Units of Length. S1 Revision Notes on Length

S1 Revision Notes on Length Units of Length The metric units of length are ... Remember: 1cm = 10 mm 1 metre = 100cm 1 km = 1000 metre Sometime...
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S1 Revision Notes on Length Units of Length

The metric units of length are ...

Remember: 1cm = 10 mm

1 metre = 100cm

1 km = 1000 metre

Sometimes you need to estimate the length of something when measuring or drawing:

You also need to be able to measure and draw lengths accurately using the following measuring instruments: a ruler for smaller lengths in cm and mm or ... a metre stick or trundle wheel for longer lengths in metres

Converting metric lengths You also need to be able to convert lengths from one metric unit to another:

Some examples: mm and cm conversions

cm and metre conversions

metre and km conversions

3.5cm = 3.5 x 10 = 35mm

6.55metres = 6.55 x 100 = 655cm

3.85km = 3.85x1000=3850m

48mm = 48 ÷ 10 = 4.8cm

745cm = 745 ÷ 10 = 7.45m

4255m=4255÷1000 = 4.255km

Here are a few more examples on calculation of perimeter:

Per = 10+7+5+14 = 36cm

per = 12+15+20+16 =63mm per= 2.8+3.4+3.8+3+3.2 = 16.2

For rectangles you have to remember that the opposite sides are equal in length ...

... so perimeter = 20 + 11 + 20 + 11 = 62cm

Sometimes you have to find the length of a missing side when given the perimeter like in these examples ...

Total of 2 sides is 10+9=19cm

Total of 3 sides is 9.3+8.1+9.4=26.8cm

So missing side is 30-19 = 11cm

so missing side is 40-26.8 = 13.2cm

Word Problems Sometimes you have to solve a word problem involving perimeters like this one:

David is putting up a fence round his garden and has bought fencing for the sides shown in her sketch below. He has measured the garden accurately and knows that it has a perimeter of 25m not including the gate. (a) How much fencing does he need to buy for section A to the nearest cm?

6m

3m

A

4m 7m

Solution: You need to add all the lengths given which is 7+4+3+6=20metres You now subtract 20 metres from the total perimeter of 25 metres. 25m – 20m = 5metres. So length A must be 5 metres

(b) Fencing is sold in 2 metre lengths which cost £8.75 per length. How much will the extra fencing cost him? Solution: David needs 5 metres of fencing so you will need to buy 3 x 2metre lengths. This will cost 3 x £8.75 = £26.25

S1 Revision Questions 1 - Length Converting metric units Please attempt the questions below at the appropriate level: 2nd Level Questions Convert these lengths into cm and mm: 1. 30 mm

2.

3. 58 mm

Convert into mm: 4. 4 cm

5.

3cm 6mm

6. 6cm 7mm

Convert these lengths into m and cm: 7. 140cm

8. 345cm

9. 65cm

Convert these lengths into cm: 10. 1m 45cm

11. 4m80cm

12. 8m93cm

13. Arrange in order of length, shortest first: 46mm, 4cm4mm, 2cm1mm, 36mm, 4cm 3rd Level Questions Convert these lengths into cm leaving answers as decimals: 1. 16mm

2. 48mm

3. 138mm

Convert these lengths into mm: 4. 5.7cm

5. 13.4cm

6. 25cm5mm

Convert these lengths into metres leaving answers as decimals: 7. 1m 35cm

8. 784cm

9. 1385cm

Convert these lengths into cm: 10. 2.45m

11. 7m40cm

12. 14.3m

Convert these lengths into km leaving answers as decimals: 13. 2400m

14. 1345m

15. 11 500m

Convert these lengths into metres: 16. 2km 250m

17. 6.38km

18. 7.455km

19. Arrange in order of length, smallest first: 1850m, 1.5km, 2435m, 1km163m, 3100m

4th Level Questions Convert these lengths into cm leaving answers as decimals: 1. 14cm 6mm

2. 8mm

3. 138mm

4. 2m 264mm

7. 7.25m

8. 14km

Convert these lengths into mm: 5. 18.8cm

6. 4.3m

Convert these lengths into metres leaving answers as decimals: 9. 18m 15cm

10. 5m 4cm

11. 3m 4mm

12. 1400mm

15. 3.6km

16. 11km125m

Convert these lengths into cm: 13. 16.5m

14. 80m

Convert these lengths into km leaving answers as decimals: 17. 4200m

18. 145m

19. 6m

20. 14 128m

23. 4200mm

24. 230mm

Convert these lengths into metres: 21. 1570cm

22. 14.75km

25. Arrange in order of length, smallest first: 195cm, 0.002km, 2250mm, 2.65m, 0.0016km

1 Week to ask your teacher for help so please do so

S1 Revision Questions 2- Length

Perimeter Please attempt the questions below at the appropriate level: 2nd Level Questions Find the perimeter of these shapes: 1.

5cm

2.

4cm

3. 6cm

6cm

2 m 3 m

3 m

3cm

2m

Find the missing length in these shapes with the perimeter given: 4. perimeter = 24cm

7cm

5.

Perimeter = 26m ?m

6cm

6cm

5m

1m

? cm

4m 2m

9m

5. Zoe knows the badminton court has a perimeter of 36 metres. She measures the length and finds that it is 13metres long. Can you work out its breadth? 13 metres

?m

3rd Level Questions Find the perimeter of these shapes, giving you answer using the appropriate units. Find the missing sides first if necessary. 1.

2.

9cm

4.9cm 6cm 2.3cm

4cm2mm

6.7cm

3.

3cm

3cm

4m 30cm

4.

4.75m

2.55m

5m35cm

3.4m

6m 5. Sara is putting up a fence round her garden and has bought fencing for the sides shown in her sketch below. She has measured the garden accurately and knows that it has a perimeter of 40.5m not including the gate. (a) How much fencing does she need to buy for section A to the nearest cm? 13.6m

A

5.05m

535cm

gate

12m45cm

(b) Fencing is sold in 2 metre lengths which cost £6.75 per length. (i) How many lengths extra lengths does she need to buy to fence section A? (ii) How much will the extra fencing cost her?

4th Level Questions Find the perimeter of these shapes, giving you answer using the appropriate units. Find the missing sides first if necessary. 1.

2.

6.345km

5.75m 5.15km 362cm

4m35cm

5.5m 3.

2.35km

3250m

46cm

4.

365mm

0.35m

5.15km

2km215m

64.2cm 5. A local council is putting a new fence round a park and has bought fencing for the sides shown. They know that the park has a perimeter of 5.25km. (a) How much fencing do they still need to buy for section A? 2.15km

A

505m

465m 3km145m

(b) Fencing is sold in 100 metre lengths which cost £2850 per length and can only been bought in whole lengths. (i) How many 100m lengths does the council need to buy to fence section A? (ii) How much will the extra fencing cost the council?

1 Week to ask your teacher for help so please do so