# Class: Rational

Inherits:
Numeric
show all
Defined in:
rational.c

## Overview

A rational number can be represented as a paired integer number; a/b (b>0). Where a is numerator and b is denominator. Integer a equals rational a/1 mathematically.

In ruby, you can create rational object with Rational, to_r or rationalize method. The return values will be irreducible.

``````Rational(1)      #=> (1/1)
Rational(2, 3)   #=> (2/3)
Rational(4, -6)  #=> (-2/3)
3.to_r           #=> (3/1)
``````

You can also create rational object from floating-point numbers or strings.

``````Rational(0.3)    #=> (5404319552844595/18014398509481984)
Rational('0.3')  #=> (3/10)
Rational('2/3')  #=> (2/3)

0.3.to_r         #=> (5404319552844595/18014398509481984)
'0.3'.to_r       #=> (3/10)
'2/3'.to_r       #=> (2/3)
0.3.rationalize  #=> (3/10)
``````

A rational object is an exact number, which helps you to write program without any rounding errors.

``````10.times.inject(0){|t,| t + 0.1}              #=> 0.9999999999999999
10.times.inject(0){|t,| t + Rational('0.1')}  #=> (1/1)
``````

However, when an expression has inexact factor (numerical value or operation), will produce an inexact result.

``````Rational(10) / 3   #=> (10/3)
Rational(10) / 3.0 #=> 3.3333333333333335

Rational(-8) ** Rational(1, 3)
#=> (1.0000000000000002+1.7320508075688772i)
``````

## Defined Under Namespace

Classes: compatible

## Instance Method Summary collapse

• Performs multiplication.

• Performs exponentiation.

• Performs subtraction.

• Performs division.

• :nodoc:.

• Performs comparison and returns -1, 0, or +1.

• Returns true if rat equals object numerically.

• Returns the truncated value (toward positive infinity).

• :nodoc:.

• Returns the denominator (always positive).

• :nodoc:.

• Performs division and returns the value as a float.

• Returns the truncated value (toward negative infinity).

• :nodoc:.

• Returns the value as a string for inspection.

• private

:nodoc:.

• Returns the numerator.

• Performs division.

• :nodoc:.

• :nodoc:.

• :nodoc:.

• Returns a simpler approximation of the value if the optional argument eps is given (rat-|eps| <= result <= rat+|eps|), self otherwise.

• Returns the truncated value (toward the nearest integer; 0.5 => 1; -0.5 => -1).

• Return the value as a float.

• Returns the truncated value as an integer.

• Returns self.

• Returns the value as a string.

• Returns the truncated value (toward zero).

## Instance Method Details

### #*(numeric) ⇒ Numeric

Performs multiplication.

``````Rational(2, 3)  * Rational(2, 3)   #=> (4/9)
Rational(900)   * Rational(1)      #=> (900/1)
Rational(-2, 9) * Rational(-9, 2)  #=> (1/1)
Rational(9, 8)  * 4                #=> (9/2)
Rational(20, 9) * 9.8              #=> 21.77777777777778
``````

Returns:

 ``` 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860``` ```# File 'rational.c', line 834 static VALUE nurat_mul(VALUE self, VALUE other) { switch (TYPE(other)) { case T_FIXNUM: case T_BIGNUM: { get_dat1(self); return f_muldiv(self, dat->num, dat->den, other, ONE, '*'); } case T_FLOAT: return f_mul(f_to_f(self), other); case T_RATIONAL: { get_dat2(self, other); return f_muldiv(self, adat->num, adat->den, bdat->num, bdat->den, '*'); } default: return rb_num_coerce_bin(self, other, '*'); } }```

### #**(numeric) ⇒ Numeric

Performs exponentiation.

``````Rational(2)    ** Rational(3)    #=> (8/1)
Rational(10)   ** -2             #=> (1/100)
Rational(10)   ** -2.0           #=> 0.01
Rational(-4)   ** Rational(1,2)  #=> (1.2246063538223773e-16+2.0i)
Rational(1, 2) ** 0              #=> (1/1)
Rational(1, 2) ** 0.0            #=> 1.0
``````

Returns:

