Round to an appropriate accuracy and estimate to check
Distinguish decimal places from significant figures · Use an estimate to detect an implausible result · Choose a precision suited to the question
Exam scope and assessment notes
Core and Extended foundations. Historical study of Cambridge IGCSE Mathematics (US) 0444, 2025 Version 2. The final assessment was June 2025; the syllabus was available only to schools in Arizona, USA. This is not a current exam-entry option. Original self-check teaching and explained practice are not Cambridge papers, official marks or predicted grades. Linked teaching foundations do not establish full syllabus mastery. Calibrated cumulative assessment, reliable drawn-work review and qualified mathematics-teacher review remain unfinished.
Before you begin
- Decimal place value
- Arithmetic
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What should you establish before applying the method in this lesson?
What you will learn
- Distinguish decimal places from significant figures
- Use an estimate to detect an implausible result
- Choose a precision suited to the question
Which digit is counted?
Decimal places count positions after the decimal point; significant figures begin at the first non-zero digit. Keep the requested number of digits, then use the next digit to decide whether to round up. In these positive-number examples, a next digit of 5 or more rounds the retained value upwards.
0.00476 to two significant figures is 0.0048; to two decimal places it is 0.00. For large rounded integers, scientific notation can show how many figures are intended: 4.70×10³ has three significant figures.
Estimate and interpret
Round inputs to convenient values for a rough calculation, not for a final accurate answer. 39.8×2.1 is around 40×2 = 80. Retain intermediate precision to avoid compounded rounding error, then round the final result as requested.
The context can require rounding a count up or down rather than to nearest: 10.2 busloads needs 11 buses, while a maximum affordable quantity of 10.2 means at most 10 whole items.
Sources for this lesson
Pause and explain
Are decimal places and significant figures the same for every number?
Worked example
Round 0.008764 to three significant figures and three decimal places.
Show the worked solution
- Significant digits begin at 8: 8, 7, 6; the next 4 does not round up.
- For three decimal places the third decimal digit is 8; the next 7 rounds it up.
Answer 0.00876 to 3 significant figures; 0.009 to 3 decimal places.
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Round 47.386 to two decimal places and three significant figures.
Give me a hint
Locate the last retained digit for each instruction.
Compare my reasoning
- Two decimal places keep 47.38 before rounding; next digit 6 gives 47.39.
- Three significant figures keep 47.3; next digit 8 gives 47.4.
47.39 and 47.4.
Look for these in your work
- Use the requested digit count
- Inspect the next digit
Estimate 198×0.049, then calculate it exactly.
Give me a hint
Use 200×0.05 as a check.
Compare my reasoning
- Estimate = 10.
- Exact product = 9.702, consistent with the estimate.
Estimate 10; exact 9.702.
Look for these in your work
- Choose useful rounded inputs
- Check the decimal scale
A trip has 103 passengers and buses hold 40 each. How many buses are needed? Why is rounding 103/40 to the nearest integer unsuitable?
Give me a hint
The capacity must cover every passenger.
Compare my reasoning
- 103/40 = 2.575.
- Two buses hold only 80, so the count must be rounded up to 3.
3 buses; always cover the required capacity rather than blindly using nearest-integer rounding.
Look for these in your work
- Check capacity
- Explain the contextual rounding rule
Common mistakes
- Leading zeros are not significant figures.
- An estimate is not a substitute for the final calculation.
What can you explain now?
Are decimal places and significant figures the same for every number?
Compare with the explanation
No; leading decimal zeros make their counts differ.
Significant figures start at the first non-zero digit, while decimal places start immediately after the point.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
Are decimal places and significant figures the same for every number?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.