Lesson 1 #26, #34, #35

This problem is a little bit tricky!  Let's think about rounding based on a number line and the place values the given number lies between.

Consider the number line below.  3996 is between 0 ten thousands and 1 ten thousand.  So when we round this number to the nearest ten thousand, we will round to whichever of these two numbers 3996 is closest.  Notice from the diagram, it is closer to 0.  So we round down to 0.

Now let's think about the same problem using the digits and place value method.  Consider the place value chart below.  If we want to round to the ten thousands place, we look at the digit to the right of the ten thousands place, namely, the thousands place.  

Applying this to the figure below we see that since the digit in the thousands place is less than 5 (it's 3)  we round down.  This means we don't add one to the 10,000's place and we change the remaining digits to 0.  But this makes all the digits 0.  So the answer is 0.

Part 2:  Round 3996 to the nearest 10.

Thinking of the number line, we can imagine that the two values that differ by 10 that 3996 lies between are 3990 and 4000 as shown below.  Since 3996 is closer to 4000 than 3990, we will round up to 4000.