 ``` 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023``` ```# File 'rational.c', line 962 static VALUE nurat_expt(VALUE self, VALUE other) { if (k_numeric_p(other) && k_exact_zero_p(other)) return f_rational_new_bang1(CLASS_OF(self), ONE); if (k_rational_p(other)) { get_dat1(other); if (f_one_p(dat->den)) other = dat->num; /* c14n */ } /* Deal with special cases of 0**n and 1**n */ if (k_numeric_p(other) && k_exact_p(other)) { get_dat1(self); if (f_one_p(dat->den)) if (f_one_p(dat->num)) return f_rational_new_bang1(CLASS_OF(self), ONE); else if (f_minus_one_p(dat->num) && k_integer_p(other)) return f_rational_new_bang1(CLASS_OF(self), INT2FIX(f_odd_p(other) ? -1 : 1)); else if (f_zero_p(dat->num)) if (FIX2INT(f_cmp(other, ZERO)) == -1) rb_raise_zerodiv(); else return f_rational_new_bang1(CLASS_OF(self), ZERO); } /* General case */ switch (TYPE(other)) { case T_FIXNUM: { VALUE num, den; get_dat1(self); switch (FIX2INT(f_cmp(other, ZERO))) { case 1: num = f_expt(dat->num, other); den = f_expt(dat->den, other); break; case -1: num = f_expt(dat->den, f_negate(other)); den = f_expt(dat->num, f_negate(other)); break; default: num = ONE; den = ONE; break; } return f_rational_new2(CLASS_OF(self), num, den); } case T_BIGNUM: rb_warn("in a**b, b may be too big"); /* fall through */ case T_FLOAT: case T_RATIONAL: return f_expt(f_to_f(self), other); default: return rb_num_coerce_bin(self, other, id_expt); } }```

### #+(numeric) ⇒ Numeric

``````Rational(2, 3)  + Rational(2, 3)   #=> (4/3)
Rational(900)   + Rational(1)      #=> (900/1)
Rational(-2, 9) + Rational(-9, 2)  #=> (-85/18)
Rational(9, 8)  + 4                #=> (41/8)
Rational(20, 9) + 9.8              #=> 12.022222222222222
``````

Returns:

 ``` 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741``` ```# File 'rational.c', line 715 static VALUE nurat_add(VALUE self, VALUE other) { switch (TYPE(other)) { case T_FIXNUM: case T_BIGNUM: { get_dat1(self); return f_addsub(self, dat->num, dat->den, other, ONE, '+'); } case T_FLOAT: return f_add(f_to_f(self), other); case T_RATIONAL: { get_dat2(self, other); return f_addsub(self, adat->num, adat->den, bdat->num, bdat->den, '+'); } default: return rb_num_coerce_bin(self, other, '+'); } }```

### #-(numeric) ⇒ Numeric

Performs subtraction.

``````Rational(2, 3)  - Rational(2, 3)   #=> (0/1)
Rational(900)   - Rational(1)      #=> (899/1)
Rational(-2, 9) - Rational(-9, 2)  #=> (77/18)
Rational(9, 8)  - 4                #=> (23/8)
Rational(20, 9) - 9.8              #=> -7.577777777777778
``````

Returns:

 ``` 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781``` ```# File 'rational.c', line 755 static VALUE nurat_sub(VALUE self, VALUE other) { switch (TYPE(other)) { case T_FIXNUM: case T_BIGNUM: { get_dat1(self); return f_addsub(self, dat->num, dat->den, other, ONE, '-'); } case T_FLOAT: return f_sub(f_to_f(self), other); case T_RATIONAL: { get_dat2(self, other); return f_addsub(self, adat->num, adat->den, bdat->num, bdat->den, '-'); } default: return rb_num_coerce_bin(self, other, '-'); } }```

### #/(numeric) ⇒ Numeric #quo(numeric) ⇒ Numeric

Performs division.

``````Rational(2, 3)  / Rational(2, 3)   #=> (1/1)
Rational(900)   / Rational(1)      #=> (900/1)
Rational(-2, 9) / Rational(-9, 2)  #=> (4/81)
Rational(9, 8)  / 4                #=> (9/32)
Rational(20, 9) / 9.8              #=> 0.22675736961451246
``````

 ``` 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919``` ```# File 'rational.c', line 875 static VALUE nurat_div(VALUE self, VALUE other) { switch (TYPE(other)) { case T_FIXNUM: case T_BIGNUM: if (f_zero_p(other)) rb_raise_zerodiv(); { get_dat1(self); return f_muldiv(self, dat->num, dat->den, other, ONE, '/'); } case T_FLOAT: { double x = RFLOAT_VALUE(other), den; get_dat1(self); if (isnan(x)) return DBL2NUM(NAN); if (isinf(x)) return INT2FIX(0); if (x != 0.0 && modf(x, &den) == 0.0) { return rb_rational_raw2(dat->num, f_mul(rb_dbl2big(den), dat->den)); } } return rb_funcall(f_to_f(self), '/', 1, other); case T_RATIONAL: if (f_zero_p(other)) rb_raise_zerodiv(); { get_dat2(self, other); if (f_one_p(self)) return f_rational_new_no_reduce2(CLASS_OF(self), bdat->den, bdat->num); return f_muldiv(self, adat->num, adat->den, bdat->num, bdat->den, '/'); } default: return rb_num_coerce_bin(self, other, '/'); } }```

### #// ⇒ Object

:nodoc:

