Norwegian is the official language of, not surprisingly, Norway. It's a North Germanic language that, along with Swedish and Danish, are the main Scandinavian languages.
In the USA, we have officially sanctioned standards of English yet few Americans can pass a test based on these standards (the standard test of SWE has an alarmingly high failure rate). Ours is a dialect-driven language, rife with misuse and, consequently, misunderstandings. However, people are able to communicate. And so it is in Norway, which doesn't have an officially sanctioned standard for people to ignore. Theirs too is a dialect-driven language, but people of different dialects can communicate in that language. Which goes to show you that sometimes breaking the rules aint all bad.
It may also help to know something about Danish, which is a similar language. Like Norwegian, Danish is a North Germanic language. It's spoken mainly in Denmark. It's also spoken among about 75,000 Danish dispora in Norway and northern Germany. It shares many aspects with Swedish and Norwegian, because all three languages derive from Norse. In fact, the Danes originally came from Sweden.
Often, speakers of one of these languages can be understood (more or less) by people who normally speak one of the other two but have no education in Danish per se. Danish also dominates some Danish enclaves in the USA, Canada, and Argentina. At one time, Danish was the language of an empire consisting of Norway, Sweden, and Denmark. The Danes controlled Greenland and Iceland, and held sway over much of Europe.
If you're an American traveling to Norway, you will likely encounter some people who speak English as a second language. Some tips on communicating with them (can also help with English speakers in the USA!):
Clearly annunciate your ending consonants. Midwesterners in the USA tend not to do this.
Use short words. They are easier to understand.
Speak a bit more slowly than usual. Your Norwegian counterpart can probably understand your rapid speech, but the opposite may not be true. By speaking more slowly and deliberately, you help slow the other person down so you can understand.
If you don't quite understand, ask the other person to repeat. But don't shout. The problem isn't deafness, but a difference in articulation.
Use the correct date format. In the USA, many people use a date format that is unclear to the rest of the world. Rather than say "3-9-2014," say "09 MAR 2014" or "03 SEP 2014" depending on which date you actually mean.
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