M4.1.8 For the adult
Accuracy and bounds
A rod is 7.4 cm long to 1 decimal place. How long could it really be?
What this chapter teaches
A rounded number stands for a stretch of true values, half a step either side. The lower bound is included and the upper bound is not, so 7.4 to 1 decimal place means 7.35 ≤ length < 7.45. The largest area of a rectangle comes from both upper bounds and the smallest from both lower bounds.
Three questions to ask
There is no one right wording. Listen for the idea.
- Why does the stretch for 7.4 cm to 1 decimal place stop at 7.45 and not 7.5?
- Why is 7.45 left out of the stretch but 7.35 is kept in?
- Which bounds do you use for the largest area of a rectangle, and why?
After the chapter, the learner can
- Round a number to 2 or 3 significant figures
- Find the bounds of 7.4 cm rounded to 1 decimal place
- Find the largest possible area from rounded lengths
What they copy into their notebook
Rounded values stand for a stretch: half a step each way. 7.4 to 1 d.p.: 7.35 ≤ length < 7.45. The largest area uses both upper bounds. The smallest uses both lower.