Select all the numbers that are irrational. Multi-select Choices: (A)-6/7 (B)4sqrt 5 (C)0.333 (D)0.{7} (E)-6.11

Analyze -6/7: Step 1: Analyze number (A) -6/7. -6/7 is a fraction that can be expressed as a ratio of two integers, -6 and 7. Since it can be expressed as a ratio, it is a rational number.Analyze 4sqrt(5): Step 2: Analyze number (B) 4sqrt(5). 4sqrt(5) involves the square root of 5, which cannot be expressed as a ratio of two integers. Since sqrt(5) is an irrational number, multiplying it by 4 does not change its irrational nature.Analyze 0.333: Step 3: Analyze number (C) 0.333. 0.333 can be expressed as 1/3, which is a repeating decimal. Repeating decimals are considered rational numbers.Analyze 0.{7}: Step 4: Analyze number (D) 0.{7}. 0.{7} represents the repeating decimal 0.7777..., which can be expressed as 7/9. Repeating decimals are rational numbers.Analyze -6.11: Step 5: Analyze number (E) -6.11. -6.11 is a terminating decimal, which can be expressed as -611/100. Terminating decimals are rational numbers.

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Select all the numbers that are irrational. $\newline$ Multi-select Choices: $\newline$ (A) $-\frac{6}{7}$ $\newline$ (B) $4\sqrt{5}$ $\newline$ (C) $0.333$ $\newline$ (D) $0.\overline{7}$ $\newline$ (E) $-6.11$

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Math Problems

Grade 8

Checkpoint: Rational and irrational numbers

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Q. Select all the numbers that are irrational.

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Multi-select Choices:

\newline

(A)

-\frac{6}{7}

\newline

(B)

4\sqrt{5}

\newline

(C)

0.333

\newline

(D)

0.\overline{7}

\newline

(E)

-6.11

Analyze $-\frac{6}{7}$ : Step $1$ : Analyze number (A) $-\frac{6}{7}$ . $-\frac{6}{7}$ is a fraction that can be expressed as a ratio of two integers, $-6$ and $7$ . Since it can be expressed as a ratio, it is a rational number.
Analyze $4\sqrt{5}$ : Step $2$ : Analyze number (B) $4\sqrt{5}$ . $4\sqrt{5}$ involves the square root of $5$ , which cannot be expressed as a ratio of two integers. Since $\sqrt{5}$ is an irrational number, multiplying it by $4$ does not change its irrational nature.
Analyze $0.333$ : Step $3$ : Analyze number (C) $0.333$ . $\newline$ $0.333$ can be expressed as $\frac{1}{3}$ , which is a repeating decimal. $\newline$ Repeating decimals are considered rational numbers.
Analyze $0.\overline{7}$ : Step $4$ : Analyze number (D) $0.\overline{7}$ . $0.\overline{7}$ represents the repeating decimal $0.7777\ldots$ , which can be expressed as $\frac{7}{9}$ . Repeating decimals are rational numbers.
Analyze $-6.11$ : Step $5$ : Analyze number (E) $-6.11$ . $\newline$ $-6.11$ is a terminating decimal, which can be expressed as $-\frac{611}{100}$ . $\newline$ Terminating decimals are rational numbers.