1-666666 - is a rational number and can be expressed in p - q form where p and q are integers- Then the value of p - q isA- The given number has a non-terminating and non-recurring decimal expansion and cannot be represented as p - qB- 7C- 8D- 6

Writing Decimals as Rational Numbers

1.666666 …… i...

Question

$1.666666......$ is a rational number and can be expressed in $\frac{p}{q}$ form where $p$ and $q$ are integers. Then the value of $p + q$ is

The given number has a non-terminating and non-recurring decimal expansion and cannot be represented as $\frac{p}{q}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$6$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$7$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$8$

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D
$8$

Let $x = 1.6666...$ ... (i)

$10 x = 16.666666...$ ... (ii)
Subtracting equation (i) from (ii), we get,
$9 x = 15$
Hence, $x = \frac{15}{9} = \frac{5}{3}$

$\Rightarrow p = 5$ and $q = 3$
So, $p + q = 5 + 3 = 8$

Suggest Corrections

Similar questions

If 1.666666...... is a rational number and can be expressed in $\frac{p}{q}$ form, then p + q is

If $\frac{p}{q}$ is a rational number with terminating decimal expansion where $p$ and $q$ are coprimes, then $q$ can be represented as:
(Here, n and m are non-negative integers.)

Let $x$ be a rational number whose simplest form is expressed as $\frac{p}{q}$ , where $p$ and $q$ are co-prime integers and $q \neq 0$ and also, $x$ is a terminating decimal, then $q$ can be expressed in the form of _____________ (where m and n are non-negative integers).

Let $x = \frac{p}{q}$ be a rational number, such that the prime factorisation of $q$ is not of the form $2^{m} 5^{n}$ , where $n, m$ are non-negative integers. Then, $x$ has a decimal expansion which is

Q. A rational number whose decimal expansion is non-terminating can be expressed in the form

\frac{p}{q}

, where

p

and

q

are coprime, and the prime factorisation of

q

is NOT of the form _____ , where

n

and

m

are non-negative integers.

Join BYJU'S Learning Program

Select...

1.666666...... is a rational number and can be expressed in pq form where p and q are integers. Then the value of p+q is

The correct option is D 8 Let x=1.6666... ... (i) 10x=16.666666... ... (ii) Subtracting equation (i) from (ii), we get, 9x=15 Hence, x=159=53 ⇒p=5 and q=3 So, p+q=5+3=8

$1.666666......$ is a rational number and can be expressed in $\frac{p}{q}$ form where $p$ and $q$ are integers. Then the value of $p + q$ is

The correct option is D
$8$

Let $x = 1.6666...$ ... (i)

$10 x = 16.666666...$ ... (ii)
Subtracting equation (i) from (ii), we get,
$9 x = 15$
Hence, $x = \frac{15}{9} = \frac{5}{3}$

$\Rightarrow p = 5$ and $q = 3$
So, $p + q = 5 + 3 = 8$