To solve the multiplication of the numbers [tex]\(2.45 \times 10^8\)[/tex] and [tex]\(8.78 \times 10^6\)[/tex], and express the result in scientific notation, follow these detailed steps:
1. Identify the components in scientific notation:
- The first number is [tex]\(2.45 \times 10^8\)[/tex].
- The second number is [tex]\(8.78 \times 10^6\)[/tex].
2. Multiply the coefficients:
- The coefficients (the non-exponential parts) are 2.45 and 8.78.
- Multiply these: [tex]\(2.45 \times 8.78 = 21.511\)[/tex].
3. Add the exponents:
- The exponential parts are [tex]\(10^8\)[/tex] and [tex]\(10^6\)[/tex].
- Adding the exponents: [tex]\(8 + 6 = 14\)[/tex].
- This results in: [tex]\(10^{14}\)[/tex].
4. Combine the products:
- The result from the coefficient multiplication and the combined exponent is [tex]\(21.511 \times 10^{14}\)[/tex].
5. Express the result in proper scientific notation:
- The proper format for scientific notation requires a single non-zero digit to the left of the decimal point.
- Convert [tex]\(21.511 \times 10^{14}\)[/tex] to [tex]\(2.1511 \times 10^{15}\)[/tex].
- Notice that shifting the decimal point one place to the left increases the exponent by 1.
6. Round the coefficient:
- Round the coefficient to two decimal places for precision: [tex]\(2.15\)[/tex].
- This gives us the final result: [tex]\(2.15 \times 10^{15}\)[/tex].
Therefore, the multiplication of [tex]\(2.45 \times 10^8\)[/tex] and [tex]\(8.78 \times 10^6\)[/tex] results in:
[tex]\[2.15 \times 10^{15}\][/tex]
