Read the scale before naming a decimal point

start. A line from 0.3 to 0.4 is split into ten equal intervals. What is the third point after 0.3?

Answer: 0.33. The displayed span is one tenth, so each of its ten equal intervals is one hundredth.

Teacher response: Listen for this idea: Ten intervals always mean steps of one tenth. Follow up: Ten intervals divide the displayed span, which may be smaller or larger than one whole. Subtract the endpoint values before dividing by the interval count.

example. A line from 0.3 to 0.4 is split into ten equal intervals. What is the third point after 0.3?

1. Read both endpoints: the span from 0.3 to 0.4 is 0.1, not one whole.
2. Partition 0.1 into ten equal distances. Each distance is 0.01. Eleven tick marks enclose the ten intervals.
3. Start at 0.30 and travel three intervals: 0.31, 0.32, 0.33. Do not count the starting tick as the first travelled step.
4. Check that 0.33 lies between the labelled endpoints and is closer to 0.3. Label the point at the endpoint of the third interval.

Worked example: 0.33. The displayed span is one tenth, so each of its ten equal intervals is one hundredth.

p1. A line from 0.2 to 0.3 has ten equal intervals. What is one interval worth?

Answer: 0.01

Teacher response: The span is 0.1; one tenth of that span is 0.01.

p2. Start at 0.2 and move five intervals of 0.01. Name the point.

Answer: 0.25

Teacher response: Five hundredths beyond twenty hundredths is twenty-five hundredths.

p3. A line from 0 to 1 has ten equal intervals. What is one interval worth?

Answer: 0.1

Teacher response: This displayed span is a whole, so each interval is one tenth.

e1. Start at 0.7 and move six intervals of 0.01. Name the point.

Answer: 0.76

Teacher response: Six hundredths beyond 0.70 is 0.76.

transfer. A line from 0.40 to 0.50 has five equal intervals. Explain why each interval is 0.02.

Answer: The span is 0.10. Five equal parts of that span are 0.10 ÷ 5 = 0.02 each.

next. If the learner uses the number of ticks as the denominator, revisit intervals. If the scale is correct, change the displayed span while keeping the same interval count.