Question

Ребят,помогите примеры решить❤ 1)0,(2461)= 2)0,22(51)= 3)3,(21)= 4)-2,(17)= 5)21,7(23)=

Answer 1

Округляем периодическую дробь:
1) 0,(2461)= 0,25
2) 0,22(51)= 0,23
3) 3,(21)= 0,32
4) -2,(17)= - 2,2
5) 21,7(23)= 21,72

Answer 2

1) 0,(2461)

To solve this problem, we need to understand the notation used. The numbers given have a repeating decimal part enclosed in parentheses. This means that the decimal part repeats indefinitely.

To convert the given number into a fraction, we can follow these steps:

Step 1: Let x = 0,(2461). This notation implies that the decimal part repeats indefinitely.

Step 2: Multiply both sides of the equation by 10,000 (the number of digits in the repeating part) to eliminate the repeating part:

10,000x = 24,610.(2461)

Step 3: Subtract x from both sides of the equation to eliminate the decimal part:

10,000x - x = 24,610.(2461) - 0.(2461)

Simplifying the equation, we get:

9,999x = 24,610

Step 4: Divide both sides of the equation by 9,999 to solve for x:

x = 24,610 / 9,999

Now we have x in the form of a fraction. We can simplify this fraction by finding the greatest common divisor (GCD) of the numerator and denominator.

The GCD of 24,610 and 9,999 is 1. Therefore, the fraction cannot be simplified any further.

So, the solution to 0,(2461) is x = 24,610 / 9,999.

2) 0,22(51)

Following the same steps as above, let's solve for x:

Step 1: Let x = 0,22(51).

Step 2: Multiply both sides of the equation by 100 (the number of digits in the repeating part):

100x = 22,51.(51)

Step 3: Subtract x from both sides of the equation:

100x - x = 22,51.(51) - 0,22(51)

Simplifying the equation, we get:

99x = 22,51

Step 4: Divide both sides of the equation by 99:

x = 22,51 / 99

To simplify the fraction, we need to find the GCD of 22,51 and 99. The GCD is 3, so we can simplify the fraction:

x = (22,51 / 99) / 3 x = 22,51 / (99 * 3) x = 22,51 / 297

Therefore, the solution to 0,22(51) is x = 22,51 / 297.

3) 3,(21)

Let's solve for x using the same steps:

Step 1: Let x = 3,(21).

Step 2: Multiply both sides of the equation by 10 (the number of digits in the repeating part):

10x = 32,1.(21)

Step 3: Subtract x from both sides of the equation:

10x - x = 32,1.(21) - 3,(21)

Simplifying the equation, we get:

9x = 32,1

Step 4: Divide both sides of the equation by 9:

x = 32,1 / 9

The fraction 32,1 can be simplified by finding the GCD of 32,1 and 9, which is 3:

x = (32,1 / 9) / 3 x = 32,1 / (9 * 3) x = 32,1 / 27

Therefore, the solution to 3,(21) is x = 32,1 / 27.

4) -2,(17)

Following the same steps:

Step 1: Let x = -2,(17).

Step 2: Multiply both sides of the equation by 100 (the number of digits in the repeating part):

100x = -217.(17)

Step 3: Subtract x from both sides of the equation:

100x - x = -217.(17) - (-2,(17))

Simplifying the equation, we get:

99x = -215

Step 4: Divide both sides of the equation by 99:

x = -215 / 99

To simplify the fraction, we need to find the GCD of 215 and 99. The GCD is 1, so the fraction cannot be simplified any further:

x = -215 / 99

Therefore, the solution to -2,(17) is x = -215 / 99.

5) 21,7(23)

Applying the same steps:

Step 1: Let x = 21,7(23).

Step 2: Multiply both sides of the equation by 100 (the number of digits in the repeating part):

100x = 2172,(23)

Step 3: Subtract x from both sides of the equation:

100x - x = 2172,(23) - 21,7(23)

Simplifying the equation, we get:

99x = 2151

Step 4: Divide both sides of the equation by 99:

x = 2151 / 99

The fraction 2151 can be simplified by finding the GCD of 2151 and 99, which is 3:

x = (2151 / 99) / 3 x = 2151 / (99 * 3) x = 2151 / 297

Therefore, the solution to 21,7(23) is x = 2151 / 297.

I hope this helps! Let me know if you have any further questions.