Subjects algebra

Scientific Notation Subtraction

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1. The problem is to subtract two numbers in scientific notation: $8.4 \times 10^{-11} - 5.1 \times 10^{-12}$. 2. To subtract numbers in scientific notation, they must have the same power of ten. Here, the powers are $10^{-11}$ and $10^{-12}$. 3. Convert $5.1 \times 10^{-12}$ to have the same power of ten as $8.4 \times 10^{-11}$. Since $10^{-12} = 10^{-11} \times 10^{-1}$, we write: $$5.1 \times 10^{-12} = 5.1 \times 10^{-11} \times 10^{-1} = 0.51 \times 10^{-11}$$ 4. Now subtract the coefficients: $$8.4 \times 10^{-11} - 0.51 \times 10^{-11} = (8.4 - 0.51) \times 10^{-11} = 7.89 \times 10^{-11}$$ 5. The answer in standard form is: $$7.89 \times 10^{-11}$$ This means the result is $7.89$ times ten to the power of negative eleven.