Round decimals by finding the nearest endpoint

start. Why does 0.96 round to 1.0 to the nearest tenth?

Answer: Its neighbouring tenths are 0.9 and 1.0. It is 0.04 away from 1.0 and 0.06 away from 0.9, so 1.0 is nearer.

Teacher response: Listen for this idea: Rounding only changes a digit and can never cross a whole-number boundary. Follow up: Name the two surrounding multiples of the required place. The upper tenth after 0.9 is 1.0. Use distance to choose, rather than attaching a rule to an isolated digit.

example. Why does 0.96 round to 1.0 to the nearest tenth?

1. To round to the nearest tenth, identify the tenth immediately below and the tenth immediately above the number.
2. Locate their midpoint. Between 0.9 and 1.0, the midpoint is 0.95.
3. Place 0.96 beyond that midpoint, nearer to 1.0. Record 1.0 so the requested tenths place remains visible.
4. For nonnegative midpoint cases in these tasks, use the classroom convention of rounding up. State that convention when the distances are equal.

Worked example: Its neighbouring tenths are 0.9 and 1.0. It is 0.04 away from 1.0 and 0.06 away from 0.9, so 1.0 is nearer.

p1. Round 0.84 to the nearest tenth.

Answer: 0.8

Teacher response: 0.84 is below the midpoint 0.85.

p2. Round 1.27 to the nearest tenth.

Answer: 1.3

Teacher response: 1.27 is closer to 1.3 than to 1.2.

p3. Round 2.95 to the nearest tenth, using midpoint-up rounding.

Answer: 3.0

Teacher response: 2.95 is halfway between 2.9 and 3.0; the stated convention selects 3.0.

e1. Round 0.995 to the nearest hundredth, using midpoint-up rounding.

Answer: 1.00

Teacher response: The neighbouring hundredths are 0.99 and 1.00.

transfer. Explain why 0.949 rounds to 0.9 to the nearest tenth even though its final digit is 9.

Answer: The whole number 0.949 is below the midpoint 0.95. The last digit alone does not choose the nearest tenth.

next. If the learner rounds the final digit first, return to the original number on the line. Avoid repeated rounding through intermediate places.