Chapter 7: Accuracy, error and surds

Solving accuracy questions

• 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

Problem solved

• Choose an answer that both bounds will round to

• Check 2 significant figures

Examiners report

• 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

Error intervals

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

Exact answers

• 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

Rules for simplifying square roots

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

  • /ab = /a x /b

  • /a / b = /a /

Rationalising the denominator

• 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

Good form

• 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

Practice questions

• Simplify /180 + /20 +/5^3

• Simplify /60 + /45