7 in Chinese counting rods
× 1
The unit-form seven combines a five-bar and two unit rods.
HISTORICAL · BASE 10
Chinese counting rods
算筹
Decimal place values represented by counting rods. Rod orientation alternates between adjacent positions.
Convert numbers- Place
- China · later used across East Asia
- Period / variant
- Song-dynasty orientation convention · 960–1279 CE
EXAMPLES
6708 · Base 10
6 × 1000 + 7 × 100 + an empty tens cell + 8. Alternating forms distinguish places.
Worked example
Show 6708 in Chinese counting rods
Place the rod groups in decimal columns. From right to left the columns count ones, tens, hundreds, and so on; adjacent columns alternate orientations.
- × 1000
A horizontal five-bar and 1 vertical unit rod give 5 + 1 = 6. In the thousands place, 6 × 1,000 = 6,000.
- × 100
A vertical five-bar and 2 horizontal unit rods give 5 + 2 = 7. In the hundreds place, 7 × 100 = 700.
- × 10
Leave this board cell empty for zero. Keep the empty tens place so the other groups retain their values.
- × 1
A vertical five-bar and 3 horizontal unit rods give 5 + 3 = 8. In the ones place, it contributes 8.
Check
6 × 1,000 + 7 × 100 + 0 × 10 + 8 = 6,708
Sources and notation notes
The Unicode Standard 17.0, chapter 22 · Unicode Counting Rod Numerals character chart
Meet the symbols
Each tile shows a sign and what it means. A sign can stand for a whole amount, such as 10 or 100.
- 0 · empty place
- 1 · ones / hundreds form
- 2 · ones / hundreds form
- 3 · ones / hundreds form
- 4 · ones / hundreds form
- 5 · ones / hundreds form
- 6 · ones / hundreds form
- 7 · ones / hundreds form
- 8 · ones / hundreds form
- 9 · ones / hundreds form
- 1 · tens / thousands form
- 2 · tens / thousands form
- 3 · tens / thousands form
- 4 · tens / thousands form
- 5 · tens / thousands form
- 6 · tens / thousands form
- 7 · tens / thousands form
- 8 · tens / thousands form
- 9 · tens / thousands form
How the symbols fit together
Read the rod groups by their positions. Alternating rod directions helps keep neighboring digits separate.
- First read a digit’s shape: the five-bar contributes five, and the extra rods add ones. A five-bar with two extra rods is 7.
- The rightmost position counts ones, then tens, hundreds, and thousands as you move left. Ones and hundreds use one rod orientation; tens and thousands use the other.
- For 42, the 4 in the tens position means 40. The 2 in the ones position means 2. Add 40 + 2 = 42.
- For 6,708, read six thousands, seven hundreds, a blank tens position, and eight ones: 6,000 + 700 + 0 + 8. The blank represents zero; the cells and labels are teaching aids.
42 in Chinese counting rods
× 10× 1
Four in the tens orientation, then two in the units orientation.
6708 in Chinese counting rods
× 1000× 100× 10× 1
6 × 1000 + 7 × 100 + an empty tens cell + 8. Alternating forms distinguish places.
A blank cell is intentional. Our separated cells and place labels are a modern teaching aid, not additional historical signs. The overall zero is shown as an empty board cell. Negative-rod color conventions and fractional board layouts are outside this adapter.
History
Counting rods were arranged on a board to perform mathematics. The app adopts the Song-period forms used in Unicode’s chart; earlier Han texts can exchange the orientations.
How to read it
Read the rod groups by their positions. Alternating rod directions helps keep neighboring digits separate.
- First read a digit’s shape: the five-bar contributes five, and the extra rods add ones. A five-bar with two extra rods is 7.
- The rightmost position counts ones, then tens, hundreds, and thousands as you move left. Ones and hundreds use one rod orientation; tens and thousands use the other.
- For 42, the 4 in the tens position means 40. The 2 in the ones position means 2. Add 40 + 2 = 42.
- For 6,708, read six thousands, seven hundreds, a blank tens position, and eight ones: 6,000 + 700 + 0 + 8. The blank represents zero; the cells and labels are teaching aids.
Limits
A blank cell is intentional. Our separated cells and place labels are a modern teaching aid, not additional historical signs. The overall zero is shown as an empty board cell. Negative-rod color conventions and fractional board layouts are outside this adapter.
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