Why is there a difference between round(x) and round(np.float64(x))?

Question

From what i understand, 2.675 and numpy.float64(2.675) are both the same number. However, round(2.675, 2) gives 2.67, while round(np.float64(2.675), 2) gives 2.68. Why does this happen?

import numpy as np
from decimal import Decimal

x = 2.675
np_x = np.float64(x)
type(x) # float
Decimal(x)    # Decimal('2.67499999999999982236431605997495353221893310546875')
Decimal(np_x) # Decimal('2.67499999999999982236431605997495353221893310546875')
x == np_x # True

# This is the bit that bothers me
round(x, 2) # 2.67
round(np_x, 2) # 2.68

# Using numpy's round gives 2.68 for both the numpy float as well as the Python built-in float...
np.round(x, 2) # 2.68
np.round(np_x, 2) # 2.68

# ... but this is because it might be converting the number to a numpy float before rounding
type(np.round(x, 2)) # numpy.float64

# Versions
# Python 3.6.8 running on 64-bit Windows 10
# Numpy 1.16.2

Answer 1

Very interesting question :) Looks like it has to do with numbers that end with a 5. Numpy rounds them by excess, but not always...

# list of incoherences between Python Numpy with round(x, 2)
for i in range(1001):
    x = i/1000
    np_x = np.float64(x)
    if round(x, 2) != round(np_x, 2):
        print(x)

# 0.005
# 0.015
# 0.025   <<< some values are missing!
# 0.065
# 0.075
# 0.085
# ...