display.precision not honored for float values in an object index

[simonjayhawkins]

see also #17280, #25917

Code Sample, a copy-pastable example if possible

import pandas as pd
float_val = 0.55555555
df = pd.DataFrame([float_val, 'foo'], index=[float_val, 'foo'])
pd.set_option('display.precision', 3)
df

	0
0.55555555	0.556
foo	foo

Problem description

the float valued index values are not displayed with a precision of 3. The expected behavior is observed with a Float64Index when all index values are floats.

Expected Output

	0
0.556	0.556
foo	foo

Output of pd.show_versions()

INSTALLED VERSIONS

commit: None
python: 3.7.2.final.0
python-bits: 64
OS: Windows
OS-release: 10
machine: AMD64
processor: Intel64 Family 6 Model 58 Stepping 9, GenuineIntel
byteorder: little
LC_ALL: None
LANG: None
LOCALE: None.None

pandas: 0.25.0.dev0+332.g96a128eaa
pytest: 4.3.0
pip: 19.0.3
setuptools: 40.6.3
Cython: 0.29.5
numpy: 1.16.2
scipy: 1.2.1
pyarrow: 0.11.1
xarray: 0.11.3
IPython: 7.3.0
sphinx: 1.8.4
patsy: 0.5.1
dateutil: 2.8.0
pytz: 2018.9
blosc: None
bottleneck: 1.2.1
tables: 3.4.4
numexpr: 2.6.9
feather: None
matplotlib: 3.0.2
openpyxl: 2.6.0
xlrd: 1.2.0
xlwt: 1.3.0
xlsxwriter: 1.1.5
lxml.etree: 4.3.1
bs4: 4.7.1
html5lib: 1.0.1
sqlalchemy: 1.2.18
pymysql: None
psycopg2: None
jinja2: 2.10
s3fs: 0.2.0
fastparquet: 0.2.1
pandas_gbq: None
pandas_datareader: None
gcsfs: None

[simonjayhawkins]

see also #13021