is 1 3/7 an irrational number

Answer 1

No, \(1 \frac{3}{7}\) (which is a mixed number) is not an irrational number. It can be converted to an improper fraction:

\[ 1 \frac{3}{7} = \frac{7 \times 1 + 3}{7} = \frac{10}{7}. \]

Since it can be expressed as a fraction of two integers (where the denominator is not zero), it is classified as a rational number, not an irrational number. Rational numbers can be expressed as the quotient of two integers, while irrational numbers cannot be expressed in that form.

Answer 2

Which of the following describes 3. select all that apply
Rational number
Natural number
Integer
Real number

Answer 3

The number 3 can be described as follows:

1. Rational number: Yes, because it can be expressed as \(\frac{3}{1}\) (the ratio of two integers).
2. Natural number: Yes, because natural numbers are the positive integers starting from 1 and counting upward (1, 2, 3, ...).
3. Integer: Yes, because integers include whole numbers and their negatives (..., -3, -2, -1, 0, 1, 2, 3, ...).
4. Real number: Yes, because real numbers include all rational and irrational numbers.

In summary, all of the following apply to the number 3:

• Rational number
• Natural number
• Integer
• Real number

Answer 4

is 9.51 (theres a bar over .51) a natural number

Answer 5

The notation \(9.51\) with a bar over the \(51\) means that the decimal \(51\) repeats indefinitely, so the value can be expressed as \(9.515151...\).

Natural numbers are defined as the set of positive integers starting from 1 and counting up (1, 2, 3, ...). Since \(9.515151...\) is not a whole number (it has a decimal), it cannot be classified as a natural number.

Therefore, \(9.51\) (with the bar over \(51\)) is not a natural number.

Answer 6

Which of the following are real numbers
8
-6
4.913
4.962

Answer 7

All of the numbers you listed are real numbers. Here’s the breakdown:

1. 8: This is an integer, and all integers are real numbers.
2. -6: This is also an integer, which is a subset of real numbers.
3. 4.913: This is a decimal (rational number), which is part of the real numbers.
4. 4.962: Like 4.913, this is a decimal (rational number) and is also part of the real numbers.

In summary, all of the following are real numbers:

• 8
• -6
• 4.913
• 4.962

Answer 8

Which of the following describes 3/7
real
rational
whole
integer

Answer 9

The number \( \frac{3}{7} \) can be described as follows:

1. Real: Yes, because all rational and irrational numbers are classified as real numbers.
2. Rational: Yes, because \( \frac{3}{7} \) can be expressed as the ratio of two integers (3 and 7, where the denominator is not zero).
3. Whole: No, because whole numbers are non-negative integers (0, 1, 2, 3, ...), and \( \frac{3}{7} \) is not a whole number.
4. Integer: No, because integers are whole numbers that can be positive, negative, or zero, and \( \frac{3}{7} \) is not an integer (it is a fraction).

In summary, \( \frac{3}{7} \) is best described as:

• Real
• Rational

Answer 10

What about 1.888...

Answer 11

The notation \(1.888...\) (often written as \(1.\overline{8}\)) indicates that the digit \(8\) repeats indefinitely. Here's how it can be classified:

1. Real: Yes, \(1.888...\) is a real number because all rational and irrational numbers fall under the category of real numbers.

2. Rational: Yes, \(1.888...\) is a rational number because it can be expressed as the fraction \(\frac{17}{9}\). Any decimal that terminates or repeats is a rational number.

3. Whole: No, \(1.888...\) is not a whole number because whole numbers are non-negative integers (0, 1, 2, 3, ...), and \(1.888...\) has a decimal component.

4. Integer: No, \(1.888...\) is not an integer. Integers include whole numbers and their negatives without any fractional or decimal component.

In summary, \(1.888...\) is best described as:

• Real
• Rational