Learn Russian: Этот диаметр никогда не будет равняться девятистам семидесяти двум метрам. - This diameter will never equal nine hundred seventy-two meters.

The verb равняться (to equal) dictates the case of its object, requiring the Dative case. That is why the entire phrase девятистам семидесяти двум метрам is in the Dative.

How exactly does the word for 900 decline into девятистам?

The nominative form is девятьсот. For hundreds from 500 to 900, both parts of the word decline. The first half (девять) takes the Dative ending -и to become девяти-, and the second half (-сот) takes the Dative plural noun ending -стам. Together, they form девятистам.

Does the word for 70 (семидесяти) also decline both halves?

Yes! For numbers ending in -десят (50 to 80), both halves decline like feminine nouns ending in a soft sign. The first part семь becomes семи-, and -десят becomes -десяти. Combined, you get семидесяти.

Why is метрам in the Dative plural? Doesn't the number 2 usually take the Genitive singular?

In the Nominative and inanimate Accusative cases, compound numbers ending in 2 do take the Genitive singular (like два метра). However, in all other cases (the oblique cases), the noun simply matches the case of the number and is always plural. Since the number is Dative here, the noun becomes the Dative plural метрам.