der Zähler
meter
A device that measures the consumption of something, for example electricity, water, or gas.
Einmal im Jahr muss der Zähler für den Strom abgelesen werden.
Once a year, the electricity meter has to be read.

meter / numerator / counter
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meter
A device that measures the consumption of something, for example electricity, water, or gas.
Einmal im Jahr muss der Zähler für den Strom abgelesen werden.
Once a year, the electricity meter has to be read.

The noun 'der Zähler' (meter/numerator/counter) is derived from the verb 'zählen' (to count). The ending '-er' refers to a person or device that performs the action of counting. This principle applies to all meanings.
Bitte zähle, wie viele Stühle im Raum stehen.
Please count how many chairs are in the room.
You can recognize the meaning of 'Zähler' from the context. If it is about 'Strom' (electricity), 'Wasser' (water), or 'Gas' (gas), it means the measuring device. In the context of 'Bruch' (fraction) and 'Nenner' (denominator), it is about mathematics. With 'Punkten' (points) or 'Besuchern' (visitors), it means a counter.
Der Zähler im Keller misst unseren Wasserverbrauch.
The meter in the basement measures our water consumption.
When referring to the measuring device, the most common and important action is 'Ablesen' (reading) the meter. This usually happens in order to determine consumption.
Ein Mitarbeiter kommt einmal im Jahr, um den Gaszähler abzulesen.
An employee comes once a year to read the gas meter.
'Zähler' (meter/counter) is a very productive base word for compound nouns. Examples are 'Stromzähler' (electricity meter), 'Wasserzähler' (water meter), 'Gaszähler' (gas meter), 'Kilometerzähler' (odometer), or 'Besucherzähler' (visitor counter).
Der Kilometerzähler meines Autos ist kaputt.
The odometer in my car is broken.
denominator
'der Zähler' and 'der Nenner' both belong to a fraction in mathematics. However, they are in different positions and have different functions. The numerator, 'Zähler', is above the fraction bar and says how many parts are meant. The denominator, 'Nenner', is below the fraction bar and says into how many equal parts the whole has been divided. Learners can easily confuse the words because they always occur together. A simple orientation is: the 'Zähler' is on top, the 'Nenner' is on the bottom.

Bei dem Bruch drei Viertel ist die Drei der Zähler.
In the fraction three quarters, the three is the numerator.
Wenn der Nenner vier ist, wurde das Ganze in vier gleiche Teile geteilt.
If the denominator is four, the whole has been divided into four equal parts.