To express the distance from the Earth to the Sun, which is 0.000016 light years, in standard form (scientific notation), we follow these steps:
1. Identify the Coefficient and the Exponent: Standard form is typically written as [tex]\( a \times 10^n \)[/tex], where [tex]\( 1 \leq a < 10 \)[/tex] and [tex]\( n \)[/tex] is an integer.
2. Rewrite the Number: Start with the given number 0.000016.
3. Move the Decimal Point: Move the decimal point to the right until you have a number between 1 and 10. For 0.000016, you need to move the decimal point 5 places to the right to get 1.6.
4. Determine the Exponent: Count how many places you moved the decimal point to turn the original number into the coefficient. Since you moved the decimal point 5 places to the right, this translates to multiplying by [tex]\( 10^{-5} \)[/tex].
5. Combine: Combine the coefficient and the exponent to get the number in standard form.
Therefore, 0.000016 light years can be expressed in standard form as:
[tex]\[ 1.6 \times 10^{-5} \][/tex]
So, the distance from the Earth to the Sun in light years in standard form is [tex]\( 1.60 \times 10^{-5} \)[/tex].
