Pregunta
In scientific notation is \( 4 \times 10^{12} \times 7 \times 10^{7}= \) A. \( 28 \times 10^{20} \) B. \( 2,8 \times 10^{18} \) C. \( 2,8 \times 10^{20} \) D. \( 0,28 \times 10^{18} \)
Ask by Horton Murphy. in South Africa
Mar 09,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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The answer is \(2.8 \times 10^{20}\), choice C.
Solución
1. Multiply the coefficients:
\[
4 \times 7 = 28
\]
2. Multiply the powers of ten by adding the exponents:
\[
10^{12} \times 10^{7} = 10^{12+7} = 10^{19}
\]
3. Combine the results:
\[
28 \times 10^{19}
\]
4. Convert to proper scientific notation by writing \(28\) as \(2.8 \times 10\):
\[
28 \times 10^{19} = 2.8 \times 10^{1} \times 10^{19} = 2.8 \times 10^{20}
\]
Thus, the answer is \(2.8 \times 10^{20}\), which corresponds to option C.
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Simplifique esta solución Extra Insights
To solve \( 4 \times 10^{12} \times 7 \times 10^{7} \), first, multiply the coefficients: \( 4 \times 7 = 28 \). Then, add the exponents of the powers of ten: \( 10^{12} \times 10^{7} = 10^{19} \). So, we get \( 28 \times 10^{19} \). However, in scientific notation, we want a coefficient between 1 and 10. We rewrite \( 28 \) as \( 2.8 \times 10^{1} \), giving us \( (2.8 \times 10^{1}) \times 10^{19} = 2.8 \times 10^{20} \). Therefore, the answer is **C. \( 2.8 \times 10^{20} \)**!
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