diff --git a/hledger-lib/Hledger/Data/Transaction.hs b/hledger-lib/Hledger/Data/Transaction.hs
index 111f24eb8..cbad985d8 100644
--- a/hledger-lib/Hledger/Data/Transaction.hs
+++ b/hledger-lib/Hledger/Data/Transaction.hs
@@ -375,7 +375,8 @@ transactionInferCostsFromEquity dryrun acctTypes t = first (annotateErrorWithTra
         Just Amount{aprice=Just _} -> Left $ annotateWithPostings [p] "Conversion postings must not have a cost:"
         Nothing                    -> Left $ annotateWithPostings [p] "Conversion postings must have a single-commodity amount:"
 
-    amountMatches a b = acommodity a == acommodity b && aquantity a == aquantity b
+    -- Do these amounts look the same when compared at the first's display precision ?
+    amountsMatch a b = amountLooksZero $ amountSetPrecision (asprecision $ astyle a) $ a - b
 
     -- Delete a posting from the indexed list of postings based on either its
     -- index or its posting amount.
diff --git a/hledger/hledger.m4.md b/hledger/hledger.m4.md
index 0a395f375..2f392c256 100644
--- a/hledger/hledger.m4.md
+++ b/hledger/hledger.m4.md
@@ -4938,6 +4938,7 @@ The forecast period ends on:
 - otherwise: 180 days (~6 months) from today.
 
 ## Forecast troubleshooting
+
 When --forecast is not doing what you expect, one of these tips should help:
 
 - Remember to use the `--forecast` option.
@@ -4963,7 +4964,6 @@ You can generate budget goals and forecast transactions at the same time, from t
 
 See also: [Budgeting and Forecasting](/budgeting-and-forecasting.html).
 
-
 # Cost reporting
 
 In some transactions - for example a currency conversion, or a purchase or sale of stock - one commodity is exchanged for another.
@@ -5144,7 +5144,6 @@ Downsides:
 
 - The precise format of the journal entry becomes more important.
   If hledger can't detect and match up the cost and equity postings, it will give a transaction balancing error.
-  Amounts with repeating decimals are one of the things that can cause this ([#2051](https://github.com/simonmichael/hledger/issues/2051)).
 
 - The [add](#add) command does not yet accept this kind of entry ([#2056](https://github.com/simonmichael/hledger/issues/2056)).
 
@@ -5158,8 +5157,8 @@ It will infer costs only in transactions with:
 - Two non-equity postings, in different commodities.
   Their order is significant: the cost will be added to the first of them.
 
-- Two postings to equity conversion accounts, next to one another, which balance the two non-equity postings exactly.
-  (Perhaps over-exactly, as this is currently not limited by display precision - see #2051.)
+- Two postings to equity conversion accounts, next to one another, which balance the two non-equity postings.
+  This balancing is checked to the same precision (number of decimal places) used in the conversion posting's amount.
   Equity conversion accounts are:
 
   - any accounts declared with account type `V`/`Conversion`, or their subaccounts
diff --git a/hledger/test/journal/costs.test b/hledger/test/journal/costs.test
index e9f9ffa8a..4cd6cea19 100644
--- a/hledger/test/journal/costs.test
+++ b/hledger/test/journal/costs.test
@@ -605,23 +605,22 @@ $ hledger -f- print --infer-costs
 
 >=0
 
-# # when the *cost-basis* balance has exactly two commodities, both cost-less,
-# # infer a balancing cost for the first one in terms of the second.
-# hledger -f - print
-# <<<
-# 2011/01/01
-#     expenses:foreign currency       €100
-#     assets                         $-135.00
-#     misc                              $3.1 @ 2 bob
-#     misc                             $-3.1 @ 2 bob
-#     misc                              £1 @@ 2 shekels
-#     misc                             £-1 @@ 2 shekels
-# >>>
-# 2011/01/01
-#     expenses:foreign currency   €100 @ $1.35
-#     assets                     €-100 @ $1.35
-#     misc                        $3.1 @ 2 bob
-#     misc                       $-3.1 @ 2 bob
-#     misc                          £1 @@ 2 shekels
-#     misc                         £-1 @@ 2 shekels
-#
+# 41. Matching costful postings and conversion postings is done at the precision
+# of the conversion posting, tolerating smaller decimal differences (#2041).
+# Here 84.01 * 2.495 GEL is 209.60495 GEL, which is considered to match 209.60 GEL
+# because we use the latter's 2 digit precision.
+<
+2023/05/17 * Transfer
+    Assets:BOG:Personal                          -84.01 USD @ 2.495 GEL
+    Equity:Conversion                             84.01 USD
+    Equity:Conversion                           -209.60 GEL
+    Assets:BOG:Personal                          209.60 GEL
+
+$ hledger -f- print
+2023-05-17 * Transfer
+    Assets:BOG:Personal    -84.01 USD @ 2.495 GEL
+    Equity:Conversion                   84.01 USD
+    Equity:Conversion                 -209.60 GEL
+    Assets:BOG:Personal                209.60 GEL
+
+>=