Database

db={"collection":[{"address":{"building":"1007","coord":[-73.856077,40.848447],"street":"Moris Park Ave","zipcode":"10462"},"borough":"Bronx","cuisine":"Bakery","grades":[{"date":{"$date":{"$numberLong":"1393804800000"}},"grade":"A","score":"81"},{"date":{"$date":{"$numberLong":"1378857600000"}},"grade":"A","score":"6"},{"date":{"$date":{"$numberLong":"1358985600000"}},"grade":"A","score":"99"},{"date":{"$date":{"$numberLong":"11322006400000"}},"grade":"B","score":"14"},{"date":{"$date":{"$numberLong":"1288715200000"}},"grade":"B","score":"14"}],"name":"Morris Park Bake Shop"}]}

Query

db.collection.aggregate([{/** make grades.score numeric*/"$set":{"grades":{"$map":{"input":"$grades","as":"grade","in":{"$mergeObjects":["$$grade",{"score":{"$toDecimal":"$$grade.score"}}]}}}}},{"$match":{"grades.score":{"$gt":80,"$lt":100}}},{"$project":{"_id":0,"name":1}}])

Result