When inputting large numbers it returns the final result as NaN

I am creating a SUPER basic calculator in C for a project.

/*
Declare and initialize variables and/or constants using appropriate data types -- X
Read in input from the user and output data & information to the user in a meaningful manner -- X
Use the mathematical operators – addition, subtraction, multiplication, division, and modulus (remainder) 
– in expressions and calculations -- X
Use decision making structures such as if, if/else, and switch to affect program flow -- X
Use control structures such a while, do-while, and for loops to implement repetition in code -- X
*/
//All libraries
#include <stdio.h>
#include <stdbool.h>
#include <ctype.h>
float num1 = 0; 
float num2 = 0;
float finalResult = 0;
char operator = '+';
bool opReal = false;
int main() {
//Ask for first number
printf("Enter an number: ");
scanf("%f", &num1); 
printf("\n");
//Ask for second number
printf("Enter another number: ");
scanf("%f", &num2);
printf("\n");
//Ask for operator
do {
printf("Enter either + - * or /: ");
scanf(" %c", &operator);
//Check for what operator is
if (operator == '-') {
operator = '-';
opReal = true;
} else if (operator == '+') {
operator = '+';
opReal = true;
} else if (operator == '*') {
operator = '*';
opReal = true;
} else if (operator == '/') {
operator = '/';
opReal = true;
} else {
operator = '+';
opReal = false;
}
} while (!opReal);
printf("num1: %f\n", num1);
printf("num2: %f\n", num2);
printf("operator: %c\n", operator);
//Do calculations
if (operator == '-') {
finalResult = num1 - num2;
} else if (operator == '+') {
finalResult = num1 + num2;
} else if (operator == '*') {
finalResult = num1 * num2;
} else if (operator == '/') {
finalResult = num1 / num2;
} 
printf("Final Result: %f\n", finalResult);
}

I've tried looking up different solutions and applying different ways to operate on num1 and 2, but in the end they don't work.
It should take num1 and num2 and apply operator to it.
However when a large number is applied then num1 = inf and num2 = inf.
That in turn makes finalResult Nan
Whats happening?
Please help.

I don't see anything particular wrong with your code so maybe you just need to switch from float to double or even long double? Don't use global variable unless you have to. Guard against divide by zero. No point of checking if an operator is x then assign x to the operator. Check that scanf() was successful otherwise you may be operating on uninitialized data.

#include <stdbool.h>
#include <stdio.h>
#include <string.h>
int main() {
double num1;
printf("Enter a number: ");
if(scanf("%lf", &num1) != 1) {
printf("scanf failed\n");
return 1;
}
double num2;
printf("Enter another number: ");
if(scanf("%lf", &num2) != 1) {
printf("scanf failed\n");
return 1;
}
char operator;
do {
printf("Enter either + - * or /: ");
if(scanf(" %c", &operator) != 1) {
printf("scanf failed\n");
return 1;
}
} while (!strchr("-+*/", operator));
double finalResult = 0;
if (operator == '-') {
finalResult = num1 - num2;
} else if (operator == '+') {
finalResult = num1 + num2;
} else if (operator == '*') {
finalResult = num1 * num2;
} else if (operator == '/') {
finalResult = num2 != 0 ? num1 / num2 : 0; // or ERR?
}
printf("Final Result: %lf\n", finalResult);
}

I would use an array of numbers, dedup the input with a loop and probably a switch instead of all those if-else-if:

#include <stdbool.h>
#include <stdio.h>
#include <string.h>
#define NUM_LEN 2
int main() {
const char *prompts[NUM_LEN] = { "an", "another" };
double num[NUM_LEN];
for(size_t i = 0; i < NUM_LEN; i++) {
printf("Enter %s number: ", prompts[i]);
if(scanf("%lf", &num[i]) != 1) {
printf("scanf failed\n");
return 1;
}
}
char operator;
do {
printf("Enter either + - * or /: ");
if(scanf(" %c", &operator) != 1) {
printf("scanf failed\n");
return 1;
}
} while (!strchr("-+*/", operator));
switch(operator) {
case '-':
num[0] -= num[1];
break;
case '+':
num[0] += num[1];
break;
case '*':
num[0] *= num[1];
break;
case '/':
num[0] = num[1] != 0 ? num[0] / num[1] : 0; // or ERR?
break;
default:
printf("Invalid operator\n");
break;
}
printf("Final Result: %lf\n", num[0]);
}

The next step would be to build a map from operator to a function, i.e:

struct operators {
char operator;
int (*evaluate)(double *num);
} operators[] = {
{'+', add},
{'-', subtract},
{'*', multiply},
{'/', divide}
};

Now you extract the valid operators used in strchr() from this map, and you can use lfind() to lookup the evaluate function for a given operator.

Well depending on how large those large numbers are, you might just be able to replace "float" with "double" and have it work.

Other than that you could add the following check to your code:

    if(isinf(num1) || isinf(num2) || isnan(num1) || isnan(num2)) {
        printf("Error, number out of bounds!");
        return -1;
    }

Though this requires the use of #include <math.h> though, if you are constrained to just the libraries specified in this file (as might be implied by the comment) then this might just be an unsolvable problem.