Rounding Numbers (significant figures) - Year 7 PDF Download

Introduction

• When we round numbers, one method involves considering only the initial few digits (typically 1, 2, or 3 figures) that hold significance. This approach, known as significant figures, refers to each digit in a value, particularly in measurements, contributing to its accuracy.
• Significant figures are crucial for larger or very small numbers. They play a pivotal role in determining the precision of a value. The most significant figure carries the highest place value in a number, indicating its importance within the numerical context.
• Rounding numbers using significant figures may reduce precision but enhances usability. Different strategies apply when handling small versus large numbers.

Rounding Numbers Using Significant Figures

When rounding numbers using significant figures, follow these steps:

• Identify the position of the most significant figure in terms of place value. For instance, when rounding to 1 significant figure, locate the digit in the highest place value column.
• Determine whether the digit in question should be rounded up based on the rules of rounding.
• For rounding, keep the digit unchanged if the next digit is less than 5 (rounding down), but increase it by 1 if the next digit is 5 or more (rounding up).
• The rounded value should maintain a similar magnitude to the original number, sometimes requiring additional zero digits. For instance, rounding 320 to 1 significant figure results in 300.
• Utilizing place value labels can aid in determining the level of precision to round to.

Remember that units are often referred to as 'ones'. For instance, in the number 34, there are 3 tens and 4 ones.
For the value of 37,425 – the digit with the highest place value is 3, so this is the 1st significant figure. The digit 7 has the 2nd highest place value in this number, so the 2nd significant figure is 7

Example

• Round 3892 to 2 significant figures.
  
• The digit 3 has the greatest place value. The digit 8 represents the 2nd significant figure. The digit 8 is positioned in the hundreds column, so 3892 is rounded to the nearest hundred.
  
• The digit 8 is rounded up to 9 as the next digit (9) is 5 or more (rounding up). The trailing digits after the 2nd significant figure are replaced with two zeros. 3892 rounded to 2 significant figures is 3900

Rounding small numbers using significant figures

• Significant figures begin at the first non-zero digit, disregarding zeros at the number's start, but considering those in between. Rounding follows standard rules after identifying the most significant figure. Zeros from the initial significant figure onward are all counted, with only the leading zeros being insignificant.
• Once the most significant figure is pinpointed, rounding rules are applied consistently.
• All zeros from the first significant figure onwards are included in the final count; only the leading zeros are disregarded.
• Example: For the value of 0∙0327, the digit with the highest place value is 3. This is the 1st significant figure. Ignore the place value columns at the beginning containing zero. The 2nd significant figure is the digit in the next place value column which is the 2. The 3rd significant figure is 7.
  

Example

• Round 0∙3019 to 2 significant figures.
  
• The digit 3 has the greatest place value and is the first non-zero digit in the value. The digit zero represents the 2nd significant figure. The 2nd significant figure is positioned in the hundredths column, so 0∙3019 is rounded to the nearest hundredth. The 0 is left the same because the next digit (1) is less than 5 (rounding down).
  
• There must be two significant digits in the final answer so one zero following the 3 must be included. 0∙3 would have only been rounded to 1 significant figure. 0∙3019 rounded to 2 significant figures is 0∙30

Real-world maths

• Rounding using significant figures is helpful for very large or small numbers where other methods may not be suitable.
• An engineer might round a measurement to 2 or 3 significant figures due to limitations in precision.