Me asap which numbers are rational numbers? i. π ii. 120.5 iii. 12 iv. 7.25468 v. –56 vi. 2√ question 5 options: i and iii ii, iii, iv, and v iii only all of the numbers are rational.

A rational number is any number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q.

Let us check each of them one by one:

I. π

π (Pi) is a famous irrational number. We cannot write down a simple fraction that equals Pi. The popular approximation of 22/7 = 3.1428571428571... is close but not accurate. Another clue is that the decimal goes on forever without repeating.

II.

120.5

we can write it in fraction as 1205/10

So it is a rational number

III. 12

We can write 12 as 12/1,

So it is a rational number.

IV.

7.25468

It can be written as 725468/100000

So it is a rational number.

V.

-56

We can write -56 as -56/1.

So it is a rational number.

VI.

2√

Since square root is involved, it is irrational.

Answer :

II, III, IV and V are rational numbers.

$32,660

step-by-step explanation:

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}