1 in Inka khipu
× 1
A figure-eight knot in the units position.
HISTORICAL · DECIMAL KNOT POSITIONS
Inka khipu
Khipu
Decimal place values recorded with knots on cords.
Convert numbers- Place
- Andes, South America
- Period / variant
- Inka period; continuing Andean traditions
EXAMPLES
135 · Decimal knot positions
One hundred knot, three tens knots, and a five-turn long knot.
Worked example
Show 135 in Inka khipu
Read down the pendant cord from the highest decimal place to the ones position. Position gives each knot group its value.
- × 100
1 single knot gives the digit 1. In the hundreds place, 1 × 100 = 100.
- × 10
3 single knots give the digit 3. In the tens place, 3 × 10 = 30.
- × 1
A long knot with 5 turns gives 5 in the ones place. In the ones place, it contributes 5.
Check
1 × 100 + 3 × 10 + 5 = 135
Sources and notation notes
Smarthistory — The Inka khipu (Dr. Sarahh Scher) · Smithsonian — What is a khipu?
Meet the symbols
The ones position uses different knot shapes from the higher places. These tiles show both sets; the position tells you whether to count ones, tens, or hundreds.
- 0 · ones position
- 1 · ones position
- 2 · ones position
- 3 · ones position
- 4 · ones position
- 5 · ones position
- 6 · ones position
- 7 · ones position
- 8 · ones position
- 9 · ones position
- 0 · knots in a higher place
- 1 · knots in a higher place
- 2 · knots in a higher place
- 3 · knots in a higher place
- 4 · knots in a higher place
- 5 · knots in a higher place
- 6 · knots in a higher place
- 7 · knots in a higher place
- 8 · knots in a higher place
- 9 · knots in a higher place
How the symbols fit together
Read the knots on one hanging cord. Where a knot sits tells you whether it counts hundreds, tens, or ones.
- In this schematic, read from the higher positions down toward the ones position. Groups of single knots count hundreds, tens, and other higher places.
- For 135, one single knot in the hundreds position means 100.
- Three single knots in the tens position mean three tens, or 30.
- At the bottom, a long knot with five turns means 5. Add 100 + 30 + 5 = 135. A figure-eight knot means one in the ones position; an empty position means zero.
20 in Inka khipu
× 10× 1
Two single knots in the tens position; the units remain empty.
135 in Inka khipu
× 100× 10× 1
One hundred knot, three tens knots, and a five-turn long knot.
This is a labeled schematic of the common numerical convention, not a reconstruction of a complete historical khipu. Other knot conventions and non-numerical records exist.
History
Khipus are arrangements of cords and knots used for record keeping in the Andes. A well-understood class of numerical khipus records decimal values through the positions and types of knots. Cord color, attachment, and other features carry additional information that cannot be inferred from a number alone.
How to read it
Read the knots on one hanging cord. Where a knot sits tells you whether it counts hundreds, tens, or ones.
- In this schematic, read from the higher positions down toward the ones position. Groups of single knots count hundreds, tens, and other higher places.
- For 135, one single knot in the hundreds position means 100.
- Three single knots in the tens position mean three tens, or 30.
- At the bottom, a long knot with five turns means 5. Add 100 + 30 + 5 = 135. A figure-eight knot means one in the ones position; an empty position means zero.
Limits
This is a labeled schematic of the common numerical convention, not a reconstruction of a complete historical khipu. Other knot conventions and non-numerical records exist.
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