Have a query? Ask a Tutor!!

Access to best educators and exclusive paper discussions

Offsite Campus Turito Championship

Can’t find what you’re looking for?

Our tutors are from top schools around the world, and they are waiting for you 24/7, anytime, anywhere.

Homework- One to One Solutions
Understand concepts to solve better
Get your doubts solved instantly

Maths-

General

Easy

Question

Explain whether the following are rational or irrational and justify it.
e (Euler’s number = 2.7182818284590452353602874713527)

hint Hint:

Hint:
A rational number is a type of real number, which is in the form of p/q where q is not equal to zero. For a decimal number, if a decimal expansion is a terminating decimal then it is a rational number and if a decimal expansion is non-terminating but a repeating decimal then it is also a rational number but if a decimal expansion is a non-repeating and non-terminating decimal then it is an irrational number.

The correct answer is: is an irrational number

e(Euler’s number) is an irrational number because the decimal expansion is a non-terminating decimal and the digits after the decimal point are non-repeating and we know that, if a decimal expansion is a non-repeating and non-terminating decimal then it is an irrational number.
Final Answer:
Hence, e(Euler’s number) is an irrational number.

Related Questions to study

Explain whether the following are rational or irrational and justify it.
$stack pi with _ below left parenthesis 3.1415926535897932384626433832795 right parenthesis with _ below$

Explain whether the following are rational or irrational and justify it.
$stack pi with _ below left parenthesis 3.1415926535897932384626433832795 right parenthesis with _ below$

$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell 2 x plus 3 y equals 1200 end cell row cell 3 x plus 2 y equals 1300 end cell end table$
Based on the system of equations above, what is the value of 5x 5y?

$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell 2 x plus 3 y equals 1200 end cell row cell 3 x plus 2 y equals 1300 end cell end table$
Based on the system of equations above, what is the value of 5x 5y?

A helicopter, initially hovering 40 feet above the ground, begins to gain altitude at a rate of 21 feet per second. Which of the following functions represents the helicopter's altitude above the ground y , in feet, t seconds after the helicopter begins to gain altitude?

A helicopter, initially hovering 40 feet above the ground, begins to gain altitude at a rate of 21 feet per second. Which of the following functions represents the helicopter's altitude above the ground y , in feet, t seconds after the helicopter begins to gain altitude?

parallel

Juan purchased an antique that had a value of $straight $ 200$ at the time of purchase. Each year, the value of the antique is estimated to increase $10 straight percent sign$ over its value the previous year. The estimated value of the antique, in dollars, 2 years after purchase can be represented by the expression 200a,where a is a constant what is the value of a?

Juan purchased an antique that had a value of $straight $ 200$ at the time of purchase. Each year, the value of the antique is estimated to increase $10 straight percent sign$ over its value the previous year. The estimated value of the antique, in dollars, 2 years after purchase can be represented by the expression 200a,where a is a constant what is the value of a?

$vertical line 2 x plus 1 vertical line equals 5$
If and are the solutions to the equation above, what is the value of.

$vertical line 2 x plus 1 vertical line equals 5$
If and are the solutions to the equation above, what is the value of.

$T equals 5 c plus 12 f$
A manufacturer shipped units of a certain product to two locations. The equation above shows the total shipping cost T , in dollars, for shipping c units to the closer location and shipping units to the farther location. If the total shipping cost was $text $47, end text$ 000 and 3000 units were shipped to the farther location, how many units were shipped to the closer location?

$T equals 5 c plus 12 f$
A manufacturer shipped units of a certain product to two locations. The equation above shows the total shipping cost T , in dollars, for shipping c units to the closer location and shipping units to the farther location. If the total shipping cost was $text $47, end text$ 000 and 3000 units were shipped to the farther location, how many units were shipped to the closer location?

parallel

-3x + y = 6
ax + 2y = 4
In the system of equations above, a is a constant. For which of the following values of a does the system have no solution?

-3x + y = 6
ax + 2y = 4
In the system of equations above, a is a constant. For which of the following values of a does the system have no solution?

$square root of 4 x end root equals x minus 3$
What are all values of that satisfy the given equation?
I. 1
II. 9

$square root of 4 x end root equals x minus 3$
What are all values of that satisfy the given equation?
I. 1
II. 9

In the xy -plane, the graph of the function f(x)= $x squared plus 5 x plus 4$ has two x -intercepts. What is the distance between the x-intercepts?

In the xy -plane, the graph of the function f(x)= $x squared plus 5 x plus 4$ has two x -intercepts. What is the distance between the x-intercepts?

parallel

𝑊ℎ𝑎𝑡 𝑖𝑠 𝑡ℎ𝑒 𝑠𝑢𝑚 𝑜𝑓 𝑡ℎ𝑒 𝑔𝑟𝑒𝑎𝑡𝑒𝑠𝑡 𝑎𝑛𝑑 𝑡ℎ𝑒 𝑙𝑒a𝑠𝑡 𝑛𝑢𝑚𝑏𝑒𝑟𝑠 𝑜𝑓 $5 over 9 to the power of blank comma 1 over 9$ and $11 over 9$

𝑊ℎ𝑎𝑡 𝑖𝑠 𝑡ℎ𝑒 𝑠𝑢𝑚 𝑜𝑓 𝑡ℎ𝑒 𝑔𝑟𝑒𝑎𝑡𝑒𝑠𝑡 𝑎𝑛𝑑 𝑡ℎ𝑒 𝑙𝑒a𝑠𝑡 𝑛𝑢𝑚𝑏𝑒𝑟𝑠 𝑜𝑓 $5 over 9 to the power of blank comma 1 over 9$ and $11 over 9$

Which of the following sets of rational numbers is arranged in ascending order :

Which of the following sets of rational numbers is arranged in ascending order :

In a rational number, the denominator exceeds the numerator by 4. If the numerator and denominator are both increased by 9, the rational number becomes $7 over 8$ Find the original rational number

In a rational number, the denominator exceeds the numerator by 4. If the numerator and denominator are both increased by 9, the rational number becomes $7 over 8$ Find the original rational number

parallel

Find an irrational number between 1 and 4

Find an irrational number between 1 and 4

Find an irrational number between 1 and 3

Find an irrational number between 1 and 3

Insert an irrational number between 0 and 1.

Insert an irrational number between 0 and 1.

parallel

card img

With Turito Academy.

card img

With Turito Foundation.

card img

Get an Expert Advice From Turito.

Turito Academy

card img

With Turito Academy.

Test Prep

card img

With Turito Foundation.