Pregunta
Easton broke a cell sample into 8 batches, each weighing \( 3.9 \times 10^{-5} \) grams. How much did the original sample weigh? Use scientific notation to express your answer. Answer Attempt 3 out of 3 Answer: \( \square \times 10 \) grams Submit Answer
Ask by Perkins Mckenzie. in the United States
Mar 11,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The original sample weighed \( 3.12 \times 10^{-4} \) grams.
Solución
1. Each batch weighs \(3.9 \times 10^{-5}\) grams.
2. Since there are 8 batches, the total weight is calculated by multiplying the number of batches by the weight of one batch:
\[
8 \times \left(3.9 \times 10^{-5}\right)
\]
3. Multiply the coefficients:
\[
8 \times 3.9 = 31.2
\]
so the expression becomes:
\[
31.2 \times 10^{-5} \text{ grams}
\]
4. Convert \(31.2 \times 10^{-5}\) into proper scientific notation. Write \(31.2\) as \(3.12 \times 10^1\):
\[
31.2 \times 10^{-5} = \left(3.12 \times 10^1\right) \times 10^{-5} = 3.12 \times 10^{1-5} = 3.12 \times 10^{-4} \text{ grams}
\]
Thus, the original sample weighed \( \boxed{3.12 \times 10^{-4}} \) grams.
Respondido por UpStudy AI y revisado por un tutor profesional
Como
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The Deep Dive
To find the weight of the original sample, you multiply the weight of each batch by the number of batches. So, \( 3.9 \times 10^{-5} \) grams per batch multiplied by 8 batches is calculated as follows: \[ 8 \times 3.9 \times 10^{-5} = 31.2 \times 10^{-5} \] Now, we need to express this in proper scientific notation. To do that, we can adjust it: \[ 31.2 \times 10^{-5} = 3.12 \times 10^{-4} \] So, the weight of the original sample is \( 3.12 \times 10^{-4} \) grams.

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