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Number and Algebra

Decimal Places

This is another way of giving an answer to a certain degree of accuracy.

One decimal place means to the nearest tenth

Two decimal places means to the nearest hundredth and so on.

The same rule applies as with significant figures in that if you are asked to give the answer correct to x decimal places, then you look at the (x+1)^th decimal place and if the number is less than five then the x^th value remains the same but if it is five or more then you increase the x^th value by one.

Example: Give the following numbers correct to two decimal places.

1. 35.6435 ≈ 36.64

2. 35.6465 ≈ 36.65

Percentage Error

Obviously if we are approximating numbers that we use in calculations then there is going to be a difference between the answer we get by using the approximated values and the answer we would have got if we had used the exact values. In the IB we express this difference as the percentage error.

Percentage error =

Where are the approximated value and the exact value?

Examples

1. A rectangle has sides 3.525 cm by 8.765 cm.
   Calculate the exact area of the rectangle

   Answer: Area = 3.525 x 8.765 cm² = 30.896625 cm²

2. Calculate the area of the rectangle after rounding the dimensions to one decimal place.

   Answer: Area = 3.5 x 8.8 cm² = 26.4cm²

3. Calculate the percentage error of the area in rounding the dimensions to one decimal place. Give your percentage error to one decimal place.

   Answer:

   Percentage error = = -14.4%

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