Succeed with maths: part 2
Succeed with maths: part 2

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2.1 Mass: SI units

Unlike all the other SI base units, the base unit for mass has a prefix. You may have noticed that in Week 1, when you looked at the summary of the seven SI base units.

The base unit for mass in the SI is the kilogram (abbreviated to ‘kg’), not the gram as you may have logically thought. However, the gram can be seen as the base unit from the point of view of adding prefixes to produce the other units.

Adding the prefixes gives the milligram (mg), as well as the kilogram (kg). Note that you could have a centigram as well, but this is not a unit that is commonly used.

Use your knowledge from the previous section on length in this next short activity.

Activity _unit3.2.1 Activity 1 SI units of mass

Timing: Allow approximately 5 minutes
  • a.What would you need to do to convert from kilograms (kg) to grams (g)?


Kilo means a thousand, so kilogram is the same as saying 1000 grams.

Hence to convert from kilograms to grams you should multiply by 1000.

  • b.What would you need to do to convert from grams (g) to milligrams (mg)?


Milli means a thousandth, so milligram is the same as saying a thousandth of a gram. This means that 1 gram = 1000 milligrams.

Hence, to convert from grams to milligrams you should multiply by 1000.

  • c.What would you need to do to convert from grams (g) to kilograms (kg)?


From part (a) to convert from kilograms to grams you needed to multiply by 1000, so the opposite must be true to convert from grams to kilograms.

Hence, to convert from grams to kilograms you should divide by 1000.

The findings from this activity can be summarised as:

  • kilograms (kg) to grams (g) – multiply by 1000
  • grams (g) to kilograms (kg) – divide by 1000
  • grams (g) to milligrams (mg) – multiply by 1000
  • milligrams (mg) to grams (g) – divide by 1000.

Use this information to help you in the next activity, as well as the steps from Week 1 to convert between different units. These are summarised again here for you:

  1. Find out how the two units are related to each other – the conversion factor.
  2. Ask yourself if the final answer should be bigger or smaller than the original value.
  3. Divide or multiply by the conversion factor to get your answer.

You can click on ‘reveal comment’ if you would like some additional guidance.

Activity _unit3.2.2 Activity 2 Everyday mass

Timing: Allow approximately 10 minutes
  • a.During a shopping trip you buy 1.5 kg of apples, 450 g of bananas and 0.75 kg of pears. How much fruit in grams have you bought altogether?


Remember that 1 kg = 1000 g.


  • a.As there is a mixture of different units, start by converting all the units into the same one. The final answer should be in grams, so it makes sense to convert all the masses into grams to start with.

    one kg equals 1000 g

    multiline equation line 1 Mass of apples equals open 1.5 multiplication 1000 close g times line 2 equals 1500 g

    multiline equation line 1 Mass of pears equals open 0.75 multiplication 1000 close g line 2 equals 750 g

    left parenthesis Mass of bananas equals 450 g right parenthesis

    So, multiline equation line 1 total weight of fruit bought equals 1500 g plus 750 g plus 450 g line 2 equals 2700 g

  • b.One batch of mortar mix required for building a brick wall requires 250 g of cement and 750 g of sand. If you need 5 batches to finish the wall, how much sand and cement will you need and what is the total mass in kilograms?


  • b.multiline equation line 1 Cement required equals five multiplication 250 g equals 1250 g

    multiline equation line 1 Sand required equals five multiplication 750 g equals 3750 g

    multiline equation line 1 Total mass of sand and cement equals 1250 g plus 3750 g equals 5000 g

    one kg equals 1000 g

    This time you need to divide by 1000 to convert from g to kg

    So, multiline equation line 1 total mass equals open 5000 division 1000 close kg equals five kg

  • c.The daily recommended intake of vitamin C in the UK for adults is 0.04 g. Convert this to milligrams, the more usual way to quote this value.


  • c.1 milligram (mg) is a thousandth of a gram.

    This tells us that:

    one g equals 1000 mg

    So, the multiline equation line 1 daily recommended intake equals open 0.04 multiplication 1000 close mg line 2 equals 40 mg

As with length, imperial units for mass are not quite as straightforward as the SI units. So, you may need to take your time over this next section.

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