 ``` 1150 1151 1152 1153 1154``` ```# File 'rational.c', line 1150 static VALUE nurat_idiv(VALUE self, VALUE other) { return f_idiv(self, other); }```

### #<=>(numeric) ⇒ -1, ...

Performs comparison and returns -1, 0, or +1.

``````Rational(2, 3)  <=> Rational(2, 3)  #=> 0
Rational(5)     <=> 5               #=> 0
Rational(2,3)   <=> Rational(1,3)   #=> 1
Rational(1,3)   <=> 1               #=> -1
Rational(1,3)   <=> 0.3             #=> 1
``````

Returns:

• (-1, 0, +1, nil)
 ``` 1037 1038 1039 1040 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050 1051 1052 1053 1054 1055 1056 1057 1058 1059 1060 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072``` ```# File 'rational.c', line 1037 static VALUE nurat_cmp(VALUE self, VALUE other) { switch (TYPE(other)) { case T_FIXNUM: case T_BIGNUM: { get_dat1(self); if (FIXNUM_P(dat->den) && FIX2LONG(dat->den) == 1) return f_cmp(dat->num, other); /* c14n */ return f_cmp(self, f_rational_new_bang1(CLASS_OF(self), other)); } case T_FLOAT: return f_cmp(f_to_f(self), other); case T_RATIONAL: { VALUE num1, num2; get_dat2(self, other); if (FIXNUM_P(adat->num) && FIXNUM_P(adat->den) && FIXNUM_P(bdat->num) && FIXNUM_P(bdat->den)) { num1 = f_imul(FIX2LONG(adat->num), FIX2LONG(bdat->den)); num2 = f_imul(FIX2LONG(bdat->num), FIX2LONG(adat->den)); } else { num1 = f_mul(adat->num, bdat->den); num2 = f_mul(bdat->num, adat->den); } return f_cmp(f_sub(num1, num2), ZERO); } default: return rb_num_coerce_cmp(self, other, id_cmp); } }```

### #==(object) ⇒ Boolean

Returns true if rat equals object numerically.

``````Rational(2, 3)  == Rational(2, 3)   #=> true
Rational(5)     == 5                #=> true
Rational(0)     == 0.0              #=> true
Rational('1/3') == 0.33             #=> false
Rational('1/2') == '1/2'            #=> false
``````

Returns:

• (Boolean)
 ``` 1086 1087 1088 1089 1090 1091 1092 1093 1094 1095 1096 1097 1098 1099 1100 1101 1102 1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119 1120 1121``` ```# File 'rational.c', line 1086 static VALUE nurat_eqeq_p(VALUE self, VALUE other) { switch (TYPE(other)) { case T_FIXNUM: case T_BIGNUM: { get_dat1(self); if (f_zero_p(dat->num) && f_zero_p(other)) return Qtrue; if (!FIXNUM_P(dat->den)) return Qfalse; if (FIX2LONG(dat->den) != 1) return Qfalse; if (f_eqeq_p(dat->num, other)) return Qtrue; return Qfalse; } case T_FLOAT: return f_eqeq_p(f_to_f(self), other); case T_RATIONAL: { get_dat2(self, other); if (f_zero_p(adat->num) && f_zero_p(bdat->num)) return Qtrue; return f_boolcast(f_eqeq_p(adat->num, bdat->num) && f_eqeq_p(adat->den, bdat->den)); } default: return f_eqeq_p(other, self); } }```

