Key points
One way of rounding numbers is to count only the first few digits (usually 1, 2 or 3 figures) that have a value attached to them. This method of rounding is called significant figureSignificant figures are each of the digits in a value, often a measurement, that contribute to the degree of accuracy of the value.. It is often used with larger numbers, or very small numbers.
Significant means important, for example a significant event is an important event. In maths a significant figure is an important digit within the number. The most significant figure is the digit that has the highest place valueThe value of a digit that relates to its position or place in a number. Eg, in 1482 the digits represent 1 thousand, 4 hundreds, 8 tens and 2 units..
When rounding numbers, the result is less accuracyAccuracy is how close a measured value is to the actual (true) value., but easier to use.
There are slightly different approaches when dealing with small or large numbers.
Rounding numbers using significant figures
There are steps which can be followed when rounding using significant figures:
Establish what place value column the most significant figureSignificant figures are each of the digits in a value, often a measurement, that contribute to the degree of accuracy of the value. is positioned. For example, if rounding to 1 significant figure then identify the digit that is positioned in the highest place valueThe value of a digit that relates to its position or place in a number. Eg, in 1482 the digits represent 1 thousand, 4 hundreds, 8 tens and 2 units. column.
Refer back to the rules of rounding to decide whether this digitOne of the symbols of a number system, most commonly the symbols 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 should be rounded up.
Leave the digit the same if the next digit is less than 5 (this is called rounding down) but increase it by 1 if the next digit is 5 or more (this is called rounding up).
The rounded value must be a similar size to the original number, so additional zero digits may be needed. For example, 320 to 1 significant figure is 300.
Using place value labels can help identify what degree of accuracy to round to.
Remember: Units are often referred to as ones. Eg, 34 has 3 tens and 4 units, or say 34 has 3 tens and 4 ones.
Examples
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Question
Round 241,529 to 1 significant figure.
In the number 241,529, the most significant figure is the 2
This is in the hundred thousands place value column.
241,529 rounded to 1 significant figure is 200,000
Rounding small numbers using significant figures
- Significant figures start at the first non-zero number, so ignore the zeros at the start of the number, but not the ones in between.
- Once the most significant figure has been identified the same rules of rounding are applied.
- From the first significant figure onwards, all zeros are included. It's only the zeros at the beginning that don't count.
Examples
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Practise rounding numbers using significant figures
Practise rounding numbers using significant figures in this quiz.
Quiz
Real-world maths
- Rounding using significant figures is useful when dealing with extremely large or small numbers where rounding using other methods is not always appropriate.
- An engineer may round a measurement to 2 or 3 significant figures because they can鈥檛 measure any more accurately.
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