diff --git a/doc/source/whatsnew/v1.4.0.rst b/doc/source/whatsnew/v1.4.0.rst
index e76b466ff2d87..94aed4aa295e1 100644
--- a/doc/source/whatsnew/v1.4.0.rst
+++ b/doc/source/whatsnew/v1.4.0.rst
@@ -463,6 +463,8 @@ I/O
 - Bug in unpickling a :class:`Index` with object dtype incorrectly inferring numeric dtypes (:issue:`43188`)
 - Bug in :func:`read_csv` where reading multi-header input with unequal lengths incorrectly raising uncontrolled ``IndexError`` (:issue:`43102`)
 - Bug in :func:`read_csv`, changed exception class when expecting a file path name or file-like object from ``OSError`` to ``TypeError`` (:issue:`43366`)
+- Bug in :func:`read_csv` with :code:`float_precision="round_trip"` which did not skip initial/trailing whitespace (:issue:`43713`)
+-
 
 Period
 ^^^^^^
diff --git a/pandas/_libs/src/parser/tokenizer.c b/pandas/_libs/src/parser/tokenizer.c
index 49797eea59ddc..6785bf628919a 100644
--- a/pandas/_libs/src/parser/tokenizer.c
+++ b/pandas/_libs/src/parser/tokenizer.c
@@ -1784,6 +1784,8 @@ char* _str_copy_decimal_str_c(const char *s, char **endpos, char decimal,
     size_t length = strlen(s);
     char *s_copy = malloc(length + 1);
     char *dst = s_copy;
+    // Skip leading whitespace.
+    while (isspace_ascii(*p)) p++;
     // Copy Leading sign
     if (*p == '+' || *p == '-') {
         *dst++ = *p++;
@@ -1798,10 +1800,25 @@ char* _str_copy_decimal_str_c(const char *s, char **endpos, char decimal,
        *dst++ = '.';
        p++;
     }
-    // Copy the remainder of the string as is.
-    strncpy(dst, p, length + 1 - (p - s));
+    // Copy fractional part after decimal (if any)
+    while (isdigit_ascii(*p)) {
+       *dst++ = *p++;
+    }
+    // Copy exponent if any
+    if (toupper_ascii(*p) == toupper_ascii('E')) {
+       *dst++ = *p++;
+       // Copy leading exponent sign (if any)
+       if (*p == '+' || *p == '-') {
+           *dst++ = *p++;
+       }
+       // Copy exponent digits
+       while (isdigit_ascii(*p)) {
+           *dst++ = *p++;
+       }
+    }
+    *dst++ = '\0';  // terminate
     if (endpos != NULL)
-        *endpos = (char *)(s + length);
+        *endpos = (char *)p;
     return s_copy;
 }
 
@@ -1839,6 +1856,11 @@ double round_trip(const char *p, char **q, char decimal, char sci, char tsep,
 
     PyGILState_Release(gstate);
     free(pc);
+    if (skip_trailing && q != NULL && *q != p) {
+        while (isspace_ascii(**q)) {
+            (*q)++;
+        }
+    }
     return r;
 }
 
diff --git a/pandas/tests/io/parser/dtypes/test_dtypes_basic.py b/pandas/tests/io/parser/dtypes/test_dtypes_basic.py
index ae5ddb83f7052..726cd64c6dc23 100644
--- a/pandas/tests/io/parser/dtypes/test_dtypes_basic.py
+++ b/pandas/tests/io/parser/dtypes/test_dtypes_basic.py
@@ -204,6 +204,11 @@ def test_1000_sep_decimal_float_precision(
     # test decimal and thousand sep handling in across 'float_precision'
     # parsers
     decimal_number_check(c_parser_only, numeric_decimal, thousands, float_precision)
+    text, value = numeric_decimal
+    text = " " + text + " "
+    if isinstance(value, str):  # the negative cases (parse as text)
+        value = " " + value + " "
+    decimal_number_check(c_parser_only, (text, value), thousands, float_precision)
 
 
 def decimal_number_check(parser, numeric_decimal, thousands, float_precision):
@@ -222,6 +227,24 @@ def decimal_number_check(parser, numeric_decimal, thousands, float_precision):
     assert val == numeric_decimal[1]
 
 
+@pytest.mark.parametrize("float_precision", [None, "legacy", "high", "round_trip"])
+def test_skip_whitespace(c_parser_only, float_precision):
+    DATA = """id\tnum\t
+1\t1.2 \t
+1\t 2.1\t
+2\t 1\t
+2\t 1.2 \t
+"""
+    df = c_parser_only.read_csv(
+        StringIO(DATA),
+        float_precision=float_precision,
+        sep="\t",
+        header=0,
+        dtype={1: np.float64},
+    )
+    tm.assert_series_equal(df.iloc[:, 1], pd.Series([1.2, 2.1, 1.0, 1.2], name="num"))
+
+
 def test_true_values_cast_to_bool(all_parsers):
     # GH#34655
     text = """a,b