If you want another example, try counting to 10 in hex (base 16).
Also, base 10 is always base 10, but “10” in base 2 is 2 in all counting systems above base 2 (since base 2 doesn’t actually include 2, just like base 10 doesn’t include “A”). Likewise, 10 in base 10 represented in base 2 would be 1010. ;)
If you want another example, try counting to 10 in hex (base 16).
Also, base 10 is always base 10, but “10” in base 2 is 2 in all counting systems above base 2 (since base 2 doesn’t actually include 2, just like base 10 doesn’t include “A”). Likewise, 10 in base 10 represented in base 2 would be 1010. ;)