SOLUTIONS TO ASSIGNMENT 1
Exercise 1.5
Number in Sexagesimal Form
Number in Decimal Form
2
3,1,2
1,2;6
;1,40
Exercise 1.6
Number in Decimal Form
Number in Sexagesimal Form
2
2 since
122
2,2 since
7265
2,1,5 since
.2
;12 since
1;20 since
Exercise 1.7
a)
Since
Since
b)
, this fraction is written as ;24 in sexagesimal form.
, this fraction is written as ;55 in sexagesimal form.
Adding the sexagesimal decimals from part a) we get:
;24
+ ;55
________
= ;79
Since 79 = 60 +19, this is written as 1;19 in sexagesimal form.
c)
, so this fraction sum is indeed
written as 1;19 in sexagesimal form.
Exercise 1.10
Starting with the initial guess
Heron’s method:
, we get the following approximations for
This approximation is already accurate to 8 decimal places!
(Check with your calculator:
)
Note: Other initial guesses would have also worked (for example, using
or
).
using
Exercise 1.12
a)
Say the square has side . Then the word problem translates into the following
equation:
Multiplying the equation by 12 yields:
,
or
b)
Solution of the quadratic:
This is the same answer as on the tablet since 0;30 = ½!
Exercise 1.13
Using duplation to multiply 13 by 15 yields 195 according to the following table:
1
2
4
8
13=8+4+1
15
30
60
120
195 – the answer
Exercise 1.14
Using duplation to multiply 15 by 22 yields 330 according to the following table:
1
2
4
8
15=8+4+2+1
22
44
88
176
330 – the answer
Exercise 1.17
a)
b)
or
Exercise 1.18
Let
be the quantity we seek. The equation given here is then
.
By the method of false position, suppose that
is the solution (of course.. it isn’t!) Then
plugging this (false) solution into the left-hand side of the equation yields
. Since
, we conclude that the actual solution is
.
(Check this answer:
)
Exercise 1.20
Based on a base 5 number system with digits A, B, C, D, E corresponding to 1, 2, 3, 4, 5 we get:
a)
b)
c)
d)