What is 3 5 out of 250,000

The cubic meter (m³)

You can already convert lengths, areas, time units and weights into one another. The only thing missing is the volume!

You already know that the base unit for volume is cubic meters. One cubic meter corresponds to the volume of a cube with an edge length of 1 m.

Imagine a 1 dm³ cube in the 1 m³ cube.

10 small cubes with a length of 1 dm then fit into the length of the large cube of 1 m. The same goes for width and height.

So how many small cubes fit in the big one?
There are 10 \$\$ * \$\$ 10 \$\$ * \$\$ 10 \$\$ = \$\$ 1000 small cubes.

So: 1 cubic meter \$\$ = \$\$ 1000 cubic decimeters
Or in short: 1 m³ \$\$ = \$\$ 1000 dm³

The cubes are getting smaller ...

So you can also think about how dm³ and cm³ are related.

Take a cube with an edge length of 1 dm and imagine a cube with an edge length of 1 cm.

10 small cubes with a length of 1 cm then fit into the length of the large cube of 1 dm. The same goes for width and height.

So how many small cubes fit in the big one?
There are 10 \$\$ * \$\$ 10 \$\$ * \$\$ 10 \$\$ = \$\$ 1000 small cubes.

So: 1 cubic decimeter \$\$ = \$\$ 1000 cubic centimeters
Or in short: 1 dm³ \$\$ = \$\$ 1000 cm³

Liters and milliliters

You know what:
1 dm³ is the same as 1 liter and 1 cm³ is the same as 1 milliliter.
So: 1 l \$\$ = \$\$ 1000 ml.

1 dm³ is the volume of a milk carton. 1 cm³ is about the size of half a sugar cube.

All units at a glance

These are all common units for volume:

1 m³ \$\$ = \$\$ 1000 dm³

1 dm³ \$\$ = \$\$ 1000 cm³ or 1 l \$\$ = \$\$ 1000 ml

1 cm³ \$\$ = \$\$ 1000 mm³

There are two ways to convert volume units:

• Option 1: With a place value board

• Option 2: With conversion number

1 km³ \$\$ = \$\$ 1 000 000 000 m³. But you usually don't need that.

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The place value table

A value table is the best way to help you with conversions.
For the volume, the value table looks like this:

H means hundreds, Z means tens, E means one.

Example: 3402 dm³ in the place value table

You can write the numbers in 3 different ways:

• 3402 dm³
• mixed spelling: 3 m³ 402 dm³
• with decimal point: 3.402 m³

Possibility 1: Convert with a place value table

Example 1: Convert 5 m³ to cm³.

Enter the 5 for the units of m³.

Fill in zeros up to the units of cm³.

Read from: 5 m³ \$\$ = \$\$ 5,000,000 cm³.
Finished!

5 m³ \$\$ = \$\$ 5000 dm³.

The other way around

Example 2: Convert 20,000 mm³ to cm³.

Enter the 20,000 mm³. Start from the right with the units of mm³.

Cross out zeros until you get to cc.

Read from: 20,000 mm³ \$\$ = \$\$ 20 cm³.

Caution: You can only cross out zeros, no other digits!

Memorize the value table for volume units:

Enter the given number. Start from the right with the units of the unit. Add zeros or delete them to the unit you are looking for.

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Option 2: With conversion number

The great thing is: When it comes to volume, the conversion figures between the important neighboring units are 1000.

Excerpt from the chain of units:
1 m³ \$\$ = \$\$ 1000 dm³ \$\$ = \$\$ 1 000 000 cm³ \$\$ = \$\$ 1 000 000 000 mm³

Now come the 2 examples precalculated with the conversion number.

Step sequence for conversion

Example 1: Convert 5 m³ to cm³.

1. Determine whether the unit you are looking for is the larger or the smaller unit.

One cm³ is smaller than one m³.

2. Determine whether to multiply or divide by the conversion number.

Bigger ones in smaller units: numerical value becomes greater,
so multiply
Smaller ones in larger units: numerical value becomes smaller,
so divide

The unit you are looking for is smaller, so multiply.

3. Find the conversion number.

1 m³ \$\$ = \$\$ 1000 dm³
1 dm³ \$\$ = \$\$ 1000 cm³
1000\$\$*\$\$1000\$\$=\$\$1 000 000

4. Calculate.

5\$\$*\$\$1 000 000\$\$=\$\$5 000 000
5 m³ \$\$ = \$\$ 5,000,000 cm³

For the fast:
You convert to the second smaller unit.
That means you append 6 zeros.
So: 5 m³ \$\$ = \$\$ 5,000,000 cm³.

You multiply or divide by 10s (10, 100, 1000) by adding or removing zeros.

The other way around

Example 2: Convert 20,000 mm³ to cm³.

1. Determine whether the unit you are looking for is the larger or the smaller unit.

One cm³ is larger than one mm³.

2. Determine whether you are multiplying or dividing by the conversion number.

Bigger ones in smaller units: numerical value becomes greater,
so multiply
Smaller ones in larger units: numerical value becomes smaller,
so divide

The unit you are looking for is larger, so divide.

3. Find the conversion number.

1cm³ \$\$ = \$\$ 1000 mm³

4. Calculate.

20 000\$\$ : \$\$1000\$\$ = \$\$20
20,000 mm³ \$\$ = \$\$ 20 cm³

For the fast:
You convert to the larger neighboring unit. You delete 3 zeros.
So: 20,000 mm³ \$\$ = \$\$ 20 cm³.

You multiply or divide by 10's numbers (10, 100, 1000) by adding or removing zeros.

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With a comma

For some conversions you need a point number.

Example 1: Convert 43 002 dm³ to m³.

Enter the 43 002 at dm³. Start from the right at the ones.

Put a comma after the 3, because you should convert to m³.

Read from: 43 002 dm³ \$\$ = \$\$ 43.002 m³.

Or in the mixed notation: 43 m³ 2 dm³.

All in one line:
43 002 dm³ \$\$ = \$\$ 43.002 m³ \$\$ = \$\$ 43 m³ 2 dm³

If you can't cross out enough zeros while converting, put a comma. The comma comes after the units in the units.

Mathematically precise, point numbers are called decimal fractions or decimal numbers.

Continue with a comma

Example 2: Convert 0.25 m³ to cm³.

Enter 0.25 m³ in the place value table. The units of m³ are in front of the decimal point.

Delete the comma and add zeros until you get to the ones of cm³.

Read from: 0.25 m³ \$\$ = \$\$ 250,000 cm³.

You don't write zeros in front of the ones: 00500. The number is called 500 as usual.

Calculate with volume units

You can add or subtract volumes.
Only one thing is important:
All area information must be in the same unit.

Example: Calculate 384 dm³ \$\$ + \$\$ 15 m³.

1. Convert all information into a unit, in such a way that you have no point numbers.

Convert 15 m³ to dm³.
15 m³ \$\$ = \$\$ 15,000 dm³

2. Do the math.

384 dm³ \$\$ + \$\$ 15 m³ \$\$ = \$\$ 384 dm³ \$\$ + \$\$ 15,000 dm³ \$\$ = \$\$ 15 384 dm³.

If you calculate with different volume units:

1. Convert all information into a unit, in such a way that you have no point numbers.

2. Do the math.

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