Sure, let's convert the given distance from Earth to the Sun into standard form.
1. Understanding the Problem:
We are given a distance of [tex]\(0.000016\)[/tex] light years, and we need to express this distance in standard form. Standard form is generally written as [tex]\(a \times 10^b\)[/tex], where [tex]\(a\)[/tex] is a number greater than or equal to 1 and less than 10, and [tex]\(b\)[/tex] is an integer.
2. Finding the Standard Form:
To convert [tex]\(0.000016\)[/tex] into standard form, we need to express it as a product of a number and a power of 10.
3. Step-by-Step Conversion:
- First, identify the significant digits in the number [tex]\(0.000016\)[/tex]. The significant digits here are [tex]\(1.6\)[/tex].
- To convert [tex]\(1.6\)[/tex] into the form [tex]\(0.000016\)[/tex], observe how many places the decimal point is moved to the left. We start from:
[tex]\[
0.000016 = 1.6 \times 10^{-5}
\][/tex]
- Here, the decimal point is moved 5 places to the right to convert [tex]\(1.6\)[/tex] into [tex]\(0.000016\)[/tex], thereby multiplying by [tex]\(10^{-5}\)[/tex].
4. Writing in Standard Form:
Therefore, the distance [tex]\(0.000016\)[/tex] light years can be expressed in standard form as:
[tex]\[
1.6 \times 10^{-5}
\][/tex]
5. Summary:
- The standard form of [tex]\(0.000016\)[/tex] light years is:
[tex]\[
1.6 \times 10^{-5}
\][/tex]
So, the final answer in standard form is:
[tex]\[
1.6 \times 10^{-5} \text{ light years}
\][/tex]
