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Prepositions after verbs

Denote by, as, in, or to

Denote usually takes a direct object. By is common in passive expressions such as denoted by. As, in, and to often have different grammatical roles.

Quick answer

Which prepositions are used with denote?

Denote commonly appears without a preposition or in passive forms with by. As, in, and to usually introduce roles, context, or direction rather than fixed combinations with denote.

In this diagram, X is denoted by a red circle.
The symbol denotes temperature.
Changes were denoted in the final report.

Choose the pattern by meaning

These forms are not interchangeable. Choose the construction by meaning, not by which preposition appears most often.

1
denote + meaning/object

Expressing meaning or reference

Denote usually takes a direct object showing what a sign or word means.

The abbreviation denotes a chemical compound.
Blue denotes calmness in the chart.
2
denoted by + symbol/sign

Identifying symbols in passive form

Use denoted by to identify the sign, letter, or symbol representing something.

Velocity is denoted by the letter v.
The missing values are denoted by an asterisk.
3
denote as + role/name

Using as after the object

As can introduce a role or description after the object of denote.

The report denotes the region as high risk.
Historians denote this period as the late phase.
4
denoted in + source

Showing where something appears

In usually introduces the document, chart, or context where notation appears.

The changes are denoted in bold type.
Errors were denoted in the appendix.

See the difference in context

The same subject can take different constructions because each sentence answers a different question.

Construction
Example
Meaning
denoted by
The variable is denoted by x.
x represents the variable
denote as
Researchers denote this stage as critical.
describe or classify something with a label
denoted in
Corrections are denoted in red.
in introduces the place or format where something appears
denote to
The gesture denotes respect to local elders.
to local elders belongs with respect, not with denote

Common mistakes

Some combinations appear in real text but do not mean what learners often assume.

Adding unnecessary to after denote

Denote normally does not take to directly.

✕ The sign denotes to danger. ✓ The sign denotes danger.

Confusing denote by and denote

Use denoted by in passive structures.

✕ The letter x denotes by speed. ✓ The letter x denotes speed.

Using in as a direct complement

In usually adds context or location.

✕ The symbol denotes in mathematics infinity. ✓ The symbol denotes infinity in mathematics.

Quick practice

Choose the expression that matches the intended meaning.

1. In physics, force is often ___ the letter F.
2. The red colour ___ danger in the warning system.
3. The revisions are denoted ___ blue text.

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Frequently asked questions

Is denote by common?

Yes. It is especially common in passive forms such as denoted by a symbol.

Can denote be followed directly by a noun?

Yes. For example, a sign can denote danger or authority.

Is denote to correct?

Usually no. Denote normally does not take to as its complement.

dabble, in, dabble, with "damage to" or "damage by"? dance to, with, on, in or for? "dangle from" or "dangle in"? dare to, for, on, as or at? dash to, into, out, from or on? daydream about, for, in, of or on? "debate in", "debate on" or "debate with"? deceive by, in, into, on or about? "decide on", "decide to" or "decide by"? declare in, by, on, to or as? decline in, by, from, to or for?

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