【一起学Python】第11天:数字类型Number详细使用总结

# 1. 整数 (int) - 无限精度integer = 42big_integer = 123456789012345678901234567890negative = -100# 2. 浮点数 (float) - 双精度float_num = 3.14scientific = 1.5e-4  # 0.00015negative_float = -2.5# 3. 复数 (complex)complex_num = 3 + 4jpure_imaginary = 5j# 4. 布尔 (bool) - 是int的子类boolean = True  # 等于 1boolean2 = False  # 等于 0

# 十进制decimal = 100# 二进制（0b前缀）binary = 0b1010  # 10print(binary)  # 10# 八进制（0o前缀）octal = 0o12  # 10print(octal)  # 10# 十六进制（0x前缀）hexadecimal = 0xFF  # 255print(hexadecimal)  # 255# 使用下划线分隔（提高可读性，Python 3.6+）large_num = 1_000_000print(large_num)  # 1000000billion = 1_000_000_000print(billion)  # 1000000000# 从字符串转换num1 = int('100')  # 10进制num2 = int('1010', 2)  # 2进制num3 = int('FF', 16)  # 16进制print(num1, num2, num3)  # 100 10 255# 从浮点数转换（截断小数部分）num4 = int(3.9)print(num4)  # 3num5 = int(-3.9)print(num5)  # -3

a, b = 10, 3# 基本运算print(a + b)   # 13  加法print(a - b)   # 7   减法print(a * b)   # 30  乘法print(a / b)   # 3.333... 除法（返回浮点数）print(a // b)  # 3   整除（向下取整）print(a % b)   # 1   取余print(a ** b)  # 1000 幂运算# 负数的整除和取余print(-10 // 3)  # -4 (向下取整)print(-10 % 3)   # 2print(10 // -3)  # -4print(10 % -3)   # -2# 绝对值print(abs(-10))  # 10# divmod() - 同时获取商和余数quotient, remainder = divmod(10, 3)print(quotient, remainder)  # 3 1# pow() - 幂运算（支持三参数取模）print(pow(2, 10))      # 1024print(pow(2, 10, 100)) # 24 (2^10 % 100)

a, b = 60, 13  # 60 = 0011 1100, 13 = 0000 1101# 按位与print(a & b)   # 12 (0000 1100)# 按位或print(a | b)   # 61 (0011 1101)# 按位异或print(a ^ b)   # 49 (0011 0001)# 按位取反print(~a)      # -61# 左移print(a << 2)  # 240 (1111 0000)# 右移print(a >> 2)  # 15 (0000 1111)# 实际应用：权限管理READ = 0b001    # 1WRITE = 0b010   # 2EXECUTE = 0b100 # 4# 授予读写权限permission = READ | WRITEprint(permission)  # 3# 检查是否有写权限has_write = bool(permission & WRITE)print(has_write)  # True# 撤销写权限permission = permission & ~WRITEprint(permission)  # 1

# bit_length() - 二进制位数num = 10  # 1010print(num.bit_length())  # 4num = 255  # 11111111print(num.bit_length())  # 8# to_bytes() - 转换为字节num = 1024bytes_data = num.to_bytes(2, byteorder='big')print(bytes_data)  # b'\x04\x00'# from_bytes() - 从字节创建num = int.from_bytes(b'\x04\x00', byteorder='big')print(num)  # 1024# as_integer_ratio() - 返回分数形式（对整数返回 n/1）num = 10print(num.as_integer_ratio())  # (10, 1)

# 普通表示f1 = 3.14f2 = -2.5f3 = 0.5# 科学计数法f4 = 1.5e2   # 150.0f5 = 1.5e-2  # 0.015f6 = -3e3    # -3000.0# 特殊值infinity = float('inf')      # 正无穷neg_infinity = float('-inf') # 负无穷not_a_number = float('nan')  # 非数字print(infinity)      # infprint(neg_infinity)  # -infprint(not_a_number)  # nan# 从字符串转换f7 = float('3.14')f8 = float('1.5e2')print(f7, f8)  # 3.14 150.0# 从整数转换f9 = float(10)print(f9)  # 10.0

a, b = 3.5, 2.0# 基本运算print(a + b)   # 5.5print(a - b)   # 1.5print(a * b)   # 7.0print(a / b)   # 1.75print(a // b)  # 1.0 (浮点整除)print(a % b)   # 1.5print(a ** b)  # 12.25# 四舍五入print(round(3.14159))      # 3print(round(3.14159, 2))   # 3.14print(round(3.14159, 4))   # 3.1416# ⚠️ 银行家舍入（round half to even）print(round(0.5))   # 0 (偶数)print(round(1.5))   # 2 (偶数)print(round(2.5))   # 2 (偶数)print(round(3.5))   # 4 (偶数)# 向上取整import mathprint(math.ceil(3.1))   # 4print(math.ceil(-3.1))  # -3# 向下取整print(math.floor(3.9))   # 3print(math.floor(-3.1))  # -4# 截断（去掉小数部分）print(math.trunc(3.9))   # 3print(math.trunc(-3.9))  # -3