### #ceil ⇒ Integer #ceil(precision = 0) ⇒ Object

Returns the truncated value (toward positive infinity).

``````Rational(3).ceil      #=> 3
Rational(2, 3).ceil   #=> 1
Rational(-3, 2).ceil  #=> -1

decimal      -  1  2  3 . 4  5  6
^  ^  ^  ^   ^  ^
precision      -3 -2 -1  0  +1 +2

'%f' % Rational('-123.456').ceil(+1)  #=> "-123.400000"
'%f' % Rational('-123.456').ceil(-1)  #=> "-120.000000"
``````

 ``` 1317 1318 1319 1320 1321``` ```# File 'rational.c', line 1317 static VALUE nurat_ceil_n(int argc, VALUE *argv, VALUE self) { return f_round_common(argc, argv, self, nurat_ceil); }```

### #coerce ⇒ Object

:nodoc:

 ``` 1124 1125 1126 1127 1128 1129 1130 1131 1132 1133 1134 1135 1136 1137 1138 1139 1140 1141 1142 1143 1144 1145 1146``` ```# File 'rational.c', line 1124 static VALUE nurat_coerce(VALUE self, VALUE other) { switch (TYPE(other)) { case T_FIXNUM: case T_BIGNUM: return rb_assoc_new(f_rational_new_bang1(CLASS_OF(self), other), self); case T_FLOAT: return rb_assoc_new(other, f_to_f(self)); case T_RATIONAL: return rb_assoc_new(other, self); case T_COMPLEX: if (k_exact_zero_p(RCOMPLEX(other)->imag)) return rb_assoc_new(f_rational_new_bang1 (CLASS_OF(self), RCOMPLEX(other)->real), self); else return rb_assoc_new(other, rb_Complex(self, INT2FIX(0))); } rb_raise(rb_eTypeError, "%s can't be coerced into %s", rb_obj_classname(other), rb_obj_classname(self)); return Qnil; }```

### #denominator ⇒ Integer

Returns the denominator (always positive).

``````Rational(7).denominator             #=> 1
Rational(7, 1).denominator          #=> 1
Rational(9, -4).denominator         #=> 4
Rational(-2, -10).denominator       #=> 5
rat.numerator.gcd(rat.denominator)  #=> 1
``````

Returns:

 ``` 611 612 613 614 615 616``` ```# File 'rational.c', line 611 static VALUE nurat_denominator(VALUE self) { get_dat1(self); return dat->den; }```

### #exact? ⇒ Boolean

:nodoc:

Returns:

• (Boolean)
 ``` 1174 1175 1176 1177 1178``` ```# File 'rational.c', line 1174 static VALUE nurat_true(VALUE self) { return Qtrue; }```

### #fdiv(numeric) ⇒ Float

Performs division and returns the value as a float.

``````Rational(2, 3).fdiv(1)       #=> 0.6666666666666666
Rational(2, 3).fdiv(0.5)     #=> 1.3333333333333333
Rational(2).fdiv(3)          #=> 0.6666666666666666
``````

Returns:

 ``` 931 932 933 934 935 936 937``` ```# File 'rational.c', line 931 static VALUE nurat_fdiv(VALUE self, VALUE other) { if (f_zero_p(other)) return f_div(self, f_to_f(other)); return f_to_f(f_div(self, other)); }```

### #floor ⇒ Integer #floor(precision = 0) ⇒ Object

Returns the truncated value (toward negative infinity).

``````Rational(3).floor      #=> 3
Rational(2, 3).floor   #=> 0
Rational(-3, 2).floor  #=> -1

decimal      -  1  2  3 . 4  5  6
^  ^  ^  ^   ^  ^
precision      -3 -2 -1  0  +1 +2

'%f' % Rational('-123.456').floor(+1)  #=> "-123.500000"
'%f' % Rational('-123.456').floor(-1)  #=> "-130.000000"
``````

 ``` 1293 1294 1295 1296 1297``` ```# File 'rational.c', line 1293 static VALUE nurat_floor_n(int argc, VALUE *argv, VALUE self) { return f_round_common(argc, argv, self, nurat_floor); }```

### #hash ⇒ Object

:nodoc:

 ``` 1539 1540 1541 1542 1543 1544 1545 1546 1547 1548 1549 1550 1551 1552``` ```# File 'rational.c', line 1539 static VALUE nurat_hash(VALUE self) { st_index_t v, h[2]; VALUE n; get_dat1(self); n = rb_hash(dat->num); h[0] = NUM2LONG(n); n = rb_hash(dat->den); h[1] = NUM2LONG(n); v = rb_memhash(h, sizeof(h)); return LONG2FIX(v); }```

### #inspect ⇒ String

Returns the value as a string for inspection.

