Decimal place value (age 11+)

Activities to try

1. 1

   Highlight the significant figures, round once, rebuild the size

   Why it works: Significant figures are counted from the first non-zero digit; zeros can be placeholders that hold a number's size or trailing zeros that record precision, so they cannot simply be dropped. Rounding is one nearness decision based on the next digit, after which place value must be restored.

   1. Take a number such as 34,750 and decide to round it to 2 significant figures.
   2. Mark the counted significant digits (the 3 and the 4), confirming you start at the first non-zero digit.
   3. Identify the single deciding digit immediately after the last required place (the 7) and place the number on a number line between its two candidate rounded values (34,000 and 35,000) and their midpoint (34,500); decide the round-up in one step.
   4. Reassemble the answer as 35,000, writing in the placeholder zeros that keep the number in the thousands — do NOT stop at 35.
   5. Now take 0.004982 and round to 2 significant figures: cross out the leading zeros as 'not significant', count the 4 and 9, apply the deciding digit (8) so 49 rounds up to 50, and write 0.0050 — keeping the front zeros for magnitude and the trailing zero for precision.
2. 2

   Contrast decimal places with significant figures on one number

   Why it works: Decimal places and significant figures are different rules: dp counts from the decimal point, while sf counts from the first non-zero digit. The difference is most striking with leading zeros and with large numbers that need placeholder zeros, but they also differ for ordinary numbers (3.14159 is 3.14 to 2 dp and 3.1 to 2 sf). The same number can give very different rounded values under each.

   1. Pick a single number (e.g. 0.004982) and round it both to 2 decimal places and to 2 significant figures.
   2. Record the two answers side by side (0.00 vs 0.0050) and write a sentence explaining why they differ.
   3. Do the same for a large number such as 47,320: to 2 sf it is 47,000 (zeros needed), and note how that differs from a decimal-place instruction.
   4. State in your own words when leading zeros are ignored and when zeros must be kept.
3. 3

   Choose and justify an appropriate degree of accuracy

   Why it works: Accuracy should suit the precision of the measurement or context, and learners should be able to justify both the rounded value's size and the choice of dp vs sf.

   1. Given a context such as measuring a room's length, decide whether rounding to 2 decimal places or 2 significant figures is more appropriate, and explain why.
   2. Explain to a partner (or in writing) why 47,320 to 2 sf needs its zeros on the end but 47 to 2 sf would not.
   3. Respond to a challenge like: 'You rounded 34,750 to 2 significant figures and wrote 35 — convince me that is the right size.'
   4. Justify which single digit decided each of your roundings and why the remaining digits did not matter.