Python 3.7.0 (default, Aug 22 2018, 20:50:05) 
[GCC 5.4.0 20160609] on linux
Type "help", "copyright", "credits" or "license" for more information.
>>> round(0.95,1)
0.9
>>> round(0.95)
1
>>> round(0.96,1)
1.0

0.95 is actually 278419646001971/4503599627370496 which is smaller than 95/100.

>>> from fractions import Fraction
>>> Fraction(0.95)
Fraction(4278419646001971, 4503599627370496)
>>> Fraction(0.95) - Fraction(95, 100)
Fraction(-1, 22517998136852480)

It is closer to 0.9 than to 1.0.

>>> Fraction(0.95) - Fraction(0.9)
Fraction(450359962737049, 9007199254740992)
>>> Fraction(1) - Fraction(0.95)
Fraction(225179981368525, 4503599627370496)
>>> (Fraction(1) - Fraction(0.95)) - (Fraction(0.95) - Fraction(0.9))
Fraction(1, 9007199254740992)

What Serhiy said. round is behaving as intended and as designed here.

Note: you can also see the actual value of a float object easily by using Decimal:

    >>> from decimal import Decimal
    >>> Decimal(0.95)
    Decimal('0.9499999999999999555910790149937383830547332763671875')

... which demonstrates clearly that the value being rounded is closer to 0.9 than to 1.0.

Possibly even easier than using Decimal:

py> '%.17f' % 0.95
'0.94999999999999996'

BTW, this is a FAQ:

https://docs.python.org/3/faq/design.html#why-are-floating-point-calculations-so-inaccurate

[Steven]

py> '%.17f' % 0.95
'0.94999999999999996'

That's tricky to use correctly: it's not a priori clear how many digits after the point are needed to give you a faithful representation (the "17" in "%.17f" isn't going to be the right thing for most values). You really want to specify the number of significant digits rather than the number of places after the point, and even then there are going to be cases where 17 significant digits aren't enough to show you which side of a tie the exact value lies.