When I teach rounding to a significant figure, I ask the class to discuss in pairs or small groups a definition for the word significant. It is a word that all the students have heard before but not all are able to define.
After 2 or 3 minutes of conversation I ask the students to write on their whiteboards a short definition of ‘significant’ without using the word in the description. The most common response is significant has a similar meaning to important.
I now ask the students to decide which is the most important, or significant, digit in the number 2533.9. I ask students this because it is important, they take the time to consider why we call approximating numbers in this way ‘rounding to a significant figure’. There are a variety of responses to this question. Some students think it is the 9 because that is what makes it a decimal. Some say it does not have a most important number because they are all equally important. Others explain it is the 2 because it has the highest place value.
I explain to the students that the most significant number is the digit with the highest place value. The proceeding numbers are not considered significant and therefore become zero. However, the most significant number can be rounded up depending on whether the number next to it is five or bigger. I use a number line to explain this as shown in the video below.
As the lesson progresses, we begin to consider the most significant digit of decimal numbers. When rounding a decimal, such as 0.64, to the most significant figure, the 6 is the most significant because the 0 before it has no units of value. We also discuss rounding to two or three significant numbers.
After working through the examples shown in the video at the front of the class, I check the student’s understanding by asking them to attempt some on mini-whiteboards one at a time. I feedback after each attempt and increase the difficulty when they are ready to progress. Students then work independently through the questions on slide 3.
Towards the end of the lesson we discuss how to apply rounding to a significant figure when approximating solutions. I pose the question below to the class.
It is interesting, if not slightly frustrating that two or three students will immediately attempt to calculate the exact answer as they did not read the question. The majority decide to round each number to either one or two significant places then compare their estimate with the exact solution.
In the following lesson students learn how to approximate more complex calculations involving powers and roots by rounding. Learning then progresses onto calculating the limits of accuracy of rounded numbers. Higher students also consider the upper and lower bounds of calculations.
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