Reading ١٠١٣ correctly
The leftmost symbol represents the highest place and the rightmost symbol the ones place. Keep this order when inserting ١٠١٣ into an Arabic sentence; do not reverse the characters to match the surrounding text direction.
There is one zero in 1013. Each stays in its original position in ١٠١٣, including any zeros between nonzero digits.
On a year label, 1013 becomes ١٠١٣. This changes the written digits, not the calendar: it is not a Gregorian-to-Hijri date calculation.
Method and sources
Number Digit maps each digit as text: Western 0–9 to Arabic-Indic U+0660–U+0669 or extended Arabic-Indic U+06F0–U+06F9. This preserves digit order without rounding large integers. It does not translate number words or convert calendars. With Arabic punctuation selected, recognized decimal, grouping and percent marks are replaced too; this is not automatic detection of your country's number format.
Persian and Urdu share extended Arabic-Indic code points, but fonts and language settings can give some characters different shapes. A character's Unicode code is a more reliable identifier than its appearance alone.