# ⚠️ 浮点数精度问题print(0.1 + 0.2)  # 0.30000000000000004 (不是0.3！)print(0.1 + 0.2 == 0.3)  # False# 查看精确值from decimal import Decimalprint(Decimal(0.1))  # 输出: 0.1000000000000000055511151231257827021181583404541015625# ✅ 解决方案1：使用round()result = round(0.1 + 0.2, 10)print(result == 0.3)  # True# ✅ 解决方案2：使用math.isclose()import mathprint(math.isclose(0.1 + 0.2, 0.3))  # True# ✅ 解决方案3：使用Decimalfrom decimal import Decimala = Decimal('0.1')b = Decimal('0.2')print(a + b)  # 0.3print(a + b == Decimal('0.3'))  # True# ✅ 解决方案4：比较差值epsilon = 1e-10print(abs(0.1 + 0.2 - 0.3) < epsilon)  # True

# is_integer() - 判断是否为整数print((3.0).is_integer())   # Trueprint((3.5).is_integer())   # False# as_integer_ratio() - 返回分数形式print((0.5).as_integer_ratio())   # (1, 2)print((0.25).as_integer_ratio())  # (1, 4)print((3.14).as_integer_ratio())  # (7070651414971679, 2251799813685248)# hex() - 转换为十六进制print((3.14).hex())  # '0x1.91eb851eb851fp+1'# fromhex() - 从十六进制创建f = float.fromhex('0x1.91eb851eb851fp+1')print(f)  # 3.14

# 方式1：直接创建c1 = 3 + 4jc2 = 5j  # 纯虚数c3 = 2 + 0j  # 实数# 方式2：使用complex()c4 = complex(3, 4)  # 3+4jc5 = complex(5)     # 5+0jc6 = complex('3+4j')  # 从字符串print(c1, c4)  # (3+4j) (3+4j)# ⚠️ 注意：j前面必须有数字# c = 3 + j  # 错误！c = 3 + 1j  # 正确

c = 3 + 4j# 实部print(c.real)  # 3.0# 虚部print(c.imag)  # 4.0# 共轭复数print(c.conjugate())  # (3-4j)# 模（绝对值）print(abs(c))  # 5.0 (sqrt(3^2 + 4^2))

c1 = 3 + 4jc2 = 1 + 2j# 加法print(c1 + c2)  # (4+6j)# 减法print(c1 - c2)  # (2+2j)# 乘法print(c1 * c2)  # (-5+10j)# 除法print(c1 / c2)  # (2.2-0.4j)# 幂运算print(c1 ** 2)  # (-7+24j)# 使用cmath模块import cmath# 相位角print(cmath.phase(c1))  # 0.9272952180016122 (弧度)# 极坐标形式r, theta = cmath.polar(c1)print(f"r={r}, θ={theta}")  # r=5.0, θ=0.9272952180016122# 从极坐标创建c3 = cmath.rect(5, 0.927)print(c3)  # (3+4j)# 欧拉公式：e^(iθ) = cos(θ) + i*sin(θ)print(cmath.exp(1j * cmath.pi))  # (-1+0j)

import math# 常量print(math.pi)   # 3.141592653589793print(math.e)    # 2.718281828459045print(math.tau)  # 6.283185307179586 (2π)print(math.inf)  # infprint(math.nan)  # nan# 三角函数print(math.sin(math.pi / 2))  # 1.0print(math.cos(0))            # 1.0print(math.tan(math.pi / 4))  # 1.0# 反三角函数print(math.asin(1))  # 1.5707963267948966 (π/2)print(math.acos(0))  # 1.5707963267948966print(math.atan(1))  # 0.7853981633974483 (π/4)# 双曲函数print(math.sinh(1))  # 1.1752011936438014print(math.cosh(0))  # 1.0print(math.tanh(1))  # 0.7615941559557649# 指数和对数print(math.exp(1))      # 2.718281828459045 (e^1)print(math.log(10))     # 2.302585092994046 (ln(10))print(math.log10(100))  # 2.0 (log₁₀(100))print(math.log2(8))     # 3.0 (log₂(8))# 幂和根print(math.pow(2, 3))   # 8.0print(math.sqrt(16))    # 4.0print(math.cbrt(27))    # 3.0 (立方根, Python 3.11+)# 取整print(math.ceil(3.1))   # 4print(math.floor(3.9))  # 3print(math.trunc(3.9))  # 3# 其他函数print(math.fabs(-5))    # 5.0 (绝对值)print(math.factorial(5)) # 120 (5!)print(math.gcd(12, 18))  # 6 (最大公约数)print(math.lcm(12, 18))  # 36 (最小公倍数, Python 3.9+)# 判断函数print(math.isnan(float('nan')))  # Trueprint(math.isinf(float('inf')))  # Trueprint(math.isfinite(100))        # True

