Question

Express 3.16 bar where bar is on 6 in p/q form

Answer 1

$\displaystyle \bf{ 3. 1\overline{6} = \frac{19}{6} }$

Which is of the form p/q where p , q are integers and q ≠ 0

Given :

The number $\displaystyle \sf{ 3. 1\overline{6} }$

To find :

To express in the form p/q

Solution :

Step 1 of 2 :

Write down the given number

The given number is $\displaystyle \sf{ 3. 1\overline{6} }$

Step 2 of 2 :

Express in the form p/q

$\displaystyle \sf{ Let \: \: x = 3. 1\overline{6} }$

Then x = 3.166666... - - - - - - - (1)

Multiplying both sides by 10 we get

10x = 31.66666... - - - - - - (2)

Again multiplying both sides by 10 we get

100x = 316.66666... - - - - - - (3)

Equation 3 - Equation 2 gives

90x = 285

$\displaystyle \sf{ \implies x = \frac{285}{90} }$

$\displaystyle \sf{ \implies x = \frac{19 }{6} }$

$\displaystyle \sf{ \therefore \: \: 3. 1\overline{6} = \frac{19}{6}}$

Which is of the form p/q where p , q are integers and q ≠ 0

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Answer 2

The answer is, 3.16 bar = $\frac{19}{6}$    

Which is of the form p/q where p , q are integers and q ≠ 0.

What is expression?

• A phrase having a minimum of two numbers or variables and at least one math operation is called an expression.

• Addition, subtraction, multiplication, or division are examples of math operations.

• An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is an expression.

According to the question:

Given :

The number 3.16 bar.

Step 1 :

Write down the given number.

The given number is 3.16 bar.

Step 2:

Express in the form p/q.

Let x= 3.16 bar.

Then x = 3.166666... - - - - - - - (1)

Multiplying both sides by 10 we get

10x = 31.66666... - - - - - - (2)

Again multiplying both sides by 10 we get

100x = 316.66666... - - - - - - (3)

Equation 3 - Equation 2 gives:

90x = 285

$x=\frac{285}{90} \\\\x= \frac{19}{6}$

Therefore, 3.16bar=$\frac{19}{6}$

Which is of the form p/q where p , q are integers and q ≠ 0

Learn more about expression here,

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