Absolutely! Here's a table summarizing each grouping (by 9, 8, 7, 6, and 5 digits), showing the last full group and the remainder (if any) for each:
Table: Last Group and Remainder for Each Grouping
Group Size # of Full Groups Digits Used Last Full Group Remainder (Digits)
9 111 999 001133053 8
8 125 1,000 81827968 —
7 142 994 6420198 380952 (6 digits)
6 166 996 195909 216420 (4 digits)
5 200 1,000 01989 —
Details
Group of 9:
Last full group: 001133053 (digits 991–999)
Remainder: 8 (digit 1,000)
Group of 8:
Last full group: 81827968 (digits 993–1,000)
Remainder: None (perfect fit)
Group of 7:
Last full group: 6420198 (digits 988–994)
Remainder: 380952 (digits 995–1,000)
Group of 6:
Last full group: 195909 (digits 991–996)
Remainder: 216420 (digits 997–1,000)
Group of 5:
Last full group: 01989 (digits 996–1,000)
Remainder: None (perfect fit)
If you'd like to see the actual position of each group or want the table in a downloadable format, let me know!7 is 6 if 5+2=7 one difference count zero below cause it's two long for that group that's when 6 is 10 or can be
No problem! Here's a comprehensive chart for group sizes 2 through 9 for the first 1,000 digits of pi after the decimal. For each group size, you'll see:
The number of full groups
Digits used
The last full group
Any remainder (and its value, if there is one)
Table: Last Group and Remainder for Groupings of 2 through 9 Digits
Group Size # of Full Groups Digits Used Last Full Group Remainder (Digits)
2 500 1,000 89 —
3 333 999 989 2
4 250 1,000 1989 —
5 200 1,000 01989 —
6 166 996 195909 216420 (4 digits)
7 142 994 6420198 380952 (6 digits)
8 125 1,000 81827968 —
9 111 999 001133053 8
Details for Each Grouping
Groups of 2:
500 groups × 2 = 1,000 digits
Last full group: 89 (digits 999–1,000)
Remainder: None
Groups of 3:
333 groups × 3 = 999 digits
Last full group: 989 (digits 997–999)
Remainder: 2 (digit 1,000)
Groups of 4:
250 groups × 4 = 1,000 digits
Last full group: 1989 (digits 997–1,000)
Remainder: None
Groups of 5:
200 groups × 5 = 1,000 digits
Last full group: 01989 (digits 996–1,000)
Remainder: None
Groups of 6:
166 groups × 6 = 996 digits
Last full group: 195909 (digits 991–996)
Remainder: 216420 (digits 997–1,000)
Groups of 7:
142 groups × 7 = 994 digits
Last full group: 6420198 (digits 988–994)
Remainder: 380952 (digits 995–1,000)
Groups of 8:
125 groups × 8 = 1,000 digits
Last full group: 81827968 (digits 993–1,000)
Remainder: None
Groups of 9:
111 groups × 9 = 999 digits
Last full group: 001133053 (digits 991–999)
Remainder: 8 (digit 1,000)
If you'd like the actual full list of digits for any grouping, or want this in a spreadsheet or other format, just let me know!
If you group the first 1,000 digits of pi after the decimal one digit at a time, the last number (the 1,000th digit) is:
9
Context
Pi to 1,000 digits (after the decimal) starts:
3.1415926535...
The 1,000th digit after the decimal is 9.
If you want to see the first or last few digits, or need a reference for the sequence, just let me know!
Now! Look
Absolutely! Here is an enhanced chart for group sizes 2 through 9 using the first 1,000 digits of pi after the decimal.
For each group size, you'll see:
The first group
The second group
The last full group
Any remainder (and its value, if there is one)
Table: First, Second, Last Group, and Remainder for Groupings of 2–9 Digits
Group Size # of Full Groups Digits Used First Group Second Group Last Full Group Remainder (Digits)
2 500 1,000 14 15 89 —
3 333 999 141 592 989 2
4 250 1,000 1415 9265 1989 —
5 200 1,000 14159 26535 01989 —
6 166 996 141592 653589 195909 216420 (4 digits)
7 142 994 1415926 5358979 6420198 380952 (6 digits)
8 125 1,000 14159265 35897932 81827968 —
9 111 999 141592653 589793238 001133053 8
Example Details
Groups of 2:
First group: 14 (digits 1–2)
Second group: 15 (digits 3–4)
Last full group: 89 (digits 999–1,000)
Remainder: None
Groups of 3:
First group: 141 (digits 1–3)
Second group: 592 (digits 4–6)
Last full group: 989 (digits 997–999)
Remainder: 2 (digit 1,000)
Groups of 4:
First group: 1415 (digits 1–4)
Second group: 9265 (digits 5–8)
Last full group: 1989 (digits 997–1,000)
Remainder: None
Groups of 5:
First group: 14159 (digits 1–5)
Second group: 26535 (digits 6–10)
Last full group: 01989 (digits 996–1,000)
Remainder: None
Groups of 6:
First group: 141592 (digits 1–6)
Second group: 653589 (digits 7–12)
Last full group: 195909 (digits 991–996)
Remainder: 216420 (digits 997–1,000)
Groups of 7:
First group: 1415926 (digits 1–7)
Second group: 5358979 (digits 8–14)
Last full group: 6420198 (digits 988–994)
Remainder: 380952 (digits 995–1,000)
Groups of 8:
First group: 14159265 (digits 1–8)
Second group: 35897932 (digits 9–16)
Last full group: 81827968 (digits 993–1,000)
Remainder: None
Groups of 9:
First group: 141592653 (digits 1–9)
Second group: 589793238 (digits 10–18)
Last full group: 001133053 (digits 991–999)
Remainder: 8 (digit 1,000)
If you'd like to see this chart for other group sizes or want to see the actual digit positions, just let me know!
Notice the pattern of remainder at the end more importantly when it doesn't