This is a concept that always comes up in examinations. You will be asked to round your answers to a certain number of significant figures or decimal places. So, it is an important skill to get right.

The IB expect all your answers, unless otherwise stated, to be given to three significant figures. Often, your calculator will give you a very long answer, maybe 6 decimal places long, please do not write this down as your answer. Round it to 3 significant figures.

__Estimation and Approximation__

You may be used to hearing these terms as we tend to use them in our everyday language. We often use them interchangeably however, they do have different meanings in maths.

### To Do

Create a unit cover page in your maths journal:

include the title - Estimation and Approximation

write a definition for the words

and__estimation____approximation__leave room on the bottom half to add a contents list when you finish the unit.

__Decimal Places__

When asked to use decimal places to round an answer the numbers you are interested in are the ones after the decimal place. Find the decimal point and count the required numbers after it and then decide if you need to round up or not.

For example - 34.0235 rounded to 2 decimal places (d.p.) is 34.02.

Rounded to 3 d.p. is 34.024.

When deciding whether or not to round up you need to look at the digit after the one you are rounding to. If the digit is 5 or more then you round up if it is less you leave the number the same. In the example above, 34.02 stays the same because the digit after the 2 is less than 5 but 34.024 rounds up because the digit after the 3 is 5 or greater.

This is a skill you will already have developed earlier in your maths education. However, it is very important you can round accurately. We round numbers to decimal places to improve the ** precision **of the answer.

### To Do

In your maths journal write a definition for the precision of a number.

Here is a Maths with Mr J video - How to round decimals.

### Practice

__Significant Figures__

Significant figures or digits are the digits in a number that carry meaning. Rounding to significant figures improves the ** accuracy** of the answer. There are rules you can use to decide if a number is significant or not.

### Rules

All non-zero digits are significant figures.

All zeros between non-zero digits are significant.

Zeros to the left of an implied decimal point are

Â significant.__not__Zeros to the right of an implicit decimal point

Â significant.__are__Leading zeros to the right of a decimal point are

Â significant.__not__Zero following non-zero digits to the right of the decimal point

significant.__are__

Examples -

679234 has 6 s.f. 546.39214 has 8 s.f.

7356009204 has 10 s.f. 105.034 has 6 s.f.

26 000 has 2 s.f. 26 000.0 has 6 s.f.

0.0083 has 2 s.f. 0.00830000 has 6 s.f.

### To Do

In your maths journal:-

write a definition for the accuracy of a number.

under your definitions, journal what you know about rounding to decimal places and significant figures giving examples.

### Practice

__Percentage Error__

Percentage error is used to measure the accuracy of an estimate or approximation by comparing it to the actual value. It quantifies the discrepancy between the actual value and the estimate in the form of a percentage.

### Formula

The ** approximate** value minus the

**value. Divide this by the**

__exact__**value and multiply the answer by 100. This will always give a positive answer.**

__exact__This formula is in your booklet.

VA = approximate value

VE = Exact Value

Watch OSC - Percentage error.

### Practice

Complete the worksheet below.

### To Do

Add a page to your maths journal for percentage error including:

title

formula

examples

__Upper and Lower Bounds__

If you are working with rounded numbers it is important to remember that any calculations with these numbers are just estimates of the actual value. This being the case, it is often helpful to state the largest and smallest number that the value could be. This is called finding the upper or lower bounds of a value.

### To Do

Watch the video by 1st Class Maths and create a journal page explaining how to find the upper and lower bounds of a number and the rules for the four operations.

### Practice

__Standard Form or Scientific Notation.__

When you are working with very large or very small numbers it is helpful to have a more compact way of writing them. The system we use is standard form also known as scientific notation.

This system writes a number as a product of a coefficient and a power of ten. The coefficient is a number between 1-9. The power of ten is an integer that represents how many places you need to move the decimal point to get the original number.

### Practice

__Khans Academy -__ Grade 8 Unit 1 working with powers of ten all the way to the end of Quiz 4.

### To Do

Journal what you know about standard form and add the titles of the pages you completed for this unit to your title page as a contents list.

If you have a textbook, now is a good time to look at it. Read through the information related to the unit and have a go at the questions. If you get stuck come back and look at the material again or try searching for help online, I link to some great content providers throughout the course.

Go to your syllabus, highlight the area you have completed. Then go to your progress sheet and complete it for this unit of work, note any difficulties, tasks you want to go back to in the future and any helpful sites/books you have used.

That is it! The unit is completed, well done!

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