which of these numbers can be classified as both real and rational ?
a) 1/2
b) -1.016879413894
c)square root of 5
d) 0.89089908999
To determine which of these numbers can be classified as both real and rational, we need to understand the definitions of real and rational numbers:
1. Real numbers: Real numbers include all rational and irrational numbers. They can be represented on the number line and can take any decimal form.
2. Rational numbers: Rational numbers are numbers that can be expressed as a ratio of two integers, where the denominator is not zero.
Now let's analyze each option:
a) 1/2: This number can be classified as both real and rational, as it can be expressed as a ratio of two integers.
b) -1.016879413894: This number can be classified as both real and rational, as it can be expressed as a decimal and, therefore, as a ratio of two integers.
c) Square root of 5: The square root of 5 is an irrational number. Irrational numbers cannot be expressed as a ratio of two integers, so it cannot be classified as rational. However, it is still a real number.
d) 0.89089908999: This number can be classified as both real and rational, as it can be expressed as a decimal and, therefore, as a ratio of two integers.
In summary, the numbers that can be classified as both real and rational are:
a) 1/2
b) -1.016879413894
d) 0.89089908999
To determine which numbers can be classified as both real and rational, we need to understand the definitions of real numbers and rational numbers.
1. Real Numbers: Real numbers consist of all the numbers on the number line, including both rational and irrational numbers. These numbers can be expressed as terminating or repeating decimals, or as fractions.
2. Rational Numbers: Rational numbers are numbers that can be expressed as the ratio of two integers (a fraction), where the denominator is not zero. Rational numbers can be written as terminating or repeating decimals.
Now let's analyze each option:
a) 1/2: This number can be classified as a rational number because it can be expressed as the ratio of two integers. It is also a real number because it lies on the number line.
b) -1.016879413894: This number is a decimal and can be classified as a real number because all decimal numbers are real numbers. However, without further information, we cannot determine if it is a rational number. To be sure, we need to check if it can be expressed as a fraction.
c) Square root of 5: The square root of 5 is an irrational number because it cannot be expressed as a fraction or a repeating decimal. Therefore, it is not a rational number. However, it is still a real number because it exists on the number line.
d) 0.89089908999: This decimal number can be classified as a real number because all decimal numbers are real numbers. However, without further information, we cannot determine if it is a rational number. To determine if it is rational, we need to see if it can be expressed as a fraction.
In summary, the numbers that can be classified as both real and rational are:
a) 1/2.
The other options either don't meet the criteria for rational numbers or don't have enough information to determine their rationality.
all numbers are real
a) , b) and c) are also rational
I can write each as a fraction
e.g. 0.89089908999 = 89089908999/100000000000
c) is real but irrational, (can't write it as a ratio)