# What case do numbers take in constructions where they are preceded by "на"?

While doing an exercise in the Russian textbook ТРОЙКА, I came upon the following:

Этот велоcипед на 100 долларов дешевле, чем тот велосипед.
(This bicycle is cheaper than that bicycle by 100 dollars.)*

*The book doesn't actually provide a translation; what you see is my best translation of the Russian you see above it.

The exercise just uses numerals, so I didn't really have to worry about declension (other than whether or not "доллар" should be "доллар," "доллара," or "долларов," but if you keep reading, you'll see that I question this later on). As I was doing the exercise, I got to wondering how I would say these sentences I was creating. Specifically, I was wondering how you decline the numeral. My first instinct is to think that this requires the prepositional case because there is no movement here and as I understand it, the preposition "на" only takes one of either of those two cases -- the accusative or the prepositional. I could not find this specifically stated with regard to this "на" plus numeral construct, however.

I am also unsure of the case that "доллар" should take. It's my understanding that for all cases other than the nominative and accusative, the case for the adjective (or in this case numeral acting as adjective) and the noun that follows it, simply follow ordinary rules for case declension. But, I have not read or seen that specifically with this construction using "на," and clearly, the example from the book is not using it (otherwise it would be "на 100 долларах," correct?).

So, I have come to this forum to see if someone here can clear up the confusion on this for me. I'm even going to type up a few sentences using the long form of the numeral to see if my assumptions are correct. Those examples follow:

Эта книга на одном долларе дешевле, чем та книга.
(This book is cheaper than that book by one dollar.)

Эта сковорода на пятнадцати долларах дешевле, чем та сковорода.
(This frying pan is cheaper than that frying pan by fifteen dollars.)

Этот совок на двенадцати долларах дешевле, чем тот совок.
(This dustpan is cheaper than that dustpan by twelve dollars.)

Это радио на ста долларах дешевле, чем то радио.

Эта микроволновка на двухстах долларах дешевле, чем та микроволновка.
(This microwave is cheaper than that microwave by two hundred dollars.)

Эта плита на тысяче* пятистах долларах дешевле, чем та плита.
(This oven is cheaper than that oven by one thousand, five hundred dollars.)

*I am assuming that both "тысяча" and "пятьсот" require declension.

So, is my understanding of this construct correct?

As always, I appreciate any answers to this question, especially since the practical applications of a construct like this are likely to be a bit higher than most.

After на you've got to put the following numeral into the accusative case.

The noun that follows the numeral is

• in the accusative case singular if the numeral ends in 1 except for those that end in 11 (i.e. after 1, 21, 31, 41 ... 101, 121, 131, etc.):

Этот велоcипед на 1 (один) доллар дешевле, чем тот велосипед.

В этом доме на 1 (одно) окно меньше, чем в том доме.

В этом классе на 1 (одну) девочку меньше, чем в том классе.

В этом классе на 1 (одного) мальчика меньше, чем в том классе.

• in the genitive case singular after the numerals ending in 2, 3, 4:

Этот велоcипед на 2 (два) доллара дешевле, чем тот велосипед.

В этом классе на 2 (две) девочки меньше, чем в том классе.

• in the genitive case plural after the the rest of the numerals:

Этот велоcипед на 6 (шесть) долларов дешевле, чем тот велосипед.

В этом классе на 6 (шесть) девочек меньше, чем в том классе.

As you can see, the nominative and accusative case of the Russian numerals are the same except when they end in 1, but not in 11. Here, with the inanimate masculine and neuter nouns like доллар or окно numeral 1 has its acc.=nom. (один/одно), with the animate masculine nouns have their acc.=gen. (одного), and the animate feminine nouns it has a special acc. form, одну.

• Both of your answers were quite good, but I'm going to give you the green checkmark, Yellow Sky, because the examples you gave really painted a very clear picture for me. I actually ran across something that made me think that the accusative is used after "на" in these constructs, so it was good to see that both of these answers confirm that. Commented Sep 16, 2017 at 4:42
• As a side note - it would be better to assume that a textbook is correct, and adjust your theories to the provided examples )) Commented Sep 16, 2017 at 9:07

That's a very interesting question. Itried to analyse the sentence and I came to the following conclusions. First, if you want to be sure what case is used, try to use a noun in the same construction.

100 долларов=сумма.

На сколько /на какую сумму (accusative ) один велосипед дороже другого?

So now it's clear that the numeral takes the accusative case

на один,одного,одно,одну, два,две,три, четыре, сто, тысячу,пятьсот etc.

As for nouns they always depend on the previous numeral

на один рубль,доллар, на два/три/четыре рубля,доллара(genitive singular),пять/шесть/сто/пятьсот/тысячу рублей, долларов (genitive plural )

And that's all. As simple as that.Your first example is correct. But all other examples need correction.

Эта плита на тысячу пятьсот (accusative ) долларов (genitive plural) дешевле, чем та.

We use the prepositions в and на with the Accusative case when we mean “to go somewhere” and with the Prepositional case to answer the question "where?" (not "where to").