# int → floati = 10f = float(i)print(f)  # 10.0# float → int (截断)f = 3.9i = int(f)print(i)  # 3# str → ints = '100'i = int(s)print(i)  # 100# str → floats = '3.14'f = float(s)print(f)  # 3.14# int → stri = 100s = str(i)print(s)  # '100'# float → strf = 3.14s = str(f)print(s)  # '3.14'# 进制转换num = 255# int → bin (二进制字符串)print(bin(num))  # '0b11111111'# int → oct (八进制字符串)print(oct(num))  # '0o377'# int → hex (十六进制字符串)print(hex(num))  # '0xff'# str → int (指定进制)print(int('11111111', 2))  # 255print(int('377', 8))       # 255print(int('ff', 16))       # 255# 格式化输出num = 42print(f'{num:b}')   # 101010 (二进制)print(f'{num:o}')   # 52 (八进制)print(f'{num:x}')   # 2a (十六进制)print(f'{num:X}')   # 2A (大写十六进制)

# 基本格式化num = 3.141592653589793# 保留小数位数print(f'{num:.2f}')  # 3.14print(f'{num:.4f}')  # 3.1416# 千位分隔符big_num = 1234567890print(f'{big_num:,}')   # 1,234,567,890print(f'{big_num:_}')   # 1_234_567_890# 百分比ratio = 0.85print(f'{ratio:.2%}')  # 85.00%# 科学计数法print(f'{big_num:.2e}')  # 1.23e+09print(f'{big_num:.2E}')  # 1.23E+09# 对齐和填充num = 42print(f'{num:>10}')   # '        42' (右对齐)print(f'{num:<10}')   # '42        ' (左对齐)print(f'{num:^10}')   # '    42    ' (居中)print(f'{num:0>10}')  # '0000000042' (填充0)# 正负号positive = 42negative = -42print(f'{positive:+}')  # '+42'print(f'{negative:+}')  # '-42'print(f'{positive: }')  # ' 42' (正数前加空格)# 组合使用price = 1234.5print(f'{price:>10,.2f}')  # '  1,234.50'

import random# 随机浮点数 [0.0, 1.0)print(random.random())  # 0.37444887175646646# 随机整数 [a, b]print(random.randint(1, 10))  # 7# 随机整数 [a, b)print(random.randrange(1, 10))  # 8# 随机浮点数 [a, b]print(random.uniform(1.0, 10.0))  # 5.234567# 从序列中随机选择choices = ['apple', 'banana', 'orange']print(random.choice(choices))  # 'banana'# 随机选择多个（可重复）print(random.choices(choices, k=3))  # ['apple', 'apple', 'orange']# 随机选择多个（不重复）print(random.sample(choices, k=2))  # ['orange', 'apple']# 打乱列表data = [1, 2, 3, 4, 5]random.shuffle(data)print(data)  # [3, 1, 5, 2, 4]# 设置随机种子（可重现）random.seed(42)print(random.random())  # 0.6394267984578837random.seed(42)print(random.random())  # 0.6394267984578837 (相同)# 高斯分布print(random.gauss(0, 1))  # -0.234567 (均值0，标准差1)

from decimal import Decimal, getcontext# 创建Decimald1 = Decimal('0.1')d2 = Decimal('0.2')# 精确计算print(d1 + d2)  # 0.3print(d1 + d2 == Decimal('0.3'))  # True# 设置精度getcontext().prec = 50  # 50位精度d = Decimal(1) / Decimal(7)print(d)  # 0.14285714285714285714285714285714285714285714285714# 金融计算price = Decimal('19.99')quantity = Decimal('3')tax_rate = Decimal('0.08')subtotal = price * quantitytax = subtotal * tax_ratetotal = subtotal + taxprint(f'小计: ${subtotal:.2f}')  # 小计: $59.97print(f'税: ${tax:.2f}')         # 税: $4.80print(f'总计: ${total:.2f}')     # 总计: $64.77# 四舍五入控制from decimal import ROUND_HALF_UP, ROUND_DOWN, ROUND_UPd = Decimal('2.5')print(d.quantize(Decimal('1'), rounding=ROUND_HALF_UP))  # 3print(d.quantize(Decimal('1'), rounding=ROUND_DOWN))     # 2print(d.quantize(Decimal('1'), rounding=ROUND_UP))       # 3

from fractions import Fraction# 创建分数f1 = Fraction(3, 4)  # 3/4f2 = Fraction(1, 2)  # 1/2print(f1)  # 3/4print(f2)  # 1/2# 从字符串创建f3 = Fraction('3/4')f4 = Fraction('0.5')# 从浮点数创建f5 = Fraction(0.5)print(f5)  # 1/2f6 = Fraction(0.1)print(f6)  # 3602879701896397/36028797018963968 (精确表示)# 运算print(f1 + f2)  # 5/4print(f1 - f2)  # 1/4print(f1 * f2)  # 3/8print(f1 / f2)  # 3/2# 自动约分f = Fraction(6, 8)print(f)  # 3/4 (自动约分)# 获取分子分母print(f.numerator)    # 3print(f.denominator)  # 4# 转换为浮点数print(float(f1))  # 0.75# 限制分母f = Fraction(3.14159)print(f.limit_denominator(100))  # 22/7 (π的近似)print(f.limit_denominator(1000)) # 355/113 (更精确的π近似)