Question
How many times larger is 6.945 × 1010 than 1.5 × 108?
Answers
GPT-4o mini
To find out how many times larger \( 6.945 \times 10^{10} \) is than \( 1.5 \times 10^{8} \), we can divide the two numbers:
\[
\text{Ratio} = \frac{6.945 \times 10^{10}}{1.5 \times 10^{8}}
\]
This can be simplified by separating the coefficients and the powers of ten:
\[
\text{Ratio} = \frac{6.945}{1.5} \times \frac{10^{10}}{10^{8}}
\]
Calculating the powers of ten:
\[
\frac{10^{10}}{10^{8}} = 10^{10-8} = 10^{2}
\]
Now substituting this into the equation:
\[
\text{Ratio} = \frac{6.945}{1.5} \times 10^{2}
\]
Next, we calculate \( \frac{6.945}{1.5} \):
\[
\frac{6.945}{1.5} = 4.63 \text{ (approximately)}
\]
Now substituting this back into the equation:
\[
\text{Ratio} \approx 4.63 \times 10^{2}
\]
Calculating \( 4.63 \times 10^{2} \):
\[
4.63 \times 10^{2} = 463
\]
Therefore, \( 6.945 \times 10^{10} \) is approximately **463 times larger** than \( 1.5 \times 10^{8} \).
\[
\text{Ratio} = \frac{6.945 \times 10^{10}}{1.5 \times 10^{8}}
\]
This can be simplified by separating the coefficients and the powers of ten:
\[
\text{Ratio} = \frac{6.945}{1.5} \times \frac{10^{10}}{10^{8}}
\]
Calculating the powers of ten:
\[
\frac{10^{10}}{10^{8}} = 10^{10-8} = 10^{2}
\]
Now substituting this into the equation:
\[
\text{Ratio} = \frac{6.945}{1.5} \times 10^{2}
\]
Next, we calculate \( \frac{6.945}{1.5} \):
\[
\frac{6.945}{1.5} = 4.63 \text{ (approximately)}
\]
Now substituting this back into the equation:
\[
\text{Ratio} \approx 4.63 \times 10^{2}
\]
Calculating \( 4.63 \times 10^{2} \):
\[
4.63 \times 10^{2} = 463
\]
Therefore, \( 6.945 \times 10^{10} \) is approximately **463 times larger** than \( 1.5 \times 10^{8} \).