Question

1. classify each value as natural numbers, whole numbers, integers, rational numbers or irrational numbers. circle the most specific category for each number.

value | natural # | whole # | integer | rational # | irrational #
example: -5 | | | × | × |
7π | | | | |
5\frac{1}{4} | | | | |
0.\overline{3} | | | | |
\sqrt{42} | | | | |
1.34672842... | | | | |
-9.267 | | | | |

Explanation:

To solve this, we analyze each value based on number set definitions:

1. \( 7\pi \)

• Natural/Whole/Integer: \( \pi \approx 3.14 \), so \( 7\pi \) is non - integer, non - whole, non - natural.
• Rational: \( \pi \) is irrational, so \( 7\pi \) (product of rational and irrational) is irrational.
• Irrational: \( \boldsymbol{\times} \) (circle this as most specific).

2. \( 5\frac{1}{4}=\frac{21}{4} \)

• Natural: No (not a positive integer without fraction).
• Whole: No (not a non - negative integer without fraction).
• Integer: No (has a fractional part).
• Rational: \( \boldsymbol{\times} \) (can be expressed as a fraction \( \frac{a}{b}, b

eq0 \)).

• Irrational: No.

3. \( 0.\overline{3}=\frac{1}{3} \)

• Natural: No.
• Whole: No.
• Integer: No.
• Rational: \( \boldsymbol{\times} \) (repeating decimal, so rational).
• Irrational: No.

4. \( \sqrt{42} \)

• 42 is not a perfect square, so \( \sqrt{42} \) is irrational.
• Natural/Whole/Integer: No.
• Rational: No.
• Irrational: \( \boldsymbol{\times} \) (circle this).

5. \( 1.34672842\ldots \) (non - repeating, non - terminating)

• Natural/Whole/Integer: No.
• Rational: No (not repeating/terminating).
• Irrational: \( \boldsymbol{\times} \) (circle this).

6. \( - 9.267=-\frac{9267}{1000} \)

• Natural/Whole: No (negative and fractional).
• Integer: No (has a decimal part).
• Rational: \( \boldsymbol{\times} \) (can be expressed as a fraction).
• Irrational: No.

Filling the Table:

Value	Natural #	Whole #	Integer	Rational #	Irrational #
\( 5\frac{1}{4} \)				\( \boldsymbol{\times} \)
\( 0.\overline{3} \)				\( \boldsymbol{\times} \)
\( \sqrt{42} \)					\( \boldsymbol{\times} \)
\( 1.34672842\ldots \)					\( \boldsymbol{\times} \)
\( - 9.267 \)				\( \boldsymbol{\times} \)

(For each row, circle the column with \( \boldsymbol{\times} \) as the most specific category.)

Answer:

To solve this, we analyze each value based on number set definitions:

1. \( 7\pi \)

• Natural/Whole/Integer: \( \pi \approx 3.14 \), so \( 7\pi \) is non - integer, non - whole, non - natural.
• Rational: \( \pi \) is irrational, so \( 7\pi \) (product of rational and irrational) is irrational.
• Irrational: \( \boldsymbol{\times} \) (circle this as most specific).

2. \( 5\frac{1}{4}=\frac{21}{4} \)

• Natural: No (not a positive integer without fraction).
• Whole: No (not a non - negative integer without fraction).
• Integer: No (has a fractional part).
• Rational: \( \boldsymbol{\times} \) (can be expressed as a fraction \( \frac{a}{b}, b

eq0 \)).

• Irrational: No.

3. \( 0.\overline{3}=\frac{1}{3} \)

• Natural: No.
• Whole: No.
• Integer: No.
• Rational: \( \boldsymbol{\times} \) (repeating decimal, so rational).
• Irrational: No.

4. \( \sqrt{42} \)

• 42 is not a perfect square, so \( \sqrt{42} \) is irrational.
• Natural/Whole/Integer: No.
• Rational: No.
• Irrational: \( \boldsymbol{\times} \) (circle this).

5. \( 1.34672842\ldots \) (non - repeating, non - terminating)

• Natural/Whole/Integer: No.
• Rational: No (not repeating/terminating).
• Irrational: \( \boldsymbol{\times} \) (circle this).

6. \( - 9.267=-\frac{9267}{1000} \)

• Natural/Whole: No (negative and fractional).
• Integer: No (has a decimal part).
• Rational: \( \boldsymbol{\times} \) (can be expressed as a fraction).
• Irrational: No.

Filling the Table:

Value	Natural #	Whole #	Integer	Rational #	Irrational #
\( 5\frac{1}{4} \)				\( \boldsymbol{\times} \)
\( 0.\overline{3} \)				\( \boldsymbol{\times} \)
\( \sqrt{42} \)					\( \boldsymbol{\times} \)
\( 1.34672842\ldots \)					\( \boldsymbol{\times} \)
\( - 9.267 \)				\( \boldsymbol{\times} \)

(For each row, circle the column with \( \boldsymbol{\times} \) as the most specific category.)