To convert the number [tex]\(0.13 \times 10^5\)[/tex] into correct scientific notation, follow these detailed steps:
1. Identify the given number: We start with [tex]\(0.13 \times 10^5\)[/tex].
2. Understand the format for scientific notation: Scientific notation requires the coefficient to be a number between 1 and 10. This means we need to adjust [tex]\(0.13\)[/tex] to fall within this range.
3. Adjust the coefficient:
- The current coefficient is [tex]\(0.13\)[/tex].
- To convert [tex]\(0.13\)[/tex] into a number between 1 and 10, move the decimal point to the right by one position. This gives us [tex]\(1.3\)[/tex].
4. Adjust the exponent:
- Moving the decimal point one place to the right in [tex]\(0.13\)[/tex] increases the value by a factor of 10.
- Therefore, to keep the overall value the same, we must decrease the exponent by 1.
5. Calculate the new exponent:
- The original exponent was 5.
- Subtracting 1 from this, the new exponent becomes [tex]\(5 - 1 = 4\)[/tex].
6. Write the result in scientific notation:
- The adjusted coefficient is [tex]\(1.3\)[/tex].
- The base remains [tex]\(10\)[/tex].
- The adjusted exponent is 4.
Thus, the correct scientific notation for [tex]\(0.13 \times 10^5\)[/tex] is:
[tex]$
1.3 \times 10^4
$[/tex]
So, the coefficient to enter in the green box is [tex]\(1.3\)[/tex] and the exponent to enter in the yellow box is [tex]\(4\)[/tex].
