Question
Evaluate the following expressions in scientific notation.
(2.1x10^4)(4x10^6)
(7.5x10^8)/(1.5x10^3)
(2.1x10^4)(4x10^6)
(7.5x10^8)/(1.5x10^3)
Answers
GPT-4o mini
To evaluate the given expressions in scientific notation, we will apply the rules of multiplying and dividing numbers in scientific notation.
1. **Multiplication: (2.1 × 10^4)(4 × 10^6)**
When multiplying two numbers in scientific notation, we multiply the coefficients (the numbers in front) and add the exponents of the powers of ten.
\[
(2.1)(4) = 8.4
\]
\[
(10^4)(10^6) = 10^{(4+6)} = 10^{10}
\]
Therefore,
\[
(2.1 × 10^4)(4 × 10^6) = 8.4 × 10^{10}
\]
Since \(8.4\) is already in proper scientific notation (between 1 and 10), we leave it as is.
2. **Division: (7.5 × 10^8) / (1.5 × 10^3)**
When dividing two numbers in scientific notation, we divide the coefficients and subtract the exponents of the powers of ten.
\[
\frac{7.5}{1.5} = 5.0
\]
\[
\frac{10^8}{10^3} = 10^{(8-3)} = 10^{5}
\]
Therefore,
\[
(7.5 × 10^8) / (1.5 × 10^3) = 5.0 × 10^{5}
\]
Again, since \(5.0\) is in proper scientific notation, we leave it as is.
### Final Results:
1. \((2.1 × 10^4)(4 × 10^6) = 8.4 × 10^{10}\)
2. \((7.5 × 10^8) / (1.5 × 10^3) = 5.0 × 10^{5}\)
1. **Multiplication: (2.1 × 10^4)(4 × 10^6)**
When multiplying two numbers in scientific notation, we multiply the coefficients (the numbers in front) and add the exponents of the powers of ten.
\[
(2.1)(4) = 8.4
\]
\[
(10^4)(10^6) = 10^{(4+6)} = 10^{10}
\]
Therefore,
\[
(2.1 × 10^4)(4 × 10^6) = 8.4 × 10^{10}
\]
Since \(8.4\) is already in proper scientific notation (between 1 and 10), we leave it as is.
2. **Division: (7.5 × 10^8) / (1.5 × 10^3)**
When dividing two numbers in scientific notation, we divide the coefficients and subtract the exponents of the powers of ten.
\[
\frac{7.5}{1.5} = 5.0
\]
\[
\frac{10^8}{10^3} = 10^{(8-3)} = 10^{5}
\]
Therefore,
\[
(7.5 × 10^8) / (1.5 × 10^3) = 5.0 × 10^{5}
\]
Again, since \(5.0\) is in proper scientific notation, we leave it as is.
### Final Results:
1. \((2.1 × 10^4)(4 × 10^6) = 8.4 × 10^{10}\)
2. \((7.5 × 10^8) / (1.5 × 10^3) = 5.0 × 10^{5}\)