Approximation, rounding and estimationIB MYP Maths Extended: Subtopic test

1. 1
   A calculator displays the number $0.0063584$.

   (a)

   Round the number to $3$ significant figures.

   [1 mark]

   • A$0.00636$
   • B$0.00635$
   • C$0.006$
   • D$0.0064$

   (b)

   Round the number to $3$ decimal places.

   [1 mark]

   • A$0.00636$
   • B$0.0064$
   • C$0.007$
   • D$0.006$

   (c)

   Write the number to $2$ significant figures and state how many decimal places your answer has.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   The population of a town is $48\,637$.

   (a)

   Round the population to $2$ significant figures.

   [1 mark]

   • A$48\,000$
   • B$49$
   • C$49\,000$
   • D$48\,600$

   (b)

   Round the population to the nearest hundred.

   [1 mark]

   • A$49\,000$
   • B$48\,600$
   • C$48\,640$
   • D$48\,700$

   (c)

   The council reports the population as $49\,000$. Find the percentage error, giving your answer to $2$ significant figures.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   Consider the calculation $\frac{58.7\times4.12}{0.198}$.

   (a)

   Estimate the value of the calculation by rounding each number to $1$ significant figure.

   [3 marks]

   (b)

   (i) Use a calculator to find the value of the calculation, to $3$ significant figures. (ii) Find the percentage error of the estimate from part (a), where the estimate is $1200$.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A builder in Johannesburg must tile a rectangular floor measuring $4.7$ m by $6.2$ m. Tiles are sold in packs. Each pack covers $1.5$ m$^2$ and costs R$245$.

   (a)

   (i) Estimate the area of the floor by rounding each length to $1$ significant figure. (ii) Find the exact area and the percentage error of your estimate, to $3$ significant figures. (iii) Find the number of packs the builder must buy and justify your answer.

   [6 marks]

   (b)

   The builder buys $20$ packs. (i) Find the exact cost of $20$ packs. (ii) She estimates the cost by rounding the price of a pack to $1$ significant figure. Find her estimate. (iii) Find the percentage error of this estimate, to $3$ significant figures. (iv) Round the price of a pack to $2$ significant figures instead. Find the new estimate and its percentage error, and state, with a reason, which rounding gives the better quote.

   [6 marks]

   Total for question 4: 12 marks

End of questions