A rational number can be written as the ratio of two integers. Conversely, an irrational number cannot be written as the ratio of two integers.
C
A rational number can be written as the ratio of two integers. Conversely, an irrational number cannot be written as the ratio of two integers.
A
Rational or Irrational? Rational Example Fraction: 6/1
B
Rational or Irrational? Rational Example Fraction: 62/99
C
Rational or Irrational? Irrational
Practice makes perfect
To determine whether the given number is a rational or irrational number, let's first recall the following two definitions.
Rational Numbers: Numbers that can be expressed as the ratio of two integers.
Irrational Numbers: Numbers that cannot be expressed as the ratio of two integers.
Let's now calculate the given square root using a calculator.
sqrt(36)= 6
The number that we got is a whole number. This means that it is a rational number. For example, we can rewrite sqrt(36) in the following way.
sqrt(36)= 6=6/1
We are given the following number.
0.62
We want to figure out if the number is rational or irrational. Notice that the symbol on top of the digits 6 and 3 means that these numbers are repeated indefinitely.
0.62=0. 62626262...
The number has infinitely many digits after the decimal point and the pattern of the digits repeats indefinitely. This means that the number is a repeating decimal number. Since each repeating decimal can be written as the ratio of two integers, the number is rational. To find the fraction form of 0.62 let's first represent the number with x.
x=0.62
Since 0.62 has two repeating digits, we will multiply both sides of the equation we got by 10^2.
Next, we can subtract x from both sides of the equation. Since x=0.62, we will substitute 0.62 for x on the right-hand side. Finally, we will solve the obtained equation for x.
We found that x is equal to 6299. Remember that x is also equal to 0.62. By the Transitive Property of Equality, we can conclude that the fraction is equal to the given repeating decimal number.
x= 0.62 x= 62/99 ⇒ 0.62= 62/99
Let's consider the given number.
sqrt(92)
We can express the given number as a decimal using a calculator.
9.591663...
The number we got has infinitely many digits after the decimal point that do not follow a specific pattern. This means that the digits do not terminate or repeat and the number cannot be written as the ratio of two integers. Therefore, the given decimal is an irrational number.
