Here's a simpler, and probably faster, approach:

(df[col] % 1  == 0).all()

To ignore nulls:

(df[col].fillna(-9999) % 1  == 0).all()

You can use np.issubdtype to check if the dtype is a sub dtype of np.number. Examples:

np.issubdtype(arr.dtype, np.number)  # where arr is a numpy array
np.issubdtype(df['X'].dtype, np.number)  # where df['X'] is a pandas Series

This works for numpy's dtypes but fails for pandas specific types like pd.Categorical as Thomas noted. If you are using categoricals is_numeric_dtype function from pandas is a better alternative than np.issubdtype.

df = pd.DataFrame({'A': [1, 2, 3], 'B': [1.0, 2.0, 3.0], 
                   'C': [1j, 2j, 3j], 'D': ['a', 'b', 'c']})
df
Out: 
   A    B   C  D
0  1  1.0  1j  a
1  2  2.0  2j  b
2  3  3.0  3j  c

df.dtypes
Out: 
A         int64
B       float64
C    complex128
D        object
dtype: object

np.issubdtype(df['A'].dtype, np.number)
Out: True

np.issubdtype(df['B'].dtype, np.number)
Out: True

np.issubdtype(df['C'].dtype, np.number)
Out: True

np.issubdtype(df['D'].dtype, np.number)
Out: False

For multiple columns you can use np.vectorize:

is_number = np.vectorize(lambda x: np.issubdtype(x, np.number))
is_number(df.dtypes)
Out: array([ True,  True,  True, False], dtype=bool)

And for selection, pandas now has select_dtypes:

df.select_dtypes(include=[np.number])
Out: 
   A    B   C
0  1  1.0  1j
1  2  2.0  2j
2  3  3.0  3j

You can use the dtypes attribute and loc.

df.loc[:, df.dtypes <= np.integer] *= 10

Explanation
pd.DataFrame.dtypes returns a pd.Series of numpy dtype objects. We can use the comparison operators to determine subdtype status. See this document for the numpy.dtype hierarchy.

Demo

Consider the dataframe df

df = pd.DataFrame([
    [1, 2, 3, 4, 5, 6],
    [1, 2, 3, 4, 5, 6]
]).astype(pd.Series([np.int32, np.int16, np.int64, float, object, str]))

df

   0  1  2    3  4  5
0  1  2  3  4.0  5  6
1  1  2  3  4.0  5  6

The dtypes are

df.dtypes

0      int32
1      int16
2      int64
3    float64
4     object
5     object
dtype: object

We'd like to change columns 0, 1, and 2
Conveniently

df.dtypes <= np.integer

0     True
1     True
2     True
3    False
4    False
5    False
dtype: bool

And that is what enables us to use this within a loc assignment.

df.loc[:, df.dtypes <= np.integer] *= 10

df

    0   1   2    3  4  5
0  10  20  30  4.0  5  6
1  10  20  30  4.0  5  6

You can draw a True / False comparison using isnumeric()

Example:

 >>> df
       A      B
0      1      1
1    NaN      6
2    NaN    NaN
3      2      2
4    NaN    NaN
5      4      4
6   some   some
7  value  other

Results:

>>> df.A.str.isnumeric()
0     True
1      NaN
2      NaN
3     True
4      NaN
5     True
6    False
7    False
Name: A, dtype: object

# df.B.str.isnumeric()

with apply() method which seems more robust in case you need corner to corner comparison:

DataFrame having two different columns one with mixed type another with numbers only for test:

>>> df
       A   B
0      1   1
1    NaN   6
2    NaN  33
3      2   2
4    NaN  22
5      4   4
6   some  66
7  value  11

Result:

>>> df.apply(lambda x: x.str.isnumeric())
       A     B
0   True  True
1    NaN  True
2    NaN  True
3   True  True
4    NaN  True
5   True  True
6  False  True
7  False  True

Another example:

Let's consider the below dataframe with different data-types as follows..

>>> df
   num  rating    name  age
0    0    80.0  shakir   33
1    1   -22.0   rafiq   37
2    2   -10.0     dev   36
3  num     1.0   suraj   30

Based on the comment from OP on this answer, where it has negative value and 0's in it.

1- This is a pseudo-internal method to return only the numeric type data.

>>> df._get_numeric_data()
   rating  age
0    80.0   33
1   -22.0   37
2   -10.0   36
3     1.0   30

OR

2- there is an option to use method select_dtypes in module pandas.core.frame which return a subset of the DataFrame's columns based on the column dtypes. One can use Parameters with include, exclude options.

>>> df.select_dtypes(include=['int64','float64']) # choosing int & float
   rating  age
0    80.0   33
1   -22.0   37
2   -10.0   36
3     1.0   30

>>> df.select_dtypes(include=['int64'])  # choose int
   age
0   33
1   37
2   36
3   30