# Java Arithmetic First understand integer division (assumed by Java

```Java Arithmetic
First understand integer division (assumed by Java)
some examples of integer division
10/2
10/3
10/4
4/10
5
3
2
0
now double division
10.0/2
10.0/3
10/4.0
10.0/5.0
5.0
3.333333
2.5
2.0
Casting
To change one data type to another put the new type in parenthesis
in front of the type you want to change, as follows:
int n = 6;
(double)n
turns n into 6.0
10/4
evaluates to 2 because of integer division
but
(double)10/4 evaluates to 2.5
10/(double)
also evaluates to 2.5
BUT BE CAREFUL OF ORDER OF OPERATIONS
Casting comes before all operations EXCEPT ()
(double)(10/4) evaluates to 2.0
int x,y;
(double)(x/y) will not do the same as (double)x/y or x/(double)y
When you cast to an int you lose precision by truncating:
(int) 10.7 / 5  2
What is modulus?
You learned about the remainder long ago.
10 divided by 7 equals 1 with a remainder of 3
or 7 goes into 10, 1 time with 3 left over
examples of modulus
10 % 2
10 % 3
10 % 4
4 % 10
0 % 10
10 % 0
0
1
2
4
0
error
int x,y
consider x % y
if (x < y)
x%y=x
what are all the possible remainders for
n % 5?
(0,1,2,3,4)
what are all possible remainders for
a%b
(0, 1, …. b -1)
ASSIGNMENT PART 1: PRACTICE BY SOLVING
Assume int x = 8; int y = 5; int a = 10; int b = 3;
12 / 7
100 / 30
3/9
0/5
1/2
-4/8
100/6.0
30.0/12
x/b
y/x
a/b
(double)a / b
y / (double) b
b/(double)a
(double)(y/x)
(double)(10/7)
100 % 12
4 % 12
10 % 10
15 % 30
30 % 15
0%7
x%y
a%x
b%a
a%b
0%y
1%b
y%0
a%a
What are all possible results for n % 7?
ASSIGNMENT PART 2:
Use for loops and the methods of the Math class from the AP
Quick Reference Guide, to reproduce this table. Recall that
System.out.print() prints without advancing to next line.
N
1
6
11
16
21
26
31
36
41
46
51
56
61
66
71
76
81
86
91
96
101
106
111
116
121
126
N
Squared
1
36
121
256
441
676
961
1296
1681
2116
2601
3136
3721
4356
5041
5776
6561
7396
8281
9216
10201
11236
12321
13456
14641
15876
Square Root
of N
1
2.449489743
3.31662479
4
4.582575695
5.099019514
5.567764363
6
6.403124237
6.782329983
7.141428429
7.483314774
7.810249676
8.124038405
8.426149773
8.717797887
9
9.273618495
9.539392014
9.797958971
10.04987562
10.29563014
10.53565375
10.77032961
11
11.22497216
N
Cubed
1
216
1331
4096
9261
17576
29791
46656
68921
97336
132651
175616
226981
287496
357911
438976
531441
636056
753571
884736
1030301
1191016
1367631
1560896
1771561
2000376
N to the 1/3
1
1.817120593
2.223980091
2.5198421
2.758924176
2.962496068
3.141380652
3.301927249
3.44821724
3.583047871
3.708429769
3.825862366
3.936497183
4.041240021
4.140817749
4.235823584
4.326748711
4.414004962
4.497941445
4.57885697
4.657009508
4.732623491
4.805895534
4.876998961
4.946087443
5.013297935
ASSIGNMENT PART 3:
Write a method for 2-D Distance Formula – make it static so
you can have it in the same class as a main method for easy
testing.
Given the two points (x1, y1) and (x2, y2), the distance between these
points is given by the formula:
```
Number theory

27 Cards

Complex analysis

23 Cards