Answer :
To write the diameter of a white blood cell, 0.000591 inches, in scientific notation, we need to express it as a number between 1 and 10 multiplied by a power of 10.
Here’s the step-by-step process:
1. Identify the Significant Figures: The number we need to convert is 0.000591. Notice the significant figures here, which are 5, 9, and 1.
2. Convert to Scientific Notation:
- Move the decimal point to the right until you have a number between 1 and 10. For 0.000591, we move the decimal point 4 places to the right, which gives us 5.91.
- Count the number of places moved. In this case, it is 4 places.
3. Determine the Power of 10:
- Since we moved the decimal point 4 places to the right, we express this movement as a negative power of 10 because the original number is less than 1.
- Thus, the power of 10 will be [tex]\(-4\)[/tex].
4. Write the Number in Scientific Notation:
- Combine the number and the power of ten: [tex]\(5.91 \times 10^{-4}\)[/tex].
Therefore, 0.000591 inches written in scientific notation is [tex]\(5.91 \times 10^{-4}\)[/tex] inches, which matches the option given as [tex]$5.91 \times 10^{-4}$[/tex] in.
Here’s the step-by-step process:
1. Identify the Significant Figures: The number we need to convert is 0.000591. Notice the significant figures here, which are 5, 9, and 1.
2. Convert to Scientific Notation:
- Move the decimal point to the right until you have a number between 1 and 10. For 0.000591, we move the decimal point 4 places to the right, which gives us 5.91.
- Count the number of places moved. In this case, it is 4 places.
3. Determine the Power of 10:
- Since we moved the decimal point 4 places to the right, we express this movement as a negative power of 10 because the original number is less than 1.
- Thus, the power of 10 will be [tex]\(-4\)[/tex].
4. Write the Number in Scientific Notation:
- Combine the number and the power of ten: [tex]\(5.91 \times 10^{-4}\)[/tex].
Therefore, 0.000591 inches written in scientific notation is [tex]\(5.91 \times 10^{-4}\)[/tex] inches, which matches the option given as [tex]$5.91 \times 10^{-4}$[/tex] in.
