diff --git a/libcontainer/cgroups/systemd/apply_systemd.go b/libcontainer/cgroups/systemd/apply_systemd.go
index d9d8302d..5471ebbf 100644
--- a/libcontainer/cgroups/systemd/apply_systemd.go
+++ b/libcontainer/cgroups/systemd/apply_systemd.go
@@ -271,6 +271,13 @@ func (m *Manager) Apply(pid int) error {
 	// cpu.cfs_quota_us and cpu.cfs_period_us are controlled by systemd.
 	if c.Resources.CpuQuota != 0 && c.Resources.CpuPeriod != 0 {
 		cpuQuotaPerSecUSec := uint64(c.Resources.CpuQuota*1000000) / c.Resources.CpuPeriod
+		// systemd converts CPUQuotaPerSecUSec (microseconds per CPU second) to CPUQuota
+		// (integer percentage of CPU) internally.  This means that if a fractional percent of
+		// CPU is indicated by Resources.CpuQuota, we need to round up to the nearest
+		// 10ms (1% of a second) such that child cgroups can set the cpu.cfs_quota_us they expect.
+		if cpuQuotaPerSecUSec%10000 != 0 {
+			cpuQuotaPerSecUSec = ((cpuQuotaPerSecUSec / 10000) + 1) * 10000
+		}
 		properties = append(properties,
 			newProp("CPUQuotaPerSecUSec", cpuQuotaPerSecUSec))
 	}