Question

Solve the following and write in scientific notation:
1.2 x 10^ 8 / 4 x 10
Solve the following and write in scientific notation:
9.1 x 10^ 13 / 7 x 10 ^ 5
Solve the following and write in scientific notation:

6.3 x 10^8 / 1.8 x 10 ^ -4
Solve the following and write in scientific notation:

(1.2 x 10 ^ 8) / (5 x 10^ 9)
Solve the following and write in scientific notation:
1.6 X 10^4/
2.5 X 10^9

Answer 1

Let's solve each of these problems step by step and express the answers in scientific notation.

### Problem 1:
\[
\frac{1.2 \times 10^8}{4 \times 10}
\]

**Step 1: Divide the coefficients.**
\[
\frac{1.2}{4} = 0.3
\]

**Step 2: Subtract the exponents.**
\[
\frac{10^8}{10^1} = 10^{8-1} = 10^7
\]

**Step 3: Combine the results.**
\[
0.3 \times 10^7 = 3.0 \times 10^6
\]

### Problem 2:
\[
\frac{9.1 \times 10^{13}}{7 \times 10^{5}}
\]

**Step 1: Divide the coefficients.**
\[
\frac{9.1}{7} \approx 1.3
\]

**Step 2: Subtract the exponents.**
\[
\frac{10^{13}}{10^{5}} = 10^{13-5} = 10^8
\]

**Step 3: Combine the results.**
\[
1.3 \times 10^8
\]

### Problem 3:
\[
\frac{6.3 \times 10^{8}}{1.8 \times 10^{-4}}
\]

**Step 1: Divide the coefficients.**
\[
\frac{6.3}{1.8} = 3.5
\]

**Step 2: Subtract the exponents.**
\[
\frac{10^{8}}{10^{-4}} = 10^{8 - (-4)} = 10^{8 + 4} = 10^{12}
\]

**Step 3: Combine the results.**
\[
3.5 \times 10^{12}
\]

### Problem 4:
\[
\frac{1.2 \times 10^{8}}{5 \times 10^{9}}
\]

**Step 1: Divide the coefficients.**
\[
\frac{1.2}{5} = 0.24
\]

**Step 2: Subtract the exponents.**
\[
\frac{10^{8}}{10^{9}} = 10^{8 - 9} = 10^{-1}
\]

**Step 3: Combine the results.**
\[
0.24 \times 10^{-1} = 2.4 \times 10^{-2}
\]

### Problem 5:
\[
\frac{1.6 \times 10^{4}}{2.5 \times 10^{9}}
\]

**Step 1: Divide the coefficients.**
\[
\frac{1.6}{2.5} = 0.64
\]

**Step 2: Subtract the exponents.**
\[
\frac{10^{4}}{10^{9}} = 10^{4 - 9} = 10^{-5}
\]

**Step 3: Combine the results.**
\[
0.64 \times 10^{-5} = 6.4 \times 10^{-6}
\]

### Summary of Results:
1. \( \frac{1.2 \times 10^8}{4 \times 10} = 3.0 \times 10^6 \)
2. \( \frac{9.1 \times 10^{13}}{7 \times 10^{5}} = 1.3 \times 10^{8} \)
3. \( \frac{6.3 \times 10^{8}}{1.8 \times 10^{-4}} = 3.5 \times 10^{12} \)
4. \( \frac{1.2 \times 10^{8}}{5 \times 10^{9}} = 2.4 \times 10^{-2} \)
5. \( \frac{1.6 \times 10^{4}}{2.5 \times 10^{9}} = 6.4 \times 10^{-6} \)