Converting float4 to numeric in PostgreSQL is rounding the values
The Postgres manual (quoted below) does a good job of explaining some of the rounding issues you might have using floating-point types.
With that in mind, and if we simply accept that the least significant digits of any floating-point type are merely approximate, you have a couple of options for conversion including all the approximated low-precision digits. I've used float4/float8 to keep consistency with your question but we could equally use real/float.:


select '0.0199999996'::float4;


| float4 |
| :----- |
| 0.02   |




select '0.0199999996'::float4::numeric;


| numeric |
| ------: |
|    0.02 |




select '0.0199999996'::float4::float8::numeric;


|            numeric |
| -----------------: |
| 0.0199999995529652 |




select '0.0199999996'::float4::text::numeric;


| numeric |
| ------: |
|    0.02 |




set extra_float_digits = 3;
select '0.0199999996'::float4::text::numeric;


|      numeric |
| -----------: |
| 0.0199999996 |


db&lt;&gt;fiddle here


8.1.3. Floating-Point Types
The data types real and double precision are inexact, variable-precision numeric types. In practice, these types are usually implementations of IEEE Standard 754 for Binary Floating-Point Arithmetic (single and double precision, respectively), to the extent that the underlying processor, operating system, and compiler support it.
Inexact means that some values cannot be converted exactly to the internal format and are stored as approximations, so that storing and retrieving a value might show slight discrepancies. Managing these errors and how they propagate through calculations is the subject of an entire branch of mathematics and computer science and will not be discussed here, except for the following points:

If you require exact storage and calculations (such as for monetary amounts), use the numeric type instead.

If you want to do complicated calculations with these types for anything important, especially if you rely on certain behavior in boundary cases (infinity, underflow), you should evaluate the implementation carefully.

Comparing two floating-point values for equality might not always work as expected.