Number
Rounding & Estimation
Year 7 · Year 8 · Year 9
- ✓By the end of this lesson students will be able to round numbers to a specified number of decimal places.
- ✓By the end of this lesson students will be able to round numbers to a specified number of significant figures.
- ✓By the end of this lesson students will be able to estimate the answer to a calculation by rounding each number to one significant figure.
- ✓By the end of this lesson students will be able to understand the practical uses of rounding and estimation.
Key concepts
Rounding to decimal places means making a number simpler by reducing the number of digits after the decimal point. We decide whether to round up or down based on the value of the next digit. To round to a specified number of decimal places: 1. Identify the digit in the specified decimal place. 2. Look at the digit immediately to its right. 3. If this digit is 5 or more (5, 6, 7, 8, 9), round up the digit in the specified decimal place. 4. If this digit is less than 5 (0, 1, 2, 3, 4), keep the digit in the specified decimal place as it is. 5. Remove all digits to the right of the specified decimal place.
Significant figures are the 'important' digits in a number. They give us an idea of the precision of a number. Rounding to significant figures is a way to simplify numbers while maintaining their approximate value. How to identify significant figures: 1. All non-zero digits are significant (e.g., 123 has 3 significant figures). 2. Zeros between non-zero digits are significant (e.g., 102 has 3 significant figures). 3. Leading zeros (zeros before non-zero digits) are NOT significant. They are placeholders (e.g., 0.0012 has 2 significant figures). 4. Trailing zeros (zeros at the end of a number) are significant ONLY if there is a decimal point (e.g., 1200 has 2 significant figures, but 1200. has 4 significant figures, and 12.00 has 4 significant figures). How to round to a specified number of significant figures: 1. Identify the first significant figure (the first non-zero digit from the left). 2. Count from the first significant figure to the specified number of significant figures. 3. Look at the digit immediately to the right of the last significant figure. 4. If this digit is 5 or more, round up the last significant figure. 5. If this digit is less than 5, keep the last significant figure as it is. 6. Replace any remaining digits between the last significant figure and the decimal point with zeros (if they are to the left of the decimal point). Remove any digits to the right of the decimal point.
Estimation is finding an approximate answer to a calculation. It's useful for quickly checking if a more precise answer is reasonable, or when an exact answer isn't needed. For calculations, we usually round each number to one significant figure before performing the operation. To estimate a calculation: 1. Round each number in the calculation to one significant figure. 2. Perform the calculation using the rounded numbers.
Key facts to remember
- 1To round, look at the digit immediately to the right of the place you are rounding to.
- 2If this digit is 5 or more, round up; otherwise, keep the digit the same.
- 3All non-zero digits are significant.
- 4Zeros between non-zero digits are significant.
- 5Leading zeros (e.g., in 0.007) are NOT significant.
- 6Trailing zeros in a whole number without a decimal point (e.g., in 500) are generally NOT significant unless specified by context.
- 7Trailing zeros after a decimal point (e.g., in 5.00) ARE significant.
- 8Estimation provides a quick, approximate answer and is useful for checking the reasonableness of exact calculations.
Worked examples
Example 1
Round 3.14159 to 2 decimal places.
Answer
3.14
Example 2
Round 0.005678 to 3 significant figures.
Answer
0.00568
Leading zeros are not significant figures and are used as placeholders to maintain the value of the number.
Example 3
Estimate the answer to 48.7 × 2.13 ÷ 0.54.
Answer
200
Rounding to one significant figure makes calculations much simpler and quicker to perform mentally.
Common mistakes
- ✗Rounding multiple times (e.g., rounding to 3dp then rounding that result to 2dp, instead of rounding directly to 2dp from the original number).
- ✗Incorrectly identifying the first significant figure, especially with numbers less than 1 (e.g., thinking the '0' in 0.005 is significant).
- ✗Forgetting to replace digits with zeros when rounding whole numbers to significant figures (e.g., rounding 3456 to 2sf as 35 instead of 3500).
- ✗Not rounding *all* numbers in an estimation problem *before* performing the calculation.
- ✗Confusing decimal places with significant figures.
Exam tips
- ★Always read the question carefully to determine whether you need to round to decimal places (dp) or significant figures (sf).
- ★Show your working for estimation problems; examiners want to see the rounded numbers you used.
- ★After estimating, quickly check if your estimated answer seems reasonable compared to the original numbers.
- ★When rounding, only look at the *next* digit to the right of the required place; do not look further along the number.
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