Respuesta :

Answer:

You multiply it by 1000. If you're talking about converting decimals to fractions.

Step-by-step explanation:

2.314

2 is the whole number, you leave that alone for right now.

0.314 is the decimal part.

Rewrite the decimal with a denominator of 1.

[tex]\frac{0.314}{1}[/tex]

Because this decimal goes all way to the thousandths place, you multiply the top and the bottom by 1,000.

[tex]\frac{0.314}{1}[/tex] ×1000= [tex]\frac{314}{1000\\}[/tex]

Next you simplify divide the top and bottom by the GCF (greatest common factor) in this case 2.

[tex]\frac{3.14}{1000}[/tex]÷2

=[tex]\frac{157}{500}[/tex]

The conversion of the recurring decimal 2.31414 to a fraction gives; 2291/990

Recurring Decimal

We are given the recurring decimal 2.314 where 14 is repeating.

This can be expressed as 2.31414.

  • Thus, if the fraction is y, then we will say that; y = 2.31414 - - - (eq 1)

  • If we multiply both sides of eq(1) by 10, we will have; 10y = 23.1414 - - - (eq 2)

  • Of we multiply both sides of eq 1 by 1000, we will have; 1000y = 2314.14 - - -(eq 3)

Let's Subtract eq(2) from eq(3) to get;

1000y - 10y = 2314.1414 - 23.1414

990y = 2291

Using division property of equality to divide both sides by 990, we have;

y = 2291/990

Thus, the required fraction is 2291/990

Read more about recurring decimal at; https://brainly.com/question/12782047

Otras preguntas