Wk 5: Adding 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 written as the product of a number (between 1 and 10) and a power of ten.

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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 of ten 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 standard form of a number?

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The standard form of a number is its usual decimal representation, without exponents. For example, the standard form of 4.56 x 10⁵ is 456,000.

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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 a number greater than or equal to 1 and less than 10. It represents the significant digits of the number.

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What does it mean to convert a number from scientific notation to standard form?

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Converting a number from scientific notation to standard form involves multiplying the coefficient by 10 raised to the power of the exponent, resulting in a whole number or decimal.

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How do you determine if a number is in correct scientific notation?

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A number is in correct scientific notation if it has one non-zero digit to the left of the decimal point and the exponent is an integer.

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What is the result of adding (2.3 x 10²) and (4.1 x 10²)?

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The result is 6.4 x 10², as both numbers have the same exponent.

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What is the process for adding (5.2 x 10⁷) and (3.01 x 10⁴)?

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First, convert (3.01 x 10⁴) to (0.0301 x 10⁷) to match the exponent, then add the coefficients: 5.2 + 0.0301 = 5.20301, resulting in 5.20301 x 10⁷.

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What is the result of adding (2.8 x 10⁸) and (5.4 x 10⁹)?

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The result is 5.68 x 10⁹, as (2.8 x 10⁸) is converted to (0.28 x 10⁹) before adding.

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What is the correct scientific notation for the number 20350?

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The correct scientific notation for 20350 is 2.035 x 10⁴.