To convert the number given in scientific notation [tex]\(3.15 \times 10^7\)[/tex] into standard form, follow these steps:
1. Identify the Components: Separate the scientific notation into its two main parts: the base and the exponent. Here, the base is [tex]\(3.15\)[/tex] and the exponent is [tex]\(7\)[/tex], which represents the power of [tex]\(10\)[/tex].
2. Move the Decimal Point: The exponent [tex]\(7\)[/tex] tells us to move the decimal point in the base [tex]\(3.15\)[/tex] seven places to the right. This is because a positive exponent indicates a large number.
3. Fill in with Zeros: As you move the decimal point, fill in the empty places with zeros as needed. Starting from [tex]\(3.15\)[/tex]:
- Move the decimal point 1 place: [tex]\(31.5\)[/tex]
- Move the decimal point 2 places: [tex]\(315.\)[/tex]
- Move the decimal point 3 places: [tex]\(3150.\)[/tex]
- Move the decimal point 4 places: [tex]\(31500.\)[/tex]
- Move the decimal point 5 places: [tex]\(315000.\)[/tex]
- Move the decimal point 6 places: [tex]\(3150000.\)[/tex]
- Move the decimal point 7 places: [tex]\(31500000.\)[/tex]
4. Final Result: The number in standard form, with all positions accounted for, is [tex]\(31,500,000\)[/tex].
Therefore, the radius of each bacterium written as a decimal number in standard form is [tex]\(31,500,000\)[/tex] meters.
