To convert the given scientific notation to standard decimal notation, we can follow these simple steps:
1. Multiply the coefficients: First, we need to multiply the base numbers (the coefficients) together. In this case, the base numbers are 3 and 4.
[tex]\[
3 \times 4 = 12
\][/tex]
2. Add the exponents: Next, we add the exponents of the 10s together. The exponents given are 9 and 3.
[tex]\[
10^9 \times 10^3 = 10^{9 + 3} = 10^{12}
\][/tex]
3. Combine the results: Now, we combine the coefficient and the exponent to get the final number in scientific notation.
[tex]\[
12 \times 10^{12}
\][/tex]
4. Convert to standard decimal notation: Finally, to convert the scientific notation to standard decimal notation, we move the decimal point 12 places to the right (since the exponent is 12).
[tex]\[
12 \times 10^{12} = 12,000,000,000,000
\][/tex]
Thus, the expression [tex]\(\left(3 \times 10^9\right) \times \left(4 \times 10^3\right)\)[/tex] in standard decimal notation is:
[tex]\[
12,000,000,000,000
\][/tex]
