimal point one place to the right, you need to account for this by subtracting 1 from the exponent. Mathematically, 0.13 can be expressed as [tex]\( 1.3 \times 10^{-1} \)[/tex].
2. Combine with the Original Exponential Factor:
- You now have [tex]\( 1.3 \times 10^{-1} \)[/tex] from the base number and you need to combine it with the [tex]\( 10^5 \)[/tex] from the original expression.
- When you multiply exponential terms with the same base, you add the exponents. Thus, you add the exponent from the transformed base number (-1) to the exponent from the original exponential factor (5).
3. Add the Exponents:
- The exponent addition is: [tex]\( -1 + 5 \)[/tex].
- This results in 4.
4. Write the Final Scientific Notation:
- Now, combine the coefficient 1.3 with the new exponent 4.
- Therefore, the correct scientific notation for [tex]\( 0.13 \times 10^5 \)[/tex] is [tex]\( 1.3 \times 10^4 \)[/tex].
So, the final result is:
[tex]\[
1.3 \times 10^4
\][/tex]
