I get an error?

One tip to prevent these kind of error: next time align the { and } and you see the error very fast:

void setup()
{
  Serial.begin(9600);
  pinMode(13,OUTPUT);
}

void loop() 
{
  char s_num; 
  if(Serial.available()>0)
  {
    s_num =Serial.read();
  }

  if(s_num=='0')
  {
    digitalWrite(13,HIGH);
    delay(100); //the specified time for 0
    digitalWrite(13,LOW);
    delay(100);
  }

  if(s_num=='1')
  {
    digitalWrite(13,HIGH);
    delay(200);
    digitalWrite(13,LOW);
    delay(200);
  }

  if(s_num=='2')
  {
    digitalWrite(13,HIGH);
    delay(300);
    digitalWrite(13,LOW);
    delay(300);
  }
 
  if(s_num=='3')
  {
    digitalWrite(13,HIGH);
    delay(400);
    digitalWrite(13,LOW);
    delay(400);
  }
  
  if(s_num=='4')
  {
    digitalWrite(3,HIGH);
    delay(500);
    digitalWrite(13,LOW);
    delay(500);
  }

  if(s_num=='5')
  {
    digitalWrite(13,HIGH);
    delay(600);
    digitalWrite(13,LOW);
    delay(600);
  }

  if(s_num=='6')
  {
    digitalWrite(13,HIGH);
    delay(700);
    digitalWrite(13,LOW);
    delay(700);
  }
  if(s_num=='7')
  {
    digitalWrite(13,HIGH);
    delay(800);
    digitalWrite(13,LOW);
    delay(800);
  }
  if(s_num=='8')
  {
    digitalWrite(13,HIGH);
    delay(900);
    digitalWrite(13,LOW);
    delay(900);
  }
  if(s_num=='9')
  {
    digitalWrite(13,HIGH);
    delay(1000);
    digitalWrite(13,LOW);
    delay(1000);
  }
  digitalWrite(13,LOW);
  s_num=10;
}

As you can see char s_name needs to be be declared in the front of the method as you need it in the second line, so you get the following code that compiles:

void loop() 
{
  if(Serial.available()>0)
  {
    s_num =Serial.read();
  }

  if(s_num=='0')
  {
    digitalWrite(13,HIGH);
    delay(100); //the specified time for 0
    digitalWrite(13,LOW);
    delay(100);
  }

  if(s_num=='1')
  {
    digitalWrite(13,HIGH);
    delay(200);
    digitalWrite(13,LOW);
    delay(200);
  }

  if(s_num=='2')
  {
    digitalWrite(13,HIGH);
    delay(300);
    digitalWrite(13,LOW);
    delay(300);
  }
  char s_num; 
  
  if(s_num=='3')
  {
    digitalWrite(13,HIGH);
    delay(400);
    digitalWrite(13,LOW);
    delay(400);
  }
  
  ...
}

Now you also can see that you process the s_num variable even if there is not a new value from the serial class, so you should put it probably inside, getting:

void loop() 
{
  if(Serial.available()>0)
  {
    char s_num =Serial.read();
 
    if(s_num=='0')
    {
      digitalWrite(13,HIGH);
      delay(100); //the specified time for 0
      digitalWrite(13,LOW);
      delay(100);
    }
  }
}

The last statement s_num=10; does not anything.

Now, to greatly reduce your code, all digits perform more or less the same code. You can combine this by calculating the delay time (0 -> 100, 9 -> 1000), and you get the following code:

void setup()
{
  Serial.begin(9600);
  pinMode(13, OUTPUT);
}

void loop() 
{
  if (Serial.available() > 0)
  {
    char s_num = Serial.read();
    if ((s_num >= '0') && (s_num <= '9'))
    {
      uint16_t delayTime = (s_num - '0' + 1) * 100;
      digitalWrite(13, HIGH);
      delay(delayTime);
      digitalWrite(13, LOW);
      delay(delayTime);
    }
    else
    {
      digitalWrite(13, LOW);
    }
  }
}

By subtracting '0' from a character digit ('0' to '9'), you get its value.