Rounding decimals on a number line
MathematicsNumbers & ArithmeticAges 11–12
Use it with your class: students open it from a link or a QR code, with no account needed.
Next in Numbers & Arithmetic
A decimal number sits on two number lines: the top one is marked off by the rounding place, and the bottom one zooms into the interval containing it, split into 10 parts. Drag the point to see which mark it is closer to; the deciding digit is highlighted and the rounded result and error appear instantly. Further screens round to significant figures, give error intervals and the upper and lower bounds of a sum, difference, product or quotient with percentage errors, and show how rounding at every step of a compound-growth calculation drifts from the exact result.
Lesson: Rounding and estimation
What it shows
Rounding replaces a number with the nearest value on a coarser scale, such as the nearest tenth or 2 significant figures; only the digit straight after the rounding place decides, with 5 or more rounding up. A value rounded to a unit u lies in the error interval value − u/2 ≤ x < value + u/2. Bounds of a calculation combine these limits: the largest quotient uses the upper bound of a and the lower bound of b. Percentage error compares the maximum error with the value. Rounding at every step of a repeated calculation lets errors build up.
How to use
On Round to a place, choose the place with the arrows and drag the red point. On Significant figures, type a Number and set how many figures to keep. On Bounds, enter a and b, choose each Accuracy and the Calculation, then drag the red points to try true values. On Rounding each step, set Start, Rate, Years and the accuracy used every year, and compare the two columns of the table.
Parameters you can change
- Number to round -1000–1000
- Round to the nearest hundred, ten, one, tenth, hundredth, thousandth
- Show rounding error
- Show rule explanation
- Screen Round to a place, Significant figures, Bounds, Rounding each step
- Number to round (significant figures) -10000000–10000000
- Significant figures 1–6
- Measurement a 0.001–10000
- Accuracy of a nearest 100, nearest 10, nearest 1, nearest 0.1, nearest 0.01, nearest 0.001, 1 s.f., 2 s.f., 3 s.f.
- Measurement b 0.001–10000
- Accuracy of b nearest 100, nearest 10, nearest 1, nearest 0.1, nearest 0.01, nearest 0.001, 1 s.f., 2 s.f., 3 s.f.
- Calculation a + b, a − b, a × b, a ÷ b
- Starting amount 100–10000
- Growth rate per year 0.5–20 %
- Number of years 1–30 years
- Round every year to nearest 100, nearest 10, nearest 1, nearest 0.1, nearest 0.01, 2 s.f., 3 s.f.
Questions to explore
- What is the largest possible error when rounding to the nearest tenth, and where on the line does it occur?
- Does rounding 2.45 to the nearest tenth and then to the nearest one give the same result as rounding it directly?
- When rounding 7.2468 to the nearest tenth, which digit decides the result, and why do the later digits not matter?
