Table:
|  |  | December 31, |  |
| --- | --- | --- | --- |
|  | 2019 | 2018 | 2017 |
| Gross unrecognized tax benefits at beginning of year | $490 | $220 | $293 |
| Increases in tax positions for prior years | 7,718 | 36 | — |
| Increases in tax positions for current year | 1,839 | 320 | 32 |
| Decreases in tax positions for prior years | (412) | — | — |
| Lapse in statute of limitations | — | (86) | (105) |
| Gross unrecognized tax benefits at end of year | $9,635 | $490 | $220 |
Paragraphs:
A reconciliation of the beginning and ending balances of the total amounts of gross unrecognized tax benefits is as follows (in thousands):
The total liability for gross unrecognized tax benefits as of December 31, 2019, 2018 and 2017 includes $9.6 million, $0.4 million and $0.2 million, respectively, of unrecognized net tax benefits which, if ultimately recognized, would reduce our annual effective tax rate in a future period. These liabilities, along with liabilities for interest and penalties, are included in accounts payable and accrued expenses and Other long-term liabilities in our consolidated balance sheet. Interest, which is included in Interest expense in our consolidated statement of income, was not material for all years presented.
During the year ended December 31, 2019, we recognized an increase in unrecognized tax benefits of approximately $7.7 million related to an increase in research and development tax credits available to us for tax years 2016-2018 and $1.8 million for the 2019 tax year.
We are subject to income taxes in the U.S., various state and foreign jurisdictions. Tax statutes and regulations within each jurisdiction are subject to interpretation and require significant judgment to apply. We are no longer subject to U.S. federal or non-U.S. income tax examinations by tax authorities for the years before 2015. We are no longer subject to U.S. state tax examinations by tax authorities for the years before 2014. We believe it is reasonably possible that within the next year our unrecognized tax benefits may decrease by $1.9 million due to the acceptance of a portion of our amended research and development credits.
Question:
What is the proportion of the total increase in tax positions for the prior and current years over gross unrecognized tax benefits at the end of the year 2019?
Answer: (7718+1839)/9635 = 0.99