Teach Me Maths

Metric Unit Conversions

Question 11 mark

Which unit is most suitable for recording the mass of a bag of flour?

Hint

Decide whether mass, capacity, distance or time is being measured.

Worked solution

Which unit is most suitable for recording the mass of a bag of flour?

  1. kilograms
  2. litres
  3. kilometres
  4. minutes
  1. Flour has a mass. Kilograms measure mass; litres measure capacity, kilometres measure distance and minutes measure time.

Question 21 mark

Convert 3.6 m to centimetres.

Hint

There are 100 centimetres in one metre.

Worked solution

Convert 3.6 m to centimetres.

  1. 3.6\times100=360, so the length is 360 cm.

Question 31 mark

Convert 75 mm to centimetres.

Hint

Each centimetre contains 10 millimetres.

Worked solution

Convert 75 mm to centimetres.

  1. 75\div10=7.5, so the length is 7.5 cm.

Question 41 mark

Convert 2.4 km to metres.

Hint

There are 1000 metres in one kilometre.

Worked solution

Convert 2.4 km to metres.

  1. 2.4\times1000=2400 m.

Question 51 mark

Convert 950 g to kilograms.

Hint

A kilogram is a larger unit than a gram.

Worked solution

Convert 950 g to kilograms.

  1. 950\div1000=0.95 kg.

Question 61 mark

Convert 0.075 kg to grams.

Hint

Multiply by the number of grams in one kilogram.

Worked solution

Convert 0.075 kg to grams.

  1. 0.075\times1000=75 g.

Question 71 mark

Convert 3.25 litres to millilitres.

Hint

There are 1000 millilitres in one litre.

Worked solution

Convert 3.25 litres to millilitres.

  1. 3.25\times1000=3250 ml.

Question 81 mark

Convert 640 ml to litres.

Hint

Divide by the number of millilitres in one litre.

Worked solution

Convert 640 ml to litres.

  1. 640\div1000=0.64 litre.

Question 91 mark

Convert 1 hour 45 minutes to minutes.

Hint

Convert the whole hour first, then add the other minutes.

Worked solution

Convert 1 hour 45 minutes to minutes.

  1. 1 hour =60 minutes.
  2. 60+45=105 minutes.

Question 101 mark

Convert 2.3 hours to minutes.

Hint

The decimal part of an hour is a fraction of 60 minutes.

Worked solution

Convert 2.3 hours to minutes.

  1. 2.3\times60=138 minutes.
  2. Alternatively, two hours is 120 minutes and 0.3 hour is 18 minutes; 120+18=138.

Question 112 marks

A shelf is 0.84 m wide. A box is 79 cm wide. How many centimetres wider is the shelf than the box?

Hint

Put both widths in centimetres before subtracting.

Worked solution

A shelf is 0.84 m wide. A box is 79 cm wide. How many centimetres wider is the shelf than the box?

  1. 0.84\times100=84 cm.
  2. 84-79=5 cm, so the shelf is 5 cm wider.

Question 123 marks

A sack contains 4.5 kg of sand. After 1750 g is used, how many kilograms remain?

Hint

Convert the masses to one common unit, then give the final answer in kilograms.

Worked solution

A sack contains 4.5 kg of sand. After 1750 g is used, how many kilograms remain?

  1. 4.5 kg =4500 g.
  2. 4500-1750=2750 g.
  3. 2750\div1000=2.75 kg remain.

Question 133 marks

There are 2.4 litres of juice. Each cup holds 180 ml. What is the greatest number of completely full cups that can be filled?

Hint

Convert litres to millilitres and check whole numbers of cups.

Worked solution

There are 2.4 litres of juice. Each cup holds 180 ml. What is the greatest number of completely full cups that can be filled?

  1. 2.4 litres =2400 ml.
  2. 13\times180=2340 ml, while 14\times180=2520 ml.
  3. There is enough for 13 full cups but not 14, so the answer is 13.

Question 142 marks

A running route has a 3.6 km section followed by an 850 m section. What is its total length in kilometres?

Hint

Convert the shorter section to kilometres before adding.

Worked solution

A running route has a 3.6 km section followed by an 850 m section. What is its total length in kilometres?

  1. 850\div1000=0.85 km.
  2. 3.6+0.85=4.45 km.

Question 153 marks

A workshop starts at 08:45 and lasts 1.6 hours. Give its finishing time using a 24-hour clock.

(a)

What is the hour part of the finishing time?

2 marks

(b)

What is the minute part of the finishing time?

1 mark

Hint

Convert the decimal part of the duration to minutes, then add to the start time.

