Chapter 7: Accuracy, error and surds

When a question involves upper and lower bounds, you might need to give our answer to an appropriate degree of accuracy

You can use this strategy

Calculate the lower bound for the answer

Calculate the upper bound for the answer

Choose the most accurate value that both bounds would round to

Choose an answer that both bounds will round to

Check 2 significant figures

When you are told that values in the question have been rounded, there is a good chance that you will have to work with bound, you can score some marks on these questions just by writing down the upper and lower bounds of the rounded values

If you need to write an error interval, you should use inequalities to show the lower and upper bounds for a rounded value

You can give exact answers to calculations by leaving some numbers as square roots

This square has a side length of /10cm

You can’t write /10 exactly as a decimal numbers

It is called a surd

These are the most important rules to remember when dealing with surds

/ab = /a x /b

/a / b = /a /

Rationalising the denominator of a fraction means making the denominator a whole number

You can do this by multiplying the top and bottom of the fraction by the surd part in the denominator

Most surd questions ask you to write a number or answer in a certain form

This means you need to find integers for all the letters in the expression

Simplify /180 + /20 +/5^3

Simplify /60 + /45

When a question involves upper and lower bounds, you might need to give our answer to an appropriate degree of accuracy

You can use this strategy

Calculate the lower bound for the answer

Calculate the upper bound for the answer

Choose the most accurate value that both bounds would round to

Choose an answer that both bounds will round to

Check 2 significant figures

When you are told that values in the question have been rounded, there is a good chance that you will have to work with bound, you can score some marks on these questions just by writing down the upper and lower bounds of the rounded values

If you need to write an error interval, you should use inequalities to show the lower and upper bounds for a rounded value

You can give exact answers to calculations by leaving some numbers as square roots

This square has a side length of /10cm

You can’t write /10 exactly as a decimal numbers

It is called a surd

These are the most important rules to remember when dealing with surds

/ab = /a x /b

/a / b = /a /

Rationalising the denominator of a fraction means making the denominator a whole number

You can do this by multiplying the top and bottom of the fraction by the surd part in the denominator

Most surd questions ask you to write a number or answer in a certain form

This means you need to find integers for all the letters in the expression

Simplify /180 + /20 +/5^3

Simplify /60 + /45