Final answer:
To convert decimal to hexadecimal, divide the number by 16 repeatedly and record the remainders until reaching 0. Then, take the remainders in reverse order to get the hexadecimal representation. For example, 766 in decimal is 2FE in hexadecimal. For decimal numbers with a fractional part, divide the integer and fractional parts separately and combine them at the end.
Step-by-step explanation:
To convert from decimal to hexadecimal, we need to understand the decimal and hexadecimal systems. The decimal system is a base-10 system, meaning it uses 10 digits (0-9), while the hexadecimal system is a base-16 system, using 16 digits (0-9 and A-F).
For decimal numbers, we divide the number by 16 repeatedly and record the remainders until we reach 0. Then, we take the remainders in reverse order to get the hexadecimal representation.
Let's apply this process to the given numbers:
a. 766: Dividing 766 by 16, we get a quotient of 47 and a remainder of 14 (E in hexadecimal). Dividing 47 by 16, we get a quotient of 2 and a remainder of 15 (F in hexadecimal). Dividing 2 by 16, we get a quotient of 0 and a remainder of 2 (2 in hexadecimal). Therefore, 766 in decimal is equivalent to 2FE in hexadecimal.
b. 1982.5001: To convert the integer part of the number, we can follow the same process as in part a. Dividing 1982 by 16, we get a quotient of 123 and a remainder of 14 (E in hexadecimal). Dividing 123 by 16, we get a quotient of 7 and a remainder of 11 (B in hexadecimal). Dividing 7 by 16, we get a quotient of 0 and a remainder of 7 (7 in hexadecimal). Therefore, the integer part is 7BE. For the fractional part, we can multiply it by 16 repeatedly until it reaches 0.
However, since the fractional part is infinite, we will round it to a certain number of decimal places. Rounding 0.5001 to 3 decimal places, we get 0.500. Multiplying 0.500 by 16, we get 8. Dividing 8 by 16, we get a quotient of 0 and a remainder of 8 (8 in hexadecimal). Therefore, the fractional part is 0.8. Combining the integer and fractional parts, we have 7BE.8 in hexadecimal.