Worked solution

A workshop starts at 08:45 and lasts 1.6 hours. Give its finishing time using a 24-hour clock.

Part (a)

What is the hour part of the finishing time?

  1. 0.6\times60=36 minutes, so the workshop lasts 1 hour 36 minutes.
  2. 08:45 plus 1 hour is 09:45; plus 36 minutes is 10:21. The hour part is 10.

Part (b)

What is the minute part of the finishing time?

  1. From 09:45, 15 minutes reaches 10:00. The remaining 36-15=21 minutes reaches 10:21. The minute part is 21.

Question 16Challenge4 marks

A roll contains 8 m of ribbon. Making each bow uses 35 cm of ribbon, and an extra 2 cm is discarded for each bow. After making 18 bows, how many metres of ribbon remain?

Hint

Include the discarded length for every bow and use a common unit.

Worked solution

A roll contains 8 m of ribbon. Making each bow uses 35 cm of ribbon, and an extra 2 cm is discarded for each bow. After making 18 bows, how many metres of ribbon remain?

  1. Each bow uses 35+2=37 cm including waste.
  2. Eighteen bows use 18\times37=666 cm.
  3. The roll contains 8\times100=800 cm, so 800-666=134 cm remain.
  4. 134\div100=1.34 m remain.

Question 17Challenge4 marks

Three full bottles each contain 1.5 litres of water. Twelve cups each receive 275 ml. How many litres of water are left?

Hint

Find the total supply and total used in matching units.

Worked solution

Three full bottles each contain 1.5 litres of water. Twelve cups each receive 275 ml. How many litres of water are left?

  1. The bottles contain 3\times1.5=4.5 litres, or 4500 ml.
  2. The cups use 12\times275=3300 ml.
  3. 4500-3300=1200 ml remain.
  4. 1200\div1000=1.2 litres remain.

Question 18Challenge3 marks

A parcel must have a total mass no greater than 2.5 kg. Its box and existing contents have a combined mass of 2040 g. Each extra mug has a mass of 230 g. What is the greatest number of extra mugs that can be added?

Hint

Find the mass allowance left in grams before dividing by one mug’s mass.

Worked solution

A parcel must have a total mass no greater than 2.5 kg. Its box and existing contents have a combined mass of 2040 g. Each extra mug has a mass of 230 g. What is the greatest number of extra mugs that can be added?

  1. 2.5 kg =2500 g.
  2. The remaining allowance is 2500-2040=460 g.
  3. 460\div230=2, so at most 2 extra mugs can be added. With two mugs the mass is exactly the allowed 2500 g.

Question 19Challenge4 marks

A worker plans a 1.25-hour job, a 20-minute break and a 55-minute job. The available time is 2.4 hours. By how many minutes does the plan exceed the available time?

Hint

Convert every duration to minutes before comparing totals.

Worked solution

A worker plans a 1.25-hour job, a 20-minute break and a 55-minute job. The available time is 2.4 hours. By how many minutes does the plan exceed the available time?

  1. 1.25\times60=75 minutes and 2.4\times60=144 minutes.
  2. The plan takes 75+20+55=150 minutes.
  3. 150-144=6, so the plan exceeds the available time by 6 minutes.

Question 20Challenge4 marks

Juice A costs £1.35 for a 750 ml bottle. Juice B costs £3.40 for a 2-litre bottle.

(a)

Which juice is better value for money?

1 mark

(b)

How many pence are saved by buying 6 litres of the better-value juice instead of 6 litres of the other juice?

3 marks

Hint

Compare prices for the same amount of juice. You could use one litre or another convenient amount.

Worked solution

Juice A costs £1.35 for a 750 ml bottle. Juice B costs £3.40 for a 2-litre bottle.

Part (a)

Which juice is better value for money?

  1. Juice A
  2. Juice B
  3. They are the same value.
  1. One litre of A costs 1.35\div0.75=£1.80. One litre of B costs 3.40\div2=£1.70.
  2. Juice B is better value because the same volume costs less.

Part (b)

How many pence are saved by buying 6 litres of the better-value juice instead of 6 litres of the other juice?

  1. 6 litres is 6000 ml. For A, 6000\div750=8 bottles cost 8\times1.35=£10.80.
  2. For B, 6\div2=3 bottles cost 3\times3.40=£10.20.
  3. The saving is 10.80-10.20=£0.60, or 60 pence.
  4. Alternatively, B saves 10 pence per litre, so the saving for 6 litres is 6\times10=60 pence.

More on this topic: Metric Unit Conversions worksheet with full solutions

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