# Rounding to a significant figure

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.

## What makes something significant?

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.

## Rounding to a significant figure

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.

## Rounding decimals to a significant number

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.

## Assessing progress and applying the new skill

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.

## Applying rounding to a significant number in future lessons

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.

## Revising Limits of Accuracy and Error Intervals

Students revise how to find the limits of accuracy for...

## Making Approximations using Rounding

Students learn how make approximations by rounding numbers to one...

## Rounding Numbers to a Significant Figure

Students are introduced to rounding numbers to a significant figure....

## Rounding to a Decimal Place

Students learn how to round a number to a given...

This site uses Akismet to reduce spam. Learn how your comment data is processed.

### Mr Mathematics Blog

#### Getting Ready for a New School Year

When getting ready for a new school year I have a list of priorities to work through. Knowing my team have all the information and resources they need to teach their students gives me confidence we will start the term in the best possible way.  Mathematics Teaching and Learning Folder All teachers receive a folder […]

#### Mathematics OFSTED Inspection – The Deep Dive

Earlier this week, my school took part in a trial OFSTED inspection as part of getting ready for the new inspection framework in September 2019. This involved three Lead Inspectors visiting our school over the course of two days. The first day involved a ‘deep dive’ by each of the Lead Inspectors into Mathematics, English […]

#### How to Solve Quadratics by Factorising

The method of how to solve quadratics by factorising is now part of the foundational knowledge students aiming for higher exam grades are expected to have.   Here is an example of such a question. Solve x2 + 7x – 18 = 0 In my experience of teaching and marking exam papers students often struggle with […]