To divide the two numbers in scientific notation, you follow these steps:
- Divide the coefficients (the numbers in front).
- Subtract the exponents of 10.
Given the expression \((9 \times 10^6) \div (12 \times 10^7)\):
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Divide the coefficients: \[ \frac{9}{12} = 0.75 \]
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Subtract the exponents: \[ 10^{6 - 7} = 10^{-1} \]
Now combine the results: \[ 0.75 \times 10^{-1} \]
The conventional way to express this in scientific notation requires the coefficient to be between 1 and 10. So, we convert \(0.75\) into scientific notation: \[ 0.75 = 7.5 \times 10^{-1} \]
Now, when we multiply this with \(10^{-1}\), we get: \[ 7.5 \times 10^{-1} \times 10^{-1} = 7.5 \times 10^{-2} \]
So the final result of \((9 \times 10^6) \div (12 \times 10^7)\) in scientific notation is: \[ \boxed{7.5 \times 10^{-2}} \]