Question

Two numbers are written in scientific notation. the number with a positive exponent is divided by the number with a negative exponent. Describe the result. Explain your answer

Answer 1

Step-by-step explanation:

When the division is performed, the denominator exponent is subtracted from the numerator exponent. Subtracting a negative value from the numerator exponent will increase its value.

Example:

`(4\cdot 10^3)/(2\cdot 10^(-4))=(4)/(2)\cdot 10^(3-(-4))=2\cdot 10^7`

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Another way to think about it is this. An exponent in the denominator is the same as the opposite of that exponent in the numerator. Multiplying exponential numbers with the same base adds their exponents.

Example:

`(4\cdot 10^3)/(2\cdot 10^(-4))=(4\cdot 10^3\cdot 10^4)/(2)=(4)/(2)\cdot 10^(3+4)=2\cdot 10^7`