Read between marks and report a nearby value
Use scale intervals and rounding conventions to distinguish exact values from approximations.
Begin with the activity ↓Do more marks always mean greater accuracy?
Scale marks show the intervals you can read. For a nearby rounded value, state the rounding place and use approximately.
If the space between 3 cm and 4 cm has ten equal intervals, each interval is 0.1 cm. Count the spaces between marks, not just the marks.
Suppose an object ends between 3.4 cm and 3.5 cm. You may judge which mark is closer, but that picture alone does not justify an exact reading such as 3.467219 cm.
In this constructed rounding example, the endpoint is set to 3.46. The nearest tenth is 3.5, because the gaps to 3.4 and 3.5 are 0.06 and 0.04.
Writing 3.46=3.5 incorrectly claims equality. Write 3.46≈3.5; the symbol means approximately equal. Rounding reports a nearby value without making the numbers identical.
At the exact halfway point, 3.45, a tie-breaking convention is needed. For nonnegative numbers in this lesson, choose the larger of the tied values, giving 3.5 to the nearest tenth. Other conventions also exist.
Finer marks do not guarantee accuracy if the start is misaligned or the ruler is bent. Resolution, rounding and measurement error are related but distinct ideas.
Listen one paragraph at a time
Hold on to this distinction
Locate the two bounding marks first, then choose the nearby value using the stated convention. Do not invent unsupported digits.
Change it and check
Change the constructed endpoint and reporting interval. Compare the neighbouring marks and read where ≈ replaces =.
The selected endpoint 3.46 equals 346 hundredths. Compare its distance to the two tick marks.
3.46 ≈ 3.5
Distances are 0.06 to the left and 0.04 to the right. A tie goes upward in this activity.
Model values are specified exactly; the activity practises rounding. It does not calculate an instrument’s uncertainty or a statistical confidence interval.
Try with paper and objects
Draw ten equal intervals from 3 to 4. Mark a constructed position of 3.46 and choose its closer tenth. Keep this model separate from a real measurement.
Check and explain another example
Check your idea 1
Check your idea 2
Apply it in a new setting
Connect the answer to its unit
Return to the explanationCompare with a solution
2.8 · rounded number
The smaller gap is 0.04 to 2.8. This is an approximation to 2.76.
Does your explanation include these ideas?
Explain aloud or in a drawing, then check your ideas. Different wording can express the same meaning.
Continue, or pause here
Connect the requested quantity, units, operation and check in a new situation.