Question

Find the quotient if the dividend is 2.26 · 108 and the divisor is 0.013.

5.75 × 10 -11
1.738 × 10 10
1.738 × 10 6
2.938 × 10 6

Answer 1

To find the quotient of the dividend \(2.26 \times 10^8\) and the divisor \(0.013\), we can proceed as follows:

1. **Convert the divisor to scientific notation:**
\[
0.013 = 1.3 \times 10^{-2}
\]

2. **Now, we can compute the quotient:**
\[
\frac{2.26 \times 10^8}{0.013} = \frac{2.26 \times 10^8}{1.3 \times 10^{-2}}
\]

3. **Split this into two parts** (dividing the coefficients and subtracting the exponents):
\[
\frac{2.26}{1.3} \times 10^{8 - (-2)} = \frac{2.26}{1.3} \times 10^{8 + 2} = \frac{2.26}{1.3} \times 10^{10}
\]

4. **Now, we can calculate \(\frac{2.26}{1.3}\):**
\[
2.26 \div 1.3 \approx 1.73846
\]
(For simplicity, we can keep it as \(1.738\) for now.)

5. **Putting this back together:**
\[
1.738 \times 10^{10}
\]

Thus, the result of the division \( \frac{2.26 \times 10^8}{0.013} \) is approximately:

\[
\boxed{1.738 \times 10^{10}}
\]