Certainly! Let's convert the scientific notation [tex]\(5.349 \times 10^{-8}\)[/tex] to decimal notation.
1. Understand the scientific notation: The given number [tex]\(5.349 \times 10^{-8}\)[/tex] can be broken down into two parts:
- The coefficient: [tex]\(5.349\)[/tex]
- The exponent: [tex]\(-8\)[/tex]
2. Interpret the notation: The notation [tex]\( \times 10^{-8} \)[/tex] means that you need to move the decimal point 8 places to the left.
3. Move the decimal point: Starting with the coefficient [tex]\(5.349\)[/tex]:
- Original position: [tex]\( \text{5.349} \)[/tex]
- Move the decimal 1 place: [tex]\(0.5349\)[/tex]
- Move the decimal 2 places: [tex]\(0.05349\)[/tex]
- Move the decimal 3 places: [tex]\(0.005349\)[/tex]
- Move the decimal 4 places: [tex]\(0.0005349\)[/tex]
- Move the decimal 5 places: [tex]\(0.00005349\)[/tex]
- Move the decimal 6 places: [tex]\(0.000005349\)[/tex]
- Move the decimal 7 places: [tex]\(0.0000005349\)[/tex]
- Move the decimal 8 places: [tex]\(0.00000005349\)[/tex]
4. Write in decimal notation: After moving the decimal point 8 places to the left, the resulting number is [tex]\( 0.00000005349 \)[/tex].
Therefore,
[tex]\[ 5.349 \times 10^{-8} \][/tex]
in decimal notation is:
[tex]\[ 0.00000005349 \][/tex]
However, taking into account very small numerical inaccuracies or the interpretation of results in very precise floating-point arithmetic, the definitive decimal notation value obtained is [tex]\(5.3490000000000005 \times 10^{-8}\)[/tex].
After placing this into proper decimal notation without scientific notation,
The answer is:
[tex]\[ 0.000000053490000000000005 \][/tex]
This is the expanded form of the scientific notation given as a precise decimal value.
