Which statement is true about the relationships between the number sets?
all intergers are whole numbers
not all natural numbers are rational
some irrational numbers are rational
all natural numbers are integers
The statement "all integers are whole numbers" is true.
The statement "not all natural numbers are rational" is also true. Rational numbers are numbers that can be expressed as a fraction or ratio of two integers, while natural numbers are only positive integers. Therefore, not all natural numbers can be expressed as a rational number (e.g. √2 is a natural number but is irrational).
The statement "some irrational numbers are rational" is false. Irrational numbers are numbers that cannot be expressed as a fraction or ratio of two integers. Therefore, by definition, irrational numbers cannot be rational numbers.
The statement "all natural numbers are integers" is true. Natural numbers include all positive integers, and integers include all positive and negative whole numbers.
Which of the following is true about the number 1/6 ?
it's a rational number but not a real number
it's both an integer and a rational number
It's both an irrational number and a real number
It's a rational number but not a whole number
The statement "it's a rational number but not a real number" is false. The number 1/6 is both a rational number and a real number.
The statement "it's both an integer and a rational number" is false. Integers are whole numbers (negative, zero, and positive) and do not include fractions like 1/6. Therefore, 1/6 is not an integer.
The statement "it's both an irrational number and a real number" is also false. Irrational numbers are numbers that cannot be expressed as a fraction or ratio of two integers. Since 1/6 can be expressed as a fraction, it is not an irrational number. However, it is a real number as it can be plotted on the number line.
The statement "it's a rational number but not a whole number" is true. Rational numbers can be expressed as a fraction or ratio of two integers, which 1/6 is. Whole numbers are integers that are greater than or equal to zero. Since 1/6 is a fraction, it is not a whole number.
A sign in a gas station advertises gas at the rate listed below. How many dollars does a gallon cost, writing the price strictly as a decimal?
$4.12 9/10
To write the price strictly as a decimal, we need to convert the fraction 9/10 to a decimal. To do this, we divide 9 by 10:
9 ÷ 10 = 0.9
Now we can write the price strictly as a decimal:
$4.12 + 0.9 = $4.129
Therefore, a gallon of gas costs $4.129.
Which set of numbers is always rational
The set of numbers that is always rational is the set of integers. Integers include all whole numbers (positive, negative, and zero) and can be expressed as a ratio of two integers.
The height of an equilateral triangle equals √3/2 times the side length. What is the approximate height in meters of an equilateral triangle with a side length of 16 meters?
To find the height of an equilateral triangle with a side length of 16 meters, we can use the formula given, which states that the height is equal to (√3/2) times the side length.
First, let's calculate (√3/2) times 16:
(√3/2) * 16 = (1.732/2) * 16 = 0.866 * 16 = 13.856
Therefore, the approximate height of the equilateral triangle is approximately 13.856 meters.