PHP, 26 Bytes

<?=-~log10(abs($argn?:1));

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log of base 10 of the absolute value plus one cast to int

for zero as input use one to calculate

PHP, 27 Bytes

<?=strlen($argn)-($argn<0);

string length minus boolean is lower then zero

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PHP, 32 Bytes

<?=preg_match_all("#\d#",$argn);

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Regex count all digits

35 Bytes

<?=strlen($argn)-strspn($argn,"-");

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string length minus count -

strspn

PHP, 23 Bytes

<?=-~log10(abs($argn));

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log of base 10 of the absolute value plus one cast to int

for zero as input log10 gives back INF which is interpreted as false

The better way is to replace $argn with $argn?:1 +3 Bytes

PHP, 27 Bytes

<?=strlen($argn)-($argn<0);

string length minus boolean is lower then zero

+2 Bytes for string comparision $argn<"0"

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PHP, 32 Bytes

<?=preg_match_all("#\d#",$argn);

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Regex count all digits

35 Bytes

<?=strlen($argn)-strspn($argn,"-");

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string length minus count -

strspn

PHP, 27 Bytes

<?=strlen($argn)-($argn<0);

string length minus boolean is lower then zero

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PHP, 28 Bytes

<?=log10(abs($argn?:1))+1^0;

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log of base 10 of the absolute value plus one cast to int

for zero as input use one to calculate

PHP, 32 Bytes

<?=preg_match_all("#\d#",$argn);

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Regex count all digits

35 Bytes

<?=strlen($argn)-strspn($argn,"-");

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string length minus count -

strspn

PHP, 26 Bytes

<?=-~log10(abs($argn?:1));

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log of base 10 of the absolute value plus one cast to int

for zero as input use one to calculate

PHP, 27 Bytes

<?=strlen($argn)-($argn<0);

string length minus boolean is lower then zero

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PHP, 32 Bytes

<?=preg_match_all("#\d#",$argn);

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Regex count all digits

35 Bytes

<?=strlen($argn)-strspn($argn,"-");

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string length minus count -

strspn

PHP, 28 Bytes

<?=log10(abs($argn?:1))+1^0;

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log of base 10 of the absolute value plus one cast to int

for zero as input use one to calculate

PHP, 29 Bytes

<?=strlen($argn)-($argn<"0");

string length minus boolean string is lower then string "0"

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PHP, 32 Bytes

<?=preg_match_all("#\d#",$argn);

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Regex count all digits

35 Bytes

<?=strlen($argn)-strspn($argn,"-");

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string length minus count -

strspn

PHP, 27 Bytes

<?=strlen($argn)-($argn<0);

string length minus boolean is lower then zero

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PHP, 28 Bytes

<?=log10(abs($argn?:1))+1^0;

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log of base 10 of the absolute value plus one cast to int

for zero as input use one to calculate

PHP, 32 Bytes

<?=preg_match_all("#\d#",$argn);

Try it online!

Regex count all digits

35 Bytes

<?=strlen($argn)-strspn($argn,"-");

Try it online!

string length minus count -

strspn