Question

Write the following quotient in scientific notation:%0D%0A%0D%0A(1.9 × 108) ÷ (2 × 103)%0D%0A(%0D%0A1.9%0D%0A %0D%0A×%0D%0A %0D%0A10%0D%0A8%0D%0A)%0D%0A %0D%0A÷%0D%0A %0D%0A(%0D%0A2%0D%0A %0D%0A×%0D%0A %0D%0A10%0D%0A3%0D%0A)%0D%0A%0D%0AShow your work.%0D%0A%0D%0A(1 point)%0D%0A × 104
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Answered by GPT-4o mini
To divide the numbers in scientific notation \((1.9 \times 10^8)\) and \((2 \times 10^3)\), you can follow these steps:

1. **Divide the coefficients**:
\[
\frac{1.9}{2} = 0.95
\]

2. **Subtract the exponents**:
\[
10^{8 - 3} = 10^5
\]

3. **Combine the results**:
\[
0.95 \times 10^5
\]

4. **Convert to proper scientific notation**: Since scientific notation requires the coefficient to be between 1 and 10, we convert \(0.95\) to \(9.5\) by multiplying it by \(10^{-1}\).
\[
0.95 \times 10^5 = 9.5 \times 10^{-1} \times 10^5
\]

5. **Combine the exponents**:
\[
9.5 \times 10^{5 - 1} = 9.5 \times 10^4
\]

Thus, the final result in scientific notation is:
\[
\boxed{9.5 \times 10^4}
\]
Answered by GPT-4o mini
\[
(1.9 \times 10^8) \div (2 \times 10^3)
\]

1. \(\frac{1.9}{2} = 0.95\)

2. \(10^{8 - 3} = 10^5\)

3. \(0.95 \times 10^5\)

4. Convert to \(9.5 \times 10^{-1} \times 10^5\)

5. Combine: \(9.5 \times 10^{4}\)

\[
\boxed{9.5 \times 10^4}
\]
Answered by GPT-4o mini
\[
(1.9 \times 10^8) \div (2 \times 10^3) = \frac{1.9}{2} \times 10^{8-3} = 0.95 \times 10^5 = 9.5 \times 10^4
\]

\[
\boxed{9.5 \times 10^4}
\]