If students understand it is three-tenths, that is the most important piece. Regarding the .30 example, our math teachers at the secondary level inform students to remove the last zero. As long as the teacher can see that the numbers and decimal are in the correct place, either .3 or 0.3 should be acceptable answers.
There will be a point when students need to know that a line over the 3 indicates that it is repeating; whereas, it is terminated if there is a zero after the 3 (i.e. 3.0).
Achieve the Core offers guidance for teachers about where to focus their lessons that I think is helpful as well: http://achievethecore.org/category/774/mathematics-focus-by-grade-level.
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Yes, they are equivalent decimals. Students need to realize that those notations all represent the same quantity. Conceptually, it's important for them to understand when including or deleting a zero changes the value of a number and when it doesn't.
While I totally agree with everything that has been mentioned, I always encourage my STEM students to take everything out to the hundredths place. This level of precision helps with many of our engineering design challenges and my middle schools students tend to do better when there are consistent expectations.
That being said- I would accept the answer from the scenario.
Yes, they're all acceptable. It depends on the written instruction too. If the direction says round to the nearest tenths or hundredths then students comply.
I would say... yes... but only with an additional question too so I could check for conceptual understanding.
When I am unsure if a student understands this comparison and difference in written/verbal form, I often ask an additional question. With the help of Kristin Gray (fellow Laureate), I recently lead my class in a more or less than 10 number talk. I gave a variety of problems...
7.75 + 2.7
And asked them if the solution was more of less than 10.
With that question, I could conceptually see if the students understood the difference between 2.7 and 2.70.
I might also think about a clothesline activity. String a clothesline across the front of your room. Have a student at a time place a decimal between 0 and 1. Include equivalent decimals as well (.2 and .20). After some have been placed, have discussions regarding which placements they have questions for or would like to change. An example of a clothesline activity is linked here: http://mr-stadel.blogspot.com/2015/08/clothesline.html
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