Question

In the Egyptian system, how can I identify the largest number of

the next sentences:
a) base five, five distinct symbols.
b) base ten, d (counting number) distinct symbols

Answer 1

In base five with five distinct symbols, the largest number with one digit is '4'. In base ten with 'd' counting symbols, the largest number with one digit is 'd - 1'. Scientific notation, utilizing powers-of-ten, is often used for simplifying the representation of large numbers.

Step-by-step explanation:

To identify the largest number in base five using five distinct symbols, you need to use the highest value for each symbol which, in base five, are usually represented as 0, 1, 2, 3, and 4. So, the largest number you can represent with one digit in base five is '4'.

In base ten, which uses powers-of-ten notation due to our ten fingers, with 'd' distinct counting symbols, the largest number with one digit is 'd - 1.' This is because if you have 'd' symbols, they typically start from 0 and go up to 'd - 1.' For example, in our familiar decimal system with ten symbols (0-9), the largest one-digit number is '9'.

Examples of Using Numerical Bases:

• In a base five system: 44444 (which is the largest number with five digits).
• In a base ten system with d symbols: If d=10 then 99999 (ten being the number of symbols and 9 the largest symbol).

These systems are useful for simplifying calculations and representational purposes like in scientific notation used to express large numbers, such as writing 500,000,000 as 5 x 108.