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10. 3D Measurement
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AustraliaVIC
Level 6

10.09 Problems with mass

Lesson
Practice
Lesson

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When we are problem-solving, we might have to  convert to the same units  before we can solve. Let's try this problem to review.

Examples

Example 1

Convert 946 grams to kilograms.

Worked Solution
Create a strategy

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

Divide the number of grams by 1000 to convert grams to kilograms.

Apply the idea

Here is 946 in a place value table:

HundredsTensUnits.TenthsHundredthsThousandths
946.

To divide by 1000 we move each digit 3 place values to the right and use 0 as a place holder.

HundredsTensUnits.TenthsHundredthsThousandths
0.946
\displaystyle 946 \text{ g}\displaystyle =\displaystyle 0.946 \text{ kg}
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.

Parts of units with mass

This video introduces the connections with decimals and fractions to the units of mass.

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Examples

Example 2

How many grams is 500 miligrams?

Worked Solution
Create a strategy

Remember that 1000 \text{ miligrams} = 1 \text{ grams}.

Apply the idea

We know that 500 is half of 1000, because 500 \times 2 =1000.

This means that 500 miligrams is half of 1 gram.500 \text{ miligrams} = \dfrac{1}{2} \text{ grams}

Idea summary

If we have part of a unit, we can express that using fractions and decimals, but we can also express it with a different unit. Half a kilogram is the same as 500 grams.

Story problems with mass

This video looks at a story problem that involves adding and subtracting masses.

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Examples

Example 3

James buys a 4000 \text{ g} box of washing powder.

If he uses 2.3 \text{ kg} of the washing powder, how many grams of powder is left in the box?

Worked Solution
Create a strategy

Find the difference between the total amount of washing powder and the amount James has used.

Apply the idea

First we convert 2.3 \text{ kg} to grams by multiplying by 1000. Here is 2.3 in a place value table:

ThousandsHundredsTensUnits.Tenths
2.3

To multiply by 1000 we move each digit 3 place values to the left and use 0s as place holders.

ThousandsHundredsTensUnits.Tenths
2300.
\displaystyle 2.3 \text{ kg}\displaystyle =\displaystyle 2300 \text{ g}

Now we need to subtract 2300 \text{ g} from 4000 \text{ g} to find what is left.

\displaystyle \text{Powder left}\displaystyle =\displaystyle 4000 - 2300Subtract the powder used from the total
\displaystyle =\displaystyle 1700 \text{ g}
Idea summary

If we are solving problems, changing units can often help with solving.

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