# Understand Metric Units of Mass

In this worksheet, students will practise converting between four units of mass measurement (kilogram, centigram, milligram and gram) by finding a conversion factor and deciding whether to multiply or divide by this to find an equivalent amount.

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR

Difficulty level:

### QUESTION 1 of 10

There are a number of units that can be used to describe mass, from pounds, ounces and tonnes to stones and grams.

We are going to focus on the most common of these which is the metric measurement Grams.

All of the units you will have heard of are based around the root word 'gram' with other words tacked on to describe their relationships:

Kilogram - 'Kilo' means 1000 so 1 kg = 1000 g

Centigram - 'Centi' means 100 so 1 cg = 100 g (This one is rarely used.)

Milligram - 'Milli' means 1000 so 1 g = 1000 mg

How to Convert Between Different Units -

Step 1: Decide on our conversion factor (i.e. g to kg needs to use a conversion factor of 1000);

Step 2: Either multiply or divide by this number to reach our converted value.

Let's look at this process in action now with some examples.

e.g. Convert 150 g into kg.

Step 1: Decide on our conversion factor.

1000g = 1kg so our conversion factor is 1000.

Step 2: Multiply / divide by this conversion factor.

One way to look at this is that a kilogram is bigger than a gram, so there needs to be less of them overall.

As there needs to be less of them, we need to divide:

150 ÷ 1000 = 0.15 kg

e.g. Convert 280 g into milligrams.

Step 1: Decide on our conversion factor.

1000mg = 1g so our conversion factor is 1000.

Step 2: Multiply / divide by this conversion factor.

A milligram is smaller than a gram, so there will need to be more of them overall.

As there needs to be more of them, we need to multiply:

280 × 1000 = 280000 mg

In this activity, we will practise converting between the four units of mass measurement described above (kilogram, centigram, milligram and gram) using the method we have seen in action here.

How many grams are in 1 kg (kilogram)?

How many millgrams are in 1 g (gram)?

What is the new amount if we convert 370 g into kg (kilograms)?

37,000 kg

0.37 kg

3.7 kg

What is the new amount if we convert 1.21 kg into g (grams)?

0.0021 g

0.021 g

1210 g

Select if the following conversions have been calculated correctly or not by marking each as either 'Correct' or 'Incorrect'.

Select if the following conversions have been calculated correctly or not by marking each as either 'Correct' or 'Incorrect'.

Match each prefix below to its correct conversion factor.

## Column B

Milli-
1000
Centi-
1000
Kilo-
100

What is the new amount if we convert 375 g into kg?

You do not need to add the unit, as this has already been provided for you and may result in you being marked incorrectly.

## Column B

Milli-
1000
Centi-
1000
Kilo-
100

What is the new amount if we convert 4.3 kg into g?

## Column B

Milli-
1000
Centi-
1000
Kilo-
100

What is the new amount if we convert 204 g into mg?

## Column B

Milli-
1000
Centi-
1000
Kilo-
100
• Question 1

How many grams are in 1 kg (kilogram)?

1000
EDDIE SAYS
The prefix 'kilo-' means 1000, so there must be 1000 g in a kilogram. If you are unsure of the terms we were introduced to in the Introduction, return to it now and review them all before moving on.
• Question 2

How many millgrams are in 1 g (gram)?

1000
EDDIE SAYS
The prefix 'milli-' means 1000, so there must be 1000 mg in a gram. Did you know that?
• Question 3

What is the new amount if we convert 370 g into kg (kilograms)?

0.37 kg
EDDIE SAYS
How did you get on with this first conversion challenge? We know that the g to kg conversion factor is 1000, as there are 1000 g in 1 kg. But do we need to multiply or divide by this factor? It may be useful to think that grams are smaller than kilograms, so there needs to be less of them. To create a decrease, we need to divide: 370 ÷ 1000 = 0.37 kg Did you reach this answer?
• Question 4

What is the new amount if we convert 1.21 kg into g (grams)?

1210 g
EDDIE SAYS
We know that the kg to g conversion factor is 1000, as there are 1000 g in 1 kg. But do we need to multiply or divide here? It may be useful to think that kilograms are much larger than grams, so there needs to be more grams. To create an increase, we need to multiply: 1.21 × 1000 = 1210 g Well done if you spotted that this was the opposite conversion to the previous question, so we needed to simply apply the same conversion factor but reverse the operation.
• Question 5

Select if the following conversions have been calculated correctly or not by marking each as either 'Correct' or 'Incorrect'.

EDDIE SAYS
Did you remember to apply the conversion factors here? Try to commit to memory the three key conversion rates: mg to g = 1000 cg to g = 100 kg to g = 1000 Let's calculate each conversion one at a time, and see if our answers match those provided. g > kg = 1000; grams are smaller than kg so we need to divide 3 ÷ 1000 = 0.003 kg so this first conversion is correct kg > g = 1000; kg are larger than g so we need to multiply 3 × 1000 = 3000 g, the answer given is 300 g so this conversion is incorrect g > mg = 1000; g are larger than mg so we need to multiply 0.3 × 1000 = 300 g, the answer given is 30 mg so this conversion is incorrect too Did you spot the one correct conversion here?
• Question 6

Select if the following conversions have been calculated correctly or not by marking each as either 'Correct' or 'Incorrect'.

EDDIE SAYS
Did you remember the conversion factors we need to use from memory? Try to commit to memory the three key conversion rates: mg to g = 1000 cg to g = 100 kg to g = 1000 Let's calculate each conversion one at a time, and see if our answers match those provided. kg > g = 1000; kilograms are larger than g so we need to multiply 3.2 × 1000 = 3200 g so this first conversion is correct g > kg = 1000; g are smaller than g so we need to divide 425 ÷ 1000 = 0.425 kg, the answer given is 4.25 kg so this conversion is incorrect mg > g = 1000; mg are smaller than g so we need to divide again 35300 ÷ 1000 = 35.3 g so this conversion is also correct Did you find the two correct conversions?
• Question 7

Match each prefix below to its correct conversion factor.

## Column B

Milli-
1000
Centi-
100
Kilo-
1000
EDDIE SAYS
'Milli-' and 'Centi-' both link to a conversion factor of 1000, whilst 'Centi-' relates to 100. Even though we don't use the weight 'centigram' very often, we still need to know it. Try to commit these three terms to memory as part of your revision.
• Question 8

What is the new amount if we convert 375 g into kg?

You do not need to add the unit, as this has already been provided for you and may result in you being marked incorrectly.

EDDIE SAYS
Did you use the correct conversion factor here? 1 kg = 1000 g Remember that kg are larger than g, so we need to have less of them. This means that we need to divide: 375 ÷ 1000 = 0.375 kg
• Question 9

What is the new amount if we convert 4.3 kg into g?

EDDIE SAYS
1 kg = 1000 g Remember that g are smaller than kg, so we need to have more of them. This means that we need to multiply: 4.3 × 1000 = 4300 g
• Question 10

What is the new amount if we convert 204 g into mg?

EDDIE SAYS
1 g = 1000 mg Remember that g are larger than mg, so we need to have more of them. This means that we need to multiply: 204 × 1000 = 204000 mg Great work completing this activity. You can now convert units of mass by finding the relevant conversion factor and applying it in a multiplication / division sum. If you are feeling confident, why not move onto our Level 2 activity now which focuses on converting compound units of measurement?
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