%2F(1.5x10%5E-4).jpeg "(6x10^8)/(1.5x10^-4)")
Solving (6x10^8)/(1.5x10^-4)
This problem involves dividing two numbers written in scientific notation. Here's a breakdown of how to solve it:
Understanding Scientific Notation
Scientific notation is a way to express very large or very small numbers in a compact form. It consists of two parts:
- A coefficient: A number between 1 and 10.
- A base 10 exponent: Indicates how many places the decimal point needs to be moved to get the original number.
For example, 6x10^8 means 6 multiplied by 10 raised to the power of 8, which equals 600,000,000.
Solving the Division
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Divide the coefficients: 6 / 1.5 = 4
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Subtract the exponents: 8 - (-4) = 12
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Combine the results: The answer is 4 x 10^12.
Therefore, (6x10^8) / (1.5x10^-4) = 4 x 10^12.
Explanation
The division of the coefficients is straightforward. However, when dividing exponents, we subtract the exponent of the denominator from the exponent of the numerator. This is because dividing by 10 raised to a negative power is the same as multiplying by 10 raised to the positive power.
In this example, dividing by 10^-4 is equivalent to multiplying by 10^4. So, 8 - (-4) = 8 + 4 = 12.
Final Thoughts
Solving problems involving scientific notation can seem intimidating at first. However, breaking them down into smaller steps and understanding the rules of exponents makes the process much easier.