Topics
10. 3D Measurement
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AustraliaNSW
Stage 3

10.09 Convert units of mass

Lesson
Practice
Lesson

Are you ready?

 Multiplying and dividing  by powers of 10 will help us in this lesson. Let's try a problem to practice.

Examples

Example 1

Find the value of 29.34\times100.

Worked Solution
Create a strategy

Put the decimal in a place value table and move each digit two columns to the left.

Apply the idea

Here is 29.34 in a place value table.

ThousandsHundredsTensUnits.TenthsHundredths
29.34

To multiply by 100, move each digit two columns to the left.

ThousandsHundredsTensUnits.TenthsHundredths
2934.

29.34\times100=2934

Idea summary

For each power of 10:

  • 10
  • 100
  • 1000
  • 10\,000

When we multiply or divide by these values, each digit of the number moves up or down place values according to the number of zeros in the power of 10.

Convert milligrams to grams

This video looks at how to convert from milligrams (\text{mg}) to grams (\text{g}), or vice-versa, and how to determine whether to multiply or divide by 1000.

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Examples

Example 2

Convert 41.9 grams to milligrams.

Worked Solution
Create a strategy

Use the conversion 1\text{ g} = 1000\text{ mg}.

To convert grams into milligrams, multiply by 1000.

Apply the idea

Here is 41.9 in a place value table.

Ten ThousandsThousandsHundredsTensUnits.Tenths
41.9

To multiply by 1000, move each digit three columns to the left. Use 0s as place holders.

Ten ThousandsThousandsHundredsTensUnits.Tenths
41900.

41.9 grams = 41\,900 milligrams.

Idea summary

To convert from milligrams to grams: \div 1000

To convert from grams to milligrams: \times 1000

Convert grams to kilograms

This video looks at how to convert between grams (\text{g}) and kilograms (\text{kg}).

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Examples

Example 3

Convert 946 grams to kilograms.

Worked Solution
Create a strategy

Use the conversion 1\text{ kg} = 1000\text{ g}.

To convert grams to kilograms, divide by 1000

Apply the idea

Here is 946 in a place value table.

HundredsTensUnits.TenthsHundredthsThousandths
946.

To divide by 1000, move each digit three columns to the right. Use 0 as a place holder.

HundredsTensUnits.TenthsHundredthsThousandths
0.946

946 grams = 0.946 kilograms

Idea summary

To convert from grams to kilograms: \div 1000

To convert from kilograms to grams: \times 1000

Convert tonnes to kilograms

This video looks at how to convert between tonnes (t) and kilograms (kg).

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Examples

Example 4

Convert 11 tonnes into kilograms.

Worked Solution
Create a strategy

Remember that 1\text{ t} = 1000\text{ kg}.

Multiply the number of tonnes by 1000 to convert tonnes into kilograms.

Apply the idea
\displaystyle 11 \text{ t}\displaystyle =\displaystyle 11 \times 1000 \text{ kg}Multiply by 1000
\displaystyle =\displaystyle 11\,000 \text{ kg}Add 3 zeros
Idea summary

Converting units of mass

A diagram that shows how to convert between tonnes, kilograms, grams, and milligrams. Ask your teacher for more information.

When you convert from a larger unit to a smaller unit (e.g. \text{t} to \text{kg}), you multiply.

When you convert from a smaller unit to a larger unit (e.g.\text{g} to \text{kg}), you divide.

Outcomes

MA3-12MG

selects and uses the appropriate unit and device to measure the masses of objects, and converts between units of mass

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