Q2 Benchmark Math 24-25 - 8th Grade

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What is a rational number?

Back

A rational number is any number that can be expressed as the quotient or fraction of two integers, where the denominator is not zero.

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What is an irrational number?

Back

An irrational number is a number that cannot be expressed as a simple fraction; it cannot be written as a ratio of two integers.

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How do you determine if a number is rational or irrational?

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A number is rational if it can be expressed as a fraction (e.g., 1/2, -3, 0.75). If it cannot be expressed as a fraction, such as √2 or π, it is irrational.

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What is the Pythagorean theorem?

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The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b): a² + b² = c².

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What are the properties of right triangles?

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In a right triangle, one angle is exactly 90 degrees, and the side opposite this angle is the longest side, known as the hypotenuse.

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How do you find the length of a missing side in a right triangle?

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Use the Pythagorean theorem: if you know the lengths of two sides, you can find the third side by rearranging the formula a² + b² = c².

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What is standard form in mathematics?

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Standard form is a way of writing numbers that are too big or too small to be conveniently written in decimal form. It is expressed as a number between 1 and 10 multiplied by a power of 10.

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

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To convert from scientific notation to standard form, move the decimal point to the right for positive exponents and to the left for negative exponents.

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What is an example of a set containing an irrational number?

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The set {0.17, √3, 2.555..., √4} contains the irrational number √3.

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What is the significance of the number 0 in rational numbers?

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Zero is a rational number because it can be expressed as 0/1, which is a fraction.