To multiply the given numbers in scientific notation, follow these detailed steps:
1. Identify the numbers and their exponents:
- The first number is [tex]\( 1.7 \times 10^{-6} \)[/tex]
- The second number is [tex]\( 5.8 \times 10^{-19} \)[/tex]
2. Multiply the coefficients (the decimal parts):
- [tex]\( 1.7 \times 5.8 \)[/tex]
- To multiply these, you get:
[tex]\[
1.7 \times 5.8 = 9.86
\][/tex]
3. Add the exponents:
- The exponents are [tex]\(-6\)[/tex] and [tex]\(-19\)[/tex]
- Adding these exponents:
[tex]\[
-6 + (-19) = -25
\][/tex]
4. Combine the result from the coefficient multiplication with the sum of the exponents:
- Combine [tex]\( 9.86 \)[/tex] with [tex]\( 10^{-25} \)[/tex]
[tex]\[
9.86 \times 10^{-25}
\][/tex]
So, the product of [tex]\( \left(1.7 \times 10^{-6}\right) \times \left(5.8 \times 10^{-19}\right) \)[/tex] is
[tex]\[
9.86 \times 10^{-25}
\][/tex]
This is the final answer, expressed in appropriate scientific notation.
