diff --git a/src/preset_time.jl b/src/preset_time.jl
index 3b7e3f95..df9728af 100644
--- a/src/preset_time.jl
+++ b/src/preset_time.jl
@@ -6,9 +6,9 @@ struct PresetTimeFunction{T, T2, T3}
 end
 function (f::PresetTimeFunction)(u, t, integrator)
     return if hasproperty(integrator, :dt)
-        insorted(t, f.tstops) && (integrator.t - integrator.dt) != integrator.t
+        is_preset_time(t, f.tstops) && (integrator.t - integrator.dt) != integrator.t
     else
-        insorted(t, f.tstops)
+        is_preset_time(t, f.tstops)
     end
 end
 
@@ -26,11 +26,28 @@ function (f::PresetTimeFunction)(c, u, t, integrator)
     for tstop in _tstops
         add_tstop!(integrator, tstop)
     end
-    return if insorted(t, tstops)
+    return if is_preset_time(t, tstops)
         f.user_affect!(integrator)
     end
 end
 
+function is_preset_time(t, tstops)
+    insorted(t, tstops) && return true
+    i = searchsortedfirst(tstops, t)
+    return (i <= length(tstops) && is_close_preset_time(t, tstops[i])) ||
+        (i > firstindex(tstops) && is_close_preset_time(t, tstops[i - 1]))
+end
+
+function is_close_preset_time(t, tstop)
+    _t, _tstop = promote(t, tstop)
+    if _t isa AbstractFloat && _tstop isa AbstractFloat && isfinite(_t) && isfinite(_tstop)
+        scale = max(abs(_t), abs(_tstop))
+        return abs(_t - _tstop) <= 100 * eps(scale)
+    end
+
+    return t == tstop
+end
+
 """
 ```julia
 PresetTimeCallback(tstops, user_affect!;
diff --git a/test/preset_time.jl b/test/preset_time.jl
index c88f7bee..1ec8e717 100644
--- a/test/preset_time.jl
+++ b/test/preset_time.jl
@@ -34,6 +34,18 @@ sol = integrator.sol
 @test 0.6 ∈ sol.t
 @test p != startp
 
+struct PresetTimeRoundoffIntegrator{T}
+    t::T
+    dt::T
+end
+
+roundoff_integrator = PresetTimeRoundoffIntegrator(8.999999999999996, 0.1)
+for tstops in ([2, 9], range(2, 9; length = 2), [2.0, 9.0])
+    roundoff_cb = PresetTimeCallback(tstops, integrator -> nothing)
+    @test roundoff_cb.condition(nothing, 8.999999999999996, roundoff_integrator)
+    @test !roundoff_cb.condition(nothing, 9.0 - 1.0e-10, roundoff_integrator)
+end
+
 notcalled = true
 prob = ODEProblem(some_dynamics, u0, tspan, p)
 cb = PresetTimeCallback([1.2], integrator -> notcalled = false)