1. Lesson 7 and 8
Round a given decimal to any place using place value understanding and the vertical number line.

2. This type of rounding is very different than the way we are used to
This type of rounding is very different than the way we are used to. I hope you find the following examples helpful in how Common Core addresses this concept.

3. Example #1: Round 78.346 to the nearest tenth. 784 tenths (or 78.4)
Identify the place value you have been asked to round to. (We can view this as 783 tenths collectively or 78.3.)
Use this number as our lowest number on our number line.
Add one more (tenth) to that number and that will become our largest number on our number line.
Determine the midpoint. We have discussed that if we add a zero at the end of our low and high numbers (78.30 and 78.40) it may help us better determine our midpoint – 78.35
Determine if the number to be rounded will fall on or above the midpoint (rounds up to 78.4) or below the midpoint (rounds down to 78.3).
Answer: 78.3
784 tenths (or 78.4)
78.35
783 tenths
(or 78.3)

4. Example #2: Round 8.356 to the nearest hundredth.
Identify the place value you have been asked to round to. (We can view this as 835 hundredths collectively or 8.35.)
Use this number as our lowest number on our number line.
Add one more (hundredth) to that number and that will become our largest number on our number line.
Determine the midpoint. We have discussed that if we add a zero at the end of our low and high numbers (8.350 and 8.360) it may help us better determine our midpoint – 8.355
Determine if the number to be rounded will fall on or above the midpoint (rounds up to 8.36) or below the midpoint (rounds down to 8.35).
Answer: 8.36
836 hundredths (or 8.36)
8.355
835 hundredths
(or 8.35)

5. Example #3: (Using 9s) Round 8.396 to the nearest hundredth.
Identify the place value you have been asked to round to. (We can view this as 839 hundredths collectively or 8.39.)
Use this number as our lowest number on our number line.
Add one more (hundredth) to that number and that will become our largest number on our number line.
Determine the midpoint. We have discussed that if we add a zero at the end of our low and high numbers (8.390 and 8.400) it may help us better determine our midpoint – 8.395
Determine if the number to be rounded will fall on or above the midpoint (rounds up to 8.40) or below the midpoint (rounds down to 8.39).
Answer: 8.40
840 hundredths (or 8.40)
8.395
839 hundredths
(or 8.39)

6. Example #4: Round 432.8 to the nearest tens. 44 tens (or 440)
Identify the place value you have been asked to round to. (We can view this as 43 tens or 430.)
Use this number as our lowest number on our number line.
Add one more (tens) to that number and that will become our largest number on our number line.
Determine the midpoint - 435
Determine if the number to be rounded will fall on or above the midpoint (rounds up to 440) or below the midpoint (rounds down to 430).
Answer: 430
44 tens (or 440)
44 tens +5 ones (or 435)
43 tens
(or 430)