Operations in Scientific Notation

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What is scientific notation?

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Scientific notation is a way of expressing numbers as a product of a coefficient and a power of ten, typically in the form a × 10^n, where 1 ≤ a < 10 and n is an integer.

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How do you add numbers in scientific notation?

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To add numbers in scientific notation, they must have the same exponent. If they do not, adjust one or both numbers to have the same exponent, then add the coefficients and keep the common exponent.

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How do you subtract numbers in scientific notation?

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To subtract numbers in scientific notation, ensure they have the same exponent. If not, adjust one or both numbers to have the same exponent, then subtract the coefficients and keep the common exponent.

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What is the product of two numbers in scientific notation?

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To multiply two numbers in scientific notation, multiply the coefficients and add the exponents. The result is in the form a × 10^n.

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What is the quotient of two numbers in scientific notation?

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To divide two numbers in scientific notation, divide the coefficients and subtract the exponent of the denominator from the exponent of the numerator. The result is in the form a × 10^n.

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What is the significance of the coefficient in scientific notation?

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The coefficient in scientific notation must be between 1 and 10. It represents the significant figures of the number.

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How do you convert a number from standard form to scientific notation?

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To convert a number from standard form to scientific notation, move the decimal point to create a coefficient between 1 and 10, and count the number of places moved to determine the exponent.

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What happens when you multiply a number in scientific notation by a power of ten?

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When you multiply a number in scientific notation by a power of ten, you add the exponent of the power of ten to the exponent of the number.

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How do you handle scientific notation with negative exponents?

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Negative exponents in scientific notation indicate a number less than one. For example, 10^-3 equals 1/1000.

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What is the result of (a × 10^m) + (b × 10^n) when m ≠ n?

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When m ≠ n, convert one term to have the same exponent as the other before adding the coefficients.