Respuesta :

Answer:

Therefore, x =  [tex]\frac{2291}{990}[/tex].

Step-by-step explanation:

Given : 2.314 (14 repeating) .

To find : Express as a fraction .

Solution : We have given  2.314 (14 repeating) .

Let x = 2.31414141.......

On multiplying both sides by 100

100x = 100 * 2.31414141....

100x = 231.414141......

We can express 231.414141...... in term of x .

100x = 229 .1 +  2.31414141.......

100x = 229.1 +x

On subtracting both sides by x .

100 x -x = 229 .1

99x = 229.1

On dividing both sides by 99

x= [tex]\frac{229.1}{99}[/tex].

x =  [tex]\frac{2291}{990}[/tex].

Therefore, x =  [tex]\frac{2291}{990}[/tex].

fichoh

The repeating decimal 2.3141414... expressed as a fraction is [tex] \frac{2291}{990} [/tex]

The decimal given : 2.3141414

Let :

  • x = 2.31414 - - - (1)

Since only the 14 keeps repeating :

  • Multiply (1) by 10 in other to keep the repeating digits only to the right of the decimal Point.

  • 10x = 23.1414 - - - - (2)

Multiply (2) by 100

  • 1000x - 2314.1414 - - - - (3)

  • Subtract (2) from (3)

1000x - 10x = 2314.1414 - 23.1414

990x = 2291

  • Divide both sides by 990
  • x = 2291 / 990

Hence, 2.31414...expressed as a decimal is [tex] \frac{2291}{990} [/tex]

Learn more : https://brainly.com/question/15406832?referrer=searchResults

Otras preguntas