History of Mathematics

Homework Assignment 1

Prepared by:

Joseph Malkevitch
Department of Mathematics and Computer Studies
York College (CUNY)
Jamaica, New York 11451

1. The decimal system is based on the idea that:

347 represents 3(10)2 + 4(10)1 + 7(10)0

since (10)2 is defined to mean 10 (10) = 100

we have 347 represents 300 + 40 + 7 which is the number three hundred forty seven.

The reason we use powers of 10 is that in the decimal system we have 10 symbols including the symbol for zero.

Assuming the the digits 0, 1, 2, ...., 9 have their usual meaning and using the ideas above:

a. What number (write it down in words) is represented by:

423 in a system with 5 symbols (0, 1, 2, 3, 4)?

b. What number (write it down is words) is represented by:

101101 in a system with 2 symbols (0, 1)?

c. What number (write it down in words) is represented by:

1202 in a system with 3 symbols (0, 1, 2)?

d. What number (write it down in words( is represented by:

1202 in a system with 4 symbols (0, 1, 2, 3)?

2. What number is represented (write it down in words and Hindu-arabic symbols) by the following expressions in Roman numerals:

a. XL

b. MCIX

c. CCCXXXIV

3. a. Multiply 31 by 14 in the way you were taught using the Hindu-Arabic system.

b. Convert 31 and 14 to Roman numerals.

c. Think about what it would be like to develop an algorithm (procedure) to multiply the Roman numerals for 31 and 14 to obtain the answer in Roman numerals.

4. What number is represented by the Egyptian number: