# Unit 19 Section 1 : Measuring Lengths In this section we consider which units to use and the errors made when measuring lengths.

We need to be able to use millimetres (mm), centimetres (cm), metres (m) and kilometres (km).

## Appropriate Units

Work out which unit of length (mm, cm, m or km) would be most appropriate for measuring each item below, then click to see whether you are correct. (b) The height of a block of flats? (c) The length of your foot? (d) The thickness of your maths book? (e) The distance between your school and the nearest other school? ## Errors in measurement

It is difficult to measure any length completely accurately.
When we measure a person's height, we normally measure it to the nearest centimetre.

Example
A person's height was measured as 163cm (to the nearest cm).
What range of values could that person's actual height have been? The height must be 162.5 cm or more because a lower height would have rounded down to 162 cm.
The height must be less than 163.5 cm because 163.5 cm would have been rounded up to 164 cm.

The lowest possible height would have been 162.5 cm. We call this the lower bound.
The actual height must have been less than 163.5 cm. We call this the upper bound.

Practice Question
A line is measured to the nearest centimetre as 12 cm.

(a) What is the shortest possible length of this line? (b) What length must the actual length of the line be less than? ## Exercises

Work out the answers to the questions below and fill in the boxes. Click on the button to find out whether you have answered correctly. If you are right then will appear and you should move on to the next question. If appears then your answer is wrong. Click on to clear your original answer and have another go. If you can't work out the right answer then click on to see the answer.

Question 1
Which unit of length would be the most appropriate if you were measuring:
(a) the distance between two towns?  (b) the length of your classroom?  (c) the length of your calculator?  (d) the width of your finger?  (e) the height of your house?  Question 2
Are each of the following statements likely to be true or false?
(a) John's height is 242 cm.  (b) The height of a desk is 1.7 m.  (c) The height of a door is 190 cm.  (d) The length of a football pitch is 800 m.  (e) The length of a finger is 8 cm.  (f) The thickness of a piece of paper is 1 mm.  Question 3
The length of a line is measured as 10 cm, to the nearest cm.

(a) What is the shortest length the line could actually be?
The lower bound for the actual length is cm  (b) What length must the actual length be less than?
The upper bound for the actual length is cm  Question 4
The length of a pen is measured as 16cm, to the nearest cm.

What is the minimum possible length of the pen?
cm  Question 5
The distance between two airports is 1700 km, correct to the nearest 100 km.

(a) What are the lower and upper bounds for the actual distance?
Lower bound = km  Upper bound = km  (b) What would the lower and upper bounds be if the length had been correct to the nearest 10 km?
Lower bound = km  Upper bound = km  Question 6
The end of Andy's tape measure is broken, and all the distances that he measures are 1 cm shorter than he thinks.

How significant is this error when he measures:
 (a) 5 cm Very significant Not very significant  (b) 5 m Very significant Not very significant  (c) 20 cm Very significant Not very significant  (d) 1 m Very significant Not very significant  You have now completed Unit 19 Section 1
 Your overall score for this section is Correct Answers You answered questions correctly out of the questions in this section. Incorrect Answers There were questions where you used the Tell Me button. There were questions with wrong answers. There were questions you didn't attempt.
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