MATHEMATICAL LITERACY GRADE 10 CAPS

TOPIC 3: Measurement

Section 3.1: Conversion of units

MeasurementThe following sections will be covered:

3.1 Conversions

3.2 Measuring length and distance

3.3 Measuring weight

3.4 Measuring temperature

3.5 Calculating perimeter and area

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ConversionsIn section 3.1, learners will be able to convert units and carry out calculations with the following units of measurement and time:

⚫ Units of length

⚫ Units of capacity

⚫ Units of mass

⚫ Units of time

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ConversionsConversion within the metric system

⚫ Units of length: mm - cm - m - km

⚫ Capacity: ml – l

⚫ Mass: g – kg – ton

⚫ Time: sec – min – hr – day

⚫ Conversion of the units of measurement using given factors.

⚫ Cooking conversions: -spoon – ml - cup - ml

Conversions

The following table shows how the most commonly used units are related:

Units of length Units of mass

1 mm = 10 cm1 m = 100 cm1 km = 1000 m

1 g = 1000 mg1 kg = 1000 g1 tonne = 1000 kg

Units of Capacity Units of time

1l = 1000 ml1kl = 1000 l

1 min = 60 seconds1 hour = 60 min1 day = 24 days

ConversionsTo convert from a larger unit to a smaller unit:

⚫ Multiplication by a given factor usually some power of 10 must occur.

To convert from a smaller unit to a larger unit:

⚫ Division by a given factor usually some power of 10 must occur.

Conversions

Example 1

Convert:

1. 4 cm to mm, 2. 9 m to cm

3. 5 km to m 4. 4000 m to km

5. 650 cm to m 6. 17 mm to cm

Solutions: Example 1

1. 4 cm = 4 x 10 mm = 40 mm

2. 9 m = 9 x 100 cm

= 900 cm

3. 5 km = 5 x 1000 m = 5000 m

Remember:To convert to

small unit, multiply by

the conversion

factor

Solutions: Example 14. 4 000 m = 4 000 ÷ 1 000 km

= 4 km

5. 650 cm = 650 ÷ 100 m = 6,5 m

6. 17 mm = 17 ÷ 10 cm= 1,7 cm

Remember:To convert to a

large unit, divide by the conversion

factor

Activity 1Convert:1. 20 kg to g

2. 2,75 tonnes to kg

3. 22 000 g to kg

4. 4. 3 000 kg to tonnes

Solutions: Activity 11. 20 kg = 20 x 1000 g

= 20 000 g

2. 2,75 tonnes = 2,75 x 1000 kg = 2 750 kg

3. 22 000 g = 22 000 ÷ 1000 kg = 22 kg

4. 3000 kg = 3000 ÷ 1000 t = 3 t

Household measuring instruments

Household measures of capacityHousehold measuring utensils include sets of measuring spoons: tablespoon, teaspoon and cup. All household measures are approximations:

⚫ A cup is about 250 ml

⚫ A tablespoon is about 15 ml

⚫ A teaspoon is about 5 ml

Household measures of capacity Examples:1. Determine how many cups of milk are needed to fill a 1 litre

jug.2. How many teaspoons would you use to measure 35 ml ?

Answers:1. 1 l ÷ 250 ml

=1 000 ml ÷ 250 ml =4 cups

2. 35 ml ÷ 5 ml= 7 teaspoons

1 cup = 250 ml; Convert to the

same unit

Example 2Convert:

1. 5 days to hours.

2. 3 hours to minutes

3. 45 minutes to seconds.

4. 900 seconds to minutes

5. 240 minutes to hours

6. 168 hours to days

Solution: Example 21. 5 days = 5 x 24

= 120 h

2. 3 hours = 3 x 60 mins = 180 mins

3. 55mins = 45 x 60 seconds = 2 700 s

Solution: Example 24. 900 s = 900 ÷ 60 mins

= 15 mins

5. 240 mins = 240 ÷ 60 hours = 4 hours

6. 168 hours = 168 ÷ 24 days = 7 days

TimeWe use two systems to show time:⚫ The 12-hour clock and

⚫ The 24-hour clock.

In the 12-hour clock, the day is divided into two 12-hour time periods:o from midnight to noon, referred to as a.m.

o from noon to midnight, referred to as p.m.

Time

TimeIn the 24-hour clock, time is measured in a single 24-hour period, starting from midnight.

READING TIME

Time is expressed in ways or formats:o The analogue and

o The digital system.

TimeExample: Express half past nine in the morning: (a) as analogue time, (b) as digital time.

Answers: (a)9.30 a.m. (b)09:30

Examples (cont.)

Time in words Analogue Time Digital Timemidnight 12. a.m. 00: 00

noon 12. p.m. 12:00 hr

Twenty five past midnight 12.25 a.m. 00: 25 hr

Twenty five past midday 12.25 p.m. 12:25 hr

6 o’clock in the morning 6. a.m. 06:00hr

6 o’clock in the evening 6. p.m. 18: 00hr

10 o’ clock in the morning 10. a.m. 10: 00hr

Elapsed Time⚫ Watches and clocks are accurate for determining duration of

time for long journeys or TV programmes.

⚫ For the duration of 100 m race, a stop watch will be more accurate.

⚫ Athletes need to be more accurate and often have to determine time elapsed in hours, minutes, seconds and also parts of a second.

Activity 21. A race started at 08:45. The first athlete crossed the finish

line at 10:52. How long did he take to finish the race?

2. Banana bread requires baking time of 1 hour 40 minutes. It is put in oven at twenty five past eleven in the morning. What time will it be ready?

Solutions: Activity 2

1. Time taken = Finishing time – starting time = 10: 52 – 08: 45

= 2 h 7 mins

2. H min11 25 1 40 +13 05

It will be ready at 1:05 p.m. or 13: 05

Final Assessment Questions

Question 1 6 km in metres is:

A. 0,006 m

B. 0,06

C. 600 m

D. 6000m

Question 2 To convert m to mm

A. multiply by 100

B. multiply by 1000

C. divide by 10

D. divide by 100

Question3 900 cm in m,

A. 0,09 m

B. 9 m C. 90 m

D. 90 000m

Question 43 420 mm in m

A. 3,42 m

B. 34,20 m

C. 342,0 m

D. 342 000 m

Question 53,5 l in ml is

A. 0,035 ml

B. 35 ml

C. 350 ml

D. 3 500 ml

Question 6250 ml in l is

A. 0,5250 l

B. 5,250 l

C. 52,50 l

D. 525,0 l

Question 7A recipe requires 375 ml of milk. How many cups are needed?

A. 1,5

B. 5

C. 15

D. 37,5

Question 81 tonne =

A. 10 kg

B. 100 kg

C. 500 kg

D. 1000kg

Question 9

1 750 g =

A. 1 kg 75g

B. 1 kg 750g

C. 17kg 50g D. 175kg

Question 1025 past 2 in the morning in digital 24-hour format is

A. 2:25a.m

B. 2:25p.m.

C. 02:25

D. 14:25

Solutions: Final Assessment Questions1. B2. B3. A4. D5. B6. A7. D8. D9. B

10. C