``````Rational(2).inspect      #=> "(2/1)"
Rational(-8, 6).inspect  #=> "(-4/3)"
Rational('1/2').inspect  #=> "(1/2)"
``````

Returns:

 ``` 1593 1594 1595 1596 1597 1598 1599 1600 1601 1602 1603``` ```# File 'rational.c', line 1593 static VALUE nurat_inspect(VALUE self) { VALUE s; s = rb_usascii_str_new2("("); rb_str_concat(s, f_format(self, f_inspect)); rb_str_cat2(s, ")"); return s; }```

### #marshal_dump ⇒ Object(private)

:nodoc:

 ``` 1625 1626 1627 1628 1629 1630 1631 1632 1633 1634``` ```# File 'rational.c', line 1625 static VALUE nurat_marshal_dump(VALUE self) { VALUE a; get_dat1(self); a = rb_assoc_new(dat->num, dat->den); rb_copy_generic_ivar(a, self); return a; }```

### #numerator ⇒ Integer

Returns the numerator.

``````Rational(7).numerator        #=> 7
Rational(7, 1).numerator     #=> 7
Rational(9, -4).numerator    #=> -9
Rational(-2, -10).numerator  #=> 1
``````

Returns:

 ``` 592 593 594 595 596 597``` ```# File 'rational.c', line 592 static VALUE nurat_numerator(VALUE self) { get_dat1(self); return dat->num; }```

### #/(numeric) ⇒ Numeric #quo(numeric) ⇒ Numeric

Performs division.

``````Rational(2, 3)  / Rational(2, 3)   #=> (1/1)
Rational(900)   / Rational(1)      #=> (900/1)
Rational(-2, 9) / Rational(-9, 2)  #=> (4/81)
Rational(9, 8)  / 4                #=> (9/32)
Rational(20, 9) / 9.8              #=> 0.22675736961451246
``````

 ``` 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919``` ```# File 'rational.c', line 875 static VALUE nurat_div(VALUE self, VALUE other) { switch (TYPE(other)) { case T_FIXNUM: case T_BIGNUM: if (f_zero_p(other)) rb_raise_zerodiv(); { get_dat1(self); return f_muldiv(self, dat->num, dat->den, other, ONE, '/'); } case T_FLOAT: { double x = RFLOAT_VALUE(other), den; get_dat1(self); if (isnan(x)) return DBL2NUM(NAN); if (isinf(x)) return INT2FIX(0); if (x != 0.0 && modf(x, &den) == 0.0) { return rb_rational_raw2(dat->num, f_mul(rb_dbl2big(den), dat->den)); } } return rb_funcall(f_to_f(self), '/', 1, other); case T_RATIONAL: if (f_zero_p(other)) rb_raise_zerodiv(); { get_dat2(self, other); if (f_one_p(self)) return f_rational_new_no_reduce2(CLASS_OF(self), bdat->den, bdat->num); return f_muldiv(self, adat->num, adat->den, bdat->num, bdat->den, '/'); } default: return rb_num_coerce_bin(self, other, '/'); } }```

### #quot ⇒ Object

:nodoc:

 ``` 1157 1158 1159 1160 1161``` ```# File 'rational.c', line 1157 static VALUE nurat_quot(VALUE self, VALUE other) { return f_truncate(f_div(self, other)); }```

### #quotrem ⇒ Object

:nodoc:

 ``` 1164 1165 1166 1167 1168 1169``` ```# File 'rational.c', line 1164 static VALUE nurat_quotrem(VALUE self, VALUE other) { VALUE val = f_truncate(f_div(self, other)); return rb_assoc_new(val, f_sub(self, f_mul(other, val))); }```

### #rational? ⇒ Boolean

:nodoc:

Returns:

• (Boolean)
 ``` 1174 1175 1176 1177 1178``` ```# File 'rational.c', line 1174 static VALUE nurat_true(VALUE self) { return Qtrue; }```

### #rationalize ⇒ self #rationalize(eps) ⇒ Object

Returns a simpler approximation of the value if the optional argument eps is given (rat-|eps| <= result <= rat+|eps|), self otherwise.

``````r = Rational(5033165, 16777216)
r.rationalize                    #=> (5033165/16777216)
r.rationalize(Rational('0.01'))  #=> (3/10)
r.rationalize(Rational('0.1'))   #=> (1/3)
``````

• #rationalizeself

Returns:

