A significant amount of zombies were detected in your city

Solution 1:

You are being followed by zombies. You pick them off one at a time (shooting them in the head, of course) until there are no zombies left. Can you count the dead zombies?

Of course you can. They are countable. So the word to describe them is number.

A small number of zombies were chasing me. They were part of a large number of zombies that were detected in the city. (number + are)

Applesauce is oozing towards you, threatening to engulf you. To do so, it would need to be a very large amount of applesauce. Can you count the amount of applesauce that is threatening you?

No, you can't. Applesauce is uncountable.

A large amount of applesauce was on the ground nearby. (amount + is)

Likewise (but be careful when number is the subject; A definite number as subject is singular, but if it is an indefinite number, it's plural, and the verb reflects the plural. Check your determiner.)

A significant number of purchases were detected. One was for shoes, three purchases were for coats, and two were for umbrellas. The total number was six.

Solution 2:

To add on to Medica's answer, the reason why "number" can be both singular and plural is because it is being used differently in the two cases.

A significant number of purchases were detected. One was for shoes, three purchases were for coats, and two were for umbrellas. The total number was six.

In the first instance, the noun is "purchases", and "number of" is acting not as a noun, but as an indefinite pronoun determiner. Therefore the plural "were" should be used.

In the second instance, the noun is "number", and therefore the singular "was" should be used.

From Oxford Dictionaries:

Although the expression ‘a number’ is strictly singular, the phrase ‘a number of’' is used with plural nouns (as what grammarians call a determiner (or determiner)). The verb should therefore be plural:

A number of people are waiting for the bus.

This is not the case with ‘the number’, which is still singular:

The number of people here has increased since this morning.

Solution 3:

Amount vs. Number

General Rule:

Amount is used in reference to mass nouns

Number is used in reference to count nouns

Mass Noun

A noun denoting something which cannot be counted (e.g. a substance or quality), in English usually a noun which

lacks a plural in ordinary usage and

is not used with the indefinite article,

e.g. We say:

an amount of furniture (Two furnitures? No! a furniture? No!)

an amount of happiness. (Two happinesses? No! a happiness? No!)

Count Noun

NOUN

A noun that can form a plural and, in the singular, can be used with the indefinite article

e.g. We say:

a number of books (Two books? Sure! a book? Sure!)

a number of chairs (Two chairs? Sure! a chair? Sure!)

So let's put the definitions and rule to the test with zombies and purchases

Since zombies is the plural of zombie and it would be quite natural to say a zombie, we say: A number of zombies.
Since purchases is the plural of purchase and it would be quite natural to say a purchase, we say: A number of purchases.

Both zombie and purchase are count nouns, and we use number in in reference to count nouns.

Easy mneumonic "count the number of x"

An exception? Not really!

There is a second definition for Mass Noun

1.1 A noun denoting something which normally cannot be counted but which may be countable when it refers to different units or types

e.g. coffee

In the sense of I bought a pound of coffee We say:

an amount of coffee (Two coffees? Not in this sense! a coffee? Not in this sense!)

SO here is the confusion!

In the sense of I ordered two coffees, we say:

a number of coffees

The mass noun coffee functions as a count noun when it refers to specific:

units like cups of coffee (two coffees is two cups of coffee)

types like Columbian coffee or Kenyan coffee (two coffees is two kinds of coffee)

Plural or Singular?

The expression "an amount of..."

will always be singular, because the mass noun it refers to will always be singular. An amount of... denotes a quantity without specific number.

An amount of furniture does not consider the number of pieces of furniture.
An amount of flour does not consider the number of grains, cups, pounds or tons of flour.

Conversely,

The expression "a number of..."

SHOULD always be plural, because the count noun is assumed to be plural. If it were singular, you would not use the construction "a number of...". The indefinite article simply denotes that the number is indefinite: it could be 2, 200, 202 or 2002.

"A significant number of zombies were detected in your city." We detected more than one zombie, but we don't know exactly how many, so we say a number of zombies were detected.

In that sentence zombies is acting as the subject and "a number of" is the determiner for zombies, modifying zombies as an adjective (in place of the unspecified number.) The second example works the same way.

"A significant number of purchases were detected..." We detected more than one purchase, but we don't know exactly how many, so we say a number of purchases were detected.

So why does the "wrong one" sound so right?

"The number of..." will always be singular because the definite number is singular and is functioning as the subject of the sentence.

"The significant number of zombies being detected in your city is growing!"
"The significant number of purchase being detected...impacts the economy."

The untrained native speaker overlooks the subtle distinction between two constructions: a number of... and the number of... Specifically, the grammatical notion of the determiner is pretty obscure to most folks. It sounds close enough, and before you know it, half the world is saying aint, and there it is--in the dictionary! We don't need perfect grammar to communicate, but the better our grammar, the clearer our communication.

Solution 4:

As @Nicole stated, the proper quantifying adjective would be "number" as opposed to "amount" since it refers to a countable noun. However, you are correct in that the best way to word the sentence is:

A significant number of zombies was detected in your city.

The "was" refers to "a significant number" which is a singular collection, not plural.

If you were to use "were," you'd need to say something along the lines of:

Significant numbers of zombies were detected in your city.