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Algarismo vs. dígito

In Portuguese, both algarismo and dígito refer to numbers from 0 to 9, but they carry different connotations. Algarismo is the traditional, mathematical term for the written symbol. Dígito is a modern term heavily influenced by technology and the English language, used for codes, passwords, and electronic inputs.

Algarismo

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This is the classic term for the written symbol representing a number. It is used in educational and mathematical contexts to describe the characters that make up a larger number (units, tens, hundreds). In Portugal, this word is strictly used when referring to the actual glyphs (0-9), whereas in Brazil, it is common in formal and school settings.
O número mil é composto por quatro algarismos.
(The number one thousand is composed of four digits.)
As crianças estão aprendendo a escrever os algarismos na escola.
(The children are learning strictly how to write the digits at school.)
Por favor, preencha o cheque com algarismos e por extenso.
(Please fill out the check with figures and in words.)
Ele tem uma letra bonita, mas os seus algarismos são difíceis de ler.
(He has nice handwriting, but his numbers are hard to read.)
Existem sistemas que não utilizam algarismos arábicos.
(There are systems that do not use Arabic numerals.)

Dígito

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Originally meaning finger (like the English word digit), this term is now standard in computing and technology. It refers to a specific place value in a sequence, such as a password, a phone number, or a verification code. In Brazil, dígito is becoming interchangeable with algarismo in daily speech, while in Portugal, it is usually reserved for technical contexts or specific identification numbers (like a check digit).
A sua senha deve conter pelo menos oito dígitos.
(Your password must contain at least eight digits.)
Qual é o dígito verificador do seu CPF?
(What is the check digit of your tax ID?)
O sistema aceita entrada de dados numéricos de dois dígitos.
(The system only accepts two-digit numeric data input.)
Eu esqueci o último dígito do telefone dele.
(I forgot the last digit of his phone number.)
Na era digital, cada dígito conta para a segurança da informação.
(In the digital age, every digit counts for information security.)

Summary

Use algarismo when discussing math, writing, or the shape of the number symbol itself (0-9). Use dígito when dealing with technology, passwords, identification codes, or electronics. While Brazil often uses dígito for everything due to English influence, Portugal maintains a clearer distinction where algarismo is for general numbers and dígito is for technical sequences.