• (self)
 ``` 1515 1516 1517 1518 1519 1520 1521 1522 1523 1524 1525 1526 1527 1528 1529 1530 1531 1532 1533 1534 1535 1536``` ```# File 'rational.c', line 1515 static VALUE nurat_rationalize(int argc, VALUE *argv, VALUE self) { VALUE e, a, b, p, q; if (argc == 0) return self; if (f_negative_p(self)) return f_negate(nurat_rationalize(argc, argv, f_abs(self))); rb_scan_args(argc, argv, "01", &e); e = f_abs(e); a = f_sub(self, e); b = f_add(self, e); if (f_eqeq_p(a, b)) return self; nurat_rationalize_internal(a, b, &p, &q); return f_rational_new2(CLASS_OF(self), p, q); }```

### #round ⇒ Integer #round(precision = 0) ⇒ Object

Returns the truncated value (toward the nearest integer; 0.5 => 1; -0.5 => -1).

``````Rational(3).round      #=> 3
Rational(2, 3).round   #=> 1
Rational(-3, 2).round  #=> -2

decimal      -  1  2  3 . 4  5  6
^  ^  ^  ^   ^  ^
precision      -3 -2 -1  0  +1 +2

'%f' % Rational('-123.456').round(+1)  #=> "-123.500000"
'%f' % Rational('-123.456').round(-1)  #=> "-120.000000"
``````

 ``` 1366 1367 1368 1369 1370``` ```# File 'rational.c', line 1366 static VALUE nurat_round_n(int argc, VALUE *argv, VALUE self) { return f_round_common(argc, argv, self, nurat_round); }```

### #to_f ⇒ Float

Return the value as a float.

``````Rational(2).to_f      #=> 2.0
Rational(9, 4).to_f   #=> 2.25
Rational(-3, 4).to_f  #=> -0.75
Rational(20, 3).to_f  #=> 6.666666666666667
``````

Returns:

 ``` 1383 1384 1385 1386 1387 1388``` ```# File 'rational.c', line 1383 static VALUE nurat_to_f(VALUE self) { get_dat1(self); return f_fdiv(dat->num, dat->den); }```

### #to_i ⇒ Integer

Returns the truncated value as an integer.

Equivalent to

``````rat.truncate.

Rational(2, 3).to_i   #=> 0
Rational(3).to_i      #=> 3
Rational(300.6).to_i  #=> 300
Rational(98,71).to_i  #=> 1
Rational(-30,2).to_i  #=> -15
``````

Returns:

 ``` 1210 1211 1212 1213 1214 1215 1216 1217``` ```# File 'rational.c', line 1210 static VALUE nurat_truncate(VALUE self) { get_dat1(self); if (f_negative_p(dat->num)) return f_negate(f_idiv(f_negate(dat->num), dat->den)); return f_idiv(dat->num, dat->den); }```

### #to_r ⇒ self

Returns self.

``````Rational(2).to_r      #=> (2/1)
Rational(-8, 6).to_r  #=> (-4/3)
``````

Returns:

• (self)
 ``` 1399 1400 1401 1402 1403``` ```# File 'rational.c', line 1399 static VALUE nurat_to_r(VALUE self) { return self; }```

### #to_s ⇒ String

Returns the value as a string.

``````Rational(2).to_s      #=> "2/1"
Rational(-8, 6).to_s  #=> "-4/3"
Rational('1/2').to_s  #=> "1/2"
``````

Returns:

 ``` 1577 1578 1579 1580 1581``` ```# File 'rational.c', line 1577 static VALUE nurat_to_s(VALUE self) { return f_format(self, f_to_s); }```

### #truncate ⇒ Integer #truncate(precision = 0) ⇒ Object

Returns the truncated value (toward zero).

``````Rational(3).truncate      #=> 3
Rational(2, 3).truncate   #=> 0
Rational(-3, 2).truncate  #=> -1

decimal      -  1  2  3 . 4  5  6
^  ^  ^  ^   ^  ^
precision      -3 -2 -1  0  +1 +2

'%f' % Rational('-123.456').truncate(+1)  #=>  "-123.400000"
'%f' % Rational('-123.456').truncate(-1)  #=>  "-120.000000"
``````

 ``` 1341 1342 1343 1344 1345``` ```# File 'rational.c', line 1341 static VALUE nurat_truncate_n(int argc, VALUE *argv, VALUE self) { return f_round_common(argc, argv, self, nurat_truncate); }```