Question
To best estimate the quotient in scientific notation, what number should replace m?
StartFraction 6.33 times 10 Superscript 9 Baseline Over 1.79 times 10 Superscript 5 Baseline EndFraction almost-equals 3 times 10 Superscript m
StartFraction 6.33 times 10 Superscript 9 Baseline Over 1.79 times 10 Superscript 5 Baseline EndFraction almost-equals 3 times 10 Superscript m
Answers
GPT-4o mini
To estimate the quotient \(\frac{6.33 \times 10^9}{1.79 \times 10^5}\) and express it in scientific notation, we will first divide the coefficients and then subtract the exponents of the powers of ten.
1. **Divide the coefficients:**
\[
\frac{6.33}{1.79} \approx 3.54 \quad (\text{for estimation, we can round to } 3.5 \text{ or even } 3)
\]
2. **Subtract the exponents:**
\[
10^{9 - 5} = 10^4
\]
3. **Combine the results:**
\[
\frac{6.33 \times 10^9}{1.79 \times 10^5} \approx 3.5 \times 10^4
\]
Now, we round \(3.5\) to \(3\) for simplicity in our estimation.
Hence, the expression in scientific notation will be:
\[
3 \times 10^4
\]
Since we are told that the expression is almost equal to \(3 \times 10^m\), we can see that:
\[
m = 4
\]
Therefore, the number that should replace \(m\) is \(\boxed{4}\).
1. **Divide the coefficients:**
\[
\frac{6.33}{1.79} \approx 3.54 \quad (\text{for estimation, we can round to } 3.5 \text{ or even } 3)
\]
2. **Subtract the exponents:**
\[
10^{9 - 5} = 10^4
\]
3. **Combine the results:**
\[
\frac{6.33 \times 10^9}{1.79 \times 10^5} \approx 3.5 \times 10^4
\]
Now, we round \(3.5\) to \(3\) for simplicity in our estimation.
Hence, the expression in scientific notation will be:
\[
3 \times 10^4
\]
Since we are told that the expression is almost equal to \(3 \times 10^m\), we can see that:
\[
m = 4
\]
Therefore, the number that should replace \(m\) is \(\boxed{4}\).