Question
the radius of planet Neptune is approximately 15,300 miles how do you say this in scientific notation
Answers
GPT-4o mini
To express the radius of the planet Neptune, which is approximately 15,300 miles, in scientific notation, you write it as \( 1.53 \times 10^4 \) miles.
Here’s how it breaks down:
- Move the decimal point in 15,300 to the left until only one non-zero digit is to the left of the decimal point (1.53).
- Count how many places you moved the decimal point, which is 4 places.
- Therefore, \( 15,300 = 1.53 \times 10^4 \).
Here’s how it breaks down:
- Move the decimal point in 15,300 to the left until only one non-zero digit is to the left of the decimal point (1.53).
- Count how many places you moved the decimal point, which is 4 places.
- Therefore, \( 15,300 = 1.53 \times 10^4 \).
3.2x10^4+1.95x10^6
GPT-4o mini
To add \(3.2 \times 10^4\) and \(1.95 \times 10^6\), you'll need to express both numbers with the same exponent before you can combine them.
1. Convert \(3.2 \times 10^4\) to an equivalent value with \(10^6\) as the exponent:
\[
3.2 \times 10^4 = 3.2 \times 10^4 \times \frac{10^2}{10^2} = 3.2 \times 10^6 \times 10^{-2} = 0.032 \times 10^6
\]
2. Now we can add:
\[
\begin{align*}
0.032 \times 10^6 + 1.95 \times 10^6 &= (0.032 + 1.95) \times 10^6 \\
&= 1.982 \times 10^6
\end{align*}
\]
So, \(3.2 \times 10^4 + 1.95 \times 10^6 = 1.982 \times 10^6\).
1. Convert \(3.2 \times 10^4\) to an equivalent value with \(10^6\) as the exponent:
\[
3.2 \times 10^4 = 3.2 \times 10^4 \times \frac{10^2}{10^2} = 3.2 \times 10^6 \times 10^{-2} = 0.032 \times 10^6
\]
2. Now we can add:
\[
\begin{align*}
0.032 \times 10^6 + 1.95 \times 10^6 &= (0.032 + 1.95) \times 10^6 \\
&= 1.982 \times 10^6
\end{align*}
\]
So, \(3.2 \times 10^4 + 1.95 \times 10^6 = 1.982 \times 10^6\).
8.3x10^-8+2.56x10^-2
GPT-4o mini
To add \(8.3 \times 10^{-8}\) and \(2.56 \times 10^{-2}\), we first need to express both terms using the same exponent.
1. Convert \(2.56 \times 10^{-2}\) to an equivalent value with \(10^{-8}\) as the exponent:
\[
2.56 \times 10^{-2} = 2.56 \times 10^{-2} \times \frac{10^{6}}{10^{6}} = 2.56 \times 10^{4} \times 10^{-8} = 2560000 \times 10^{-8}
\]
This way, we can express it as:
\[
2.56 \times 10^{-2} = 2.56 \times 10^{6} \times 10^{-8} = 2560000 \times 10^{-8}
\]
2. Now we can add:
\[
8.3 \times 10^{-8} + 2.56 \times 10^{-2} = (8.3 + 2560000) \times 10^{-8} = 2560008.3 \times 10^{-8}
\]
3. Finally, to express this in proper scientific notation:
\[
= 2.5600083 \times 10^{-2}
\]
Thus, the sum \(8.3 \times 10^{-8} + 2.56 \times 10^{-2} \approx 2.56 \times 10^{-2}\), with the addition of the other term being negligible.
So, the final result in scientific notation is approximately:
\[
2.56 \times 10^{-2}
\]
1. Convert \(2.56 \times 10^{-2}\) to an equivalent value with \(10^{-8}\) as the exponent:
\[
2.56 \times 10^{-2} = 2.56 \times 10^{-2} \times \frac{10^{6}}{10^{6}} = 2.56 \times 10^{4} \times 10^{-8} = 2560000 \times 10^{-8}
\]
This way, we can express it as:
\[
2.56 \times 10^{-2} = 2.56 \times 10^{6} \times 10^{-8} = 2560000 \times 10^{-8}
\]
2. Now we can add:
\[
8.3 \times 10^{-8} + 2.56 \times 10^{-2} = (8.3 + 2560000) \times 10^{-8} = 2560008.3 \times 10^{-8}
\]
3. Finally, to express this in proper scientific notation:
\[
= 2.5600083 \times 10^{-2}
\]
Thus, the sum \(8.3 \times 10^{-8} + 2.56 \times 10^{-2} \approx 2.56 \times 10^{-2}\), with the addition of the other term being negligible.
So, the final result in scientific notation is approximately:
\[
2.56 \times 10^{-2}
\]