diff --git a/rules/ast/ast.go b/rules/ast/ast.go
index 0eeb3aae4..49d1e54e9 100644
--- a/rules/ast/ast.go
+++ b/rules/ast/ast.go
@@ -637,15 +637,12 @@ func evalScalarBinop(opType BinOpType,
 	case Mul:
 		return lhs * rhs
 	case Div:
-		if rhs != 0 {
-			return lhs / rhs
-		}
-		return clientmodel.SampleValue(math.Inf(int(rhs)))
+		return lhs / rhs
 	case Mod:
 		if rhs != 0 {
 			return clientmodel.SampleValue(int(lhs) % int(rhs))
 		}
-		return clientmodel.SampleValue(math.Inf(int(rhs)))
+		return clientmodel.SampleValue(math.NaN())
 	case EQ:
 		if lhs == rhs {
 			return 1
@@ -691,15 +688,12 @@ func evalVectorBinop(opType BinOpType,
 	case Mul:
 		return lhs * rhs, true
 	case Div:
-		if rhs != 0 {
-			return lhs / rhs, true
-		}
-		return clientmodel.SampleValue(math.Inf(int(rhs))), true
+		return lhs / rhs, true
 	case Mod:
 		if rhs != 0 {
 			return clientmodel.SampleValue(int(lhs) % int(rhs)), true
 		}
-		return clientmodel.SampleValue(math.Inf(int(rhs))), true
+		return clientmodel.SampleValue(math.NaN()), true
 	case EQ:
 		if lhs == rhs {
 			return lhs, true
diff --git a/rules/rules_test.go b/rules/rules_test.go
index 14fc46161..baecc50b7 100644
--- a/rules/rules_test.go
+++ b/rules/rules_test.go
@@ -1157,6 +1157,46 @@ func TestExpressions(t *testing.T) {
 			expr:   `999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999`,
 			output: []string{`scalar: +Inf @[%v]`},
 		},
+		{
+			expr:   `1 / 0`,
+			output: []string{`scalar: +Inf @[%v]`},
+		},
+		{
+			expr:   `-1 / 0`,
+			output: []string{`scalar: -Inf @[%v]`},
+		},
+		{
+			expr:   `0 / 0`,
+			output: []string{`scalar: NaN @[%v]`},
+		},
+		{
+			expr:   `1 % 0`,
+			output: []string{`scalar: NaN @[%v]`},
+		},
+		{
+			expr: `http_requests{group="canary", instance="0", job="api-server"} / 0`,
+			output: []string{
+				`{group="canary", instance="0", job="api-server"} => +Inf @[%v]`,
+			},
+		},
+		{
+			expr: `-1 * http_requests{group="canary", instance="0", job="api-server"} / 0`,
+			output: []string{
+				`{group="canary", instance="0", job="api-server"} => -Inf @[%v]`,
+			},
+		},
+		{
+			expr: `0 * http_requests{group="canary", instance="0", job="api-server"} / 0`,
+			output: []string{
+				`{group="canary", instance="0", job="api-server"} => NaN @[%v]`,
+			},
+		},
+		{
+			expr: `0 * http_requests{group="canary", instance="0", job="api-server"} % 0`,
+			output: []string{
+				`{group="canary", instance="0", job="api-server"} => NaN @[%v]`,
+			},
+		},
 	}
 
 	storage, closer := newTestStorage(t)