Pregunta
Work out the value of \( \left(5 \times 10^{3}\right) \times\left(6 \times 10^{7}\right) \) Give your answer in standard form.
Ask by Reyes Hodgson. in the United Kingdom
Jan 21,2025
Solución de tutoría real
Respuesta verificada por el tutor
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\( 3 \times 10^{11} \)
Solución
To evaluate \( \left(5 \times 10^{3}\right) \times \left(6 \times 10^{7}\right) \) and express the result in standard form (also known as scientific notation), follow these steps:
1. **Multiply the Coefficients:**
\( 5 \times 6 = 30 \)
2. **Multiply the Powers of 10:**
\( 10^{3} \times 10^{7} = 10^{3 + 7} = 10^{10} \)
3. **Combine the Results:**
\( 30 \times 10^{10} \)
4. **Convert to Standard Form:**
Standard form requires the coefficient to be between 1 and 10. To adjust:
\( 30 \times 10^{10} = 3 \times 10^{1} \times 10^{10} = 3 \times 10^{11} \)
**Final Answer in Standard Form:**
\[
3 \times 10^{11}
\]
Revisado y aprobado por el equipo de tutoría de UpStudy
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Simplifique esta solución The Deep Dive
To find the value of \( \left(5 \times 10^{3}\right) \times\left(6 \times 10^{7}\right) \), we can separate the constants and the powers of ten. First, multiply the constants: \( 5 \times 6 = 30 \). Next, multiply the powers of ten: \( 10^{3} \times 10^{7} = 10^{(3+7)} = 10^{10} \). Now we can combine these results: \( 30 \times 10^{10} \). To express this in standard form, we convert \( 30 \) to \( 3.0 \times 10^{1} \): \[ 30 \times 10^{10} = (3.0 \times 10^{1}) \times 10^{10} = 3.0 \times 10^{(1+10)} = 3.0 \times 10^{11}. \] Thus, the final answer in standard form is: \[ \boxed{3.0 \times 10^{11}}. \]
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