Adding and Subtracting Scientific Notation

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What is scientific notation?

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Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form. It is typically in the form of a x 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, you must first ensure that the exponents are the same. If they are not, adjust one of the numbers by converting it to an equivalent value with the same exponent. Then, add the coefficients and keep the common exponent.

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What is the first step in subtracting numbers in scientific notation?

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The first step in subtracting numbers in scientific notation is to ensure that the exponents of both numbers are the same. If they are not, convert one of the numbers to have the same exponent as the other.

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What is the result of (5.2 x 10⁷) + (3.01 x 10⁴)?

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5.20301 x 10⁷

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What is the result of (7.32 x 10⁶) - (4.01 x 10⁸)?

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-3.937 x 10⁸

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How do you convert (2 x 10³) - (1.9 x 10²) into scientific notation?

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First, convert (1.9 x 10²) to (0.19 x 10³) to match the exponent. Then, subtract: (2 x 10³) - (0.19 x 10³) = (1.81 x 10³).

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What is the significance of the exponent in scientific notation?

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The exponent in scientific notation indicates the power of ten by which the coefficient is multiplied, determining the scale or size of the number.

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What happens when you add two numbers in scientific notation with different exponents?

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You must convert one of the numbers to have the same exponent as the other before adding the coefficients.

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What is the general form of a number in scientific notation?

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The general form is a x 10^n, where 'a' is a number greater than or equal to 1 and less than 10, and 'n' is an integer.

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How do you handle significant figures when adding or subtracting in scientific notation?

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When adding or subtracting, the result should be reported with the same number of decimal places as the measurement with the least number of decimal places.