You will use the numbers pi and e (or applications which use them).
"Irrational" numbers are the name for numbers that cannot be expressed in fractions; that is, in a "ratio" of one number to another. The number .5 is 1/2; one divided by two. The most useful "irrational" number is the number "pi", the ratio of the diameter of a circle divided by its circumference. There is no fraction that exactly equals "pi", although 22/7 is close. Another irrational number is the number "e", the root of the "natural logarithms". This is extensively used in engineering and electronic calculations.
3.14 is rational. However, it is often used as an approximation for pi, which is irrational.
The square root of the number 31 is irrational. This is used in math.
Rational NumbersA rational number is a number that can be written as a ratio. That means it can be written as a fraction, in which both the numerator (the number on top) and the denominator (the number on the bottom) are whole numbers. The number 8 is a rational number because it can be written as the fraction 8/1.Likewise, 3/4 is a rational number because it can be written as a fraction.Even a big, clunky fraction like 7,324,908/56,003,492 is rational, simply because it can be written as a fraction.Every whole number is a rational number, because any whole number can be written as a fraction. For example, 4 can be written as 4/1, 65 can be written as 65/1, and 3,867 can be written as 3,867/1.Irrational NumbersAll numbers that are not rational are considered irrational. An irrational number can be written as a decimal, but not as a fraction. An irrational number has endless non-repeating digits to the right of the decimal point. Here are some irrational numbers:π = 3.141592… = 1.414213…Although irrational numbers are not often used in daily life, they do exist on the number line. In fact, between 0 and 1 on the number line, there are an infinite number of irrational numbers!
You will use the numbers pi and e (or applications which use them).
pi is an irrational number so most calculations involving circles, ellipses and other curves are likely to involve pi. All periodic motion, such as electromagnetic waves, sound, pendulums, etc are linked to pi.
There are very many uses for irrational numbers. A square, whose sides are a rational number, will have a diagonal of irrational length. The diagonals of most rectangles, with rational sides, will be irrational. The circumference and area of a circle (or ellipse) is related to pi, an irrational number. In the same way that pi is central to geometry, another irrational number, e, is fundamental to advanced calculus.
"Irrational" numbers are the name for numbers that cannot be expressed in fractions; that is, in a "ratio" of one number to another. The number .5 is 1/2; one divided by two. The most useful "irrational" number is the number "pi", the ratio of the diameter of a circle divided by its circumference. There is no fraction that exactly equals "pi", although 22/7 is close. Another irrational number is the number "e", the root of the "natural logarithms". This is extensively used in engineering and electronic calculations.
3.14 is rational. However, it is often used as an approximation for pi, which is irrational.
The square root of the number 31 is irrational. This is used in math.
3.14159 is rational. However, it is often used as an approximation for π, which is irrational. It is important to recognise that the rational number, 3.14159, is only an approximation for π.
Rational NumbersA rational number is a number that can be written as a ratio. That means it can be written as a fraction, in which both the numerator (the number on top) and the denominator (the number on the bottom) are whole numbers. The number 8 is a rational number because it can be written as the fraction 8/1.Likewise, 3/4 is a rational number because it can be written as a fraction.Even a big, clunky fraction like 7,324,908/56,003,492 is rational, simply because it can be written as a fraction.Every whole number is a rational number, because any whole number can be written as a fraction. For example, 4 can be written as 4/1, 65 can be written as 65/1, and 3,867 can be written as 3,867/1.Irrational NumbersAll numbers that are not rational are considered irrational. An irrational number can be written as a decimal, but not as a fraction. An irrational number has endless non-repeating digits to the right of the decimal point. Here are some irrational numbers:π = 3.141592… = 1.414213…Although irrational numbers are not often used in daily life, they do exist on the number line. In fact, between 0 and 1 on the number line, there are an infinite number of irrational numbers!
An irrational number is one possible answer.
The history of irrational numbers is quite simple in that any number that can't be expressed as a fraction is an irrational number as for example the value of pi as used in the square area of a circle.
Some numbers such as pi, e, and square roots are used quite commonly. Whether you use them at all will depend on what you do in your everyday life, of course. Engineers might use them commonly; others not so much.Even for an engineer, or ESPECIALLY for an engineer, the distinction between rational and irrational is irrelevant for most practical purposes; for instance, if you round pi, or the square root of 2 (which are both IRRATIONAL), to 10 or 15 significant digits, you get a RATIONAL number - and the resulting precision is more than enough for most purposes. (In fact, if you round to ANY number of digits, the result will still be rational.)
There are very many uses for irrational numbers. A square, whose sides are a rational number, will have a diagonal of irrational length. The diagonals of most rectangles, with rational sides, will be irrational. The circumference and area of a circle (or ellipse) is related to pi, an irrational number. In the same way that pi is central to geometry, another irrational number, e, is fundamental to advanced calculus.