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🔢 Number Base Lab

What if you group things
differently, not by 10s?

We usually count by grouping things into 10s (base 10), but you can represent numbers just as well by grouping into 2s, 3s, or 5s. Try grouping items yourself below!

Group 18 items into 5s and you get 3 groups with 3 left over. In base 5, this is written as 33 — the left 3 means "3 groups of five," and the right 3 means "3 leftover ones." 18 in base 10 and 33 in base 5 are just written differently; they represent the exact same count. We're just used to base 10 because we have 10 fingers — grouping by any other number works just as well.

Among the number bases, base 2 is especially important. A computer's internal circuits can only reliably tell electricity "on" from "off" — two states — so computers represent every number using only 0 and 1, in base 2.

Change the number of stars with the slider, and see for yourself how many groups are left over, and how each digit comes together, when you group by base 2, base 3, base 5, and base 10.

18
Change the number of stars (0–24)
🎉 Connect the place-digits in order and

🔢 Number Base Quiz

Question 1/3 · Correct 0