# How and where can I learn unity

### A new unit

It's the start of the school year: Class 5b wants to get to know each other. Each child creates a profile. The profile is 10x10 cm, so 1 dm². The space for the profiles is 2 m². How many profiles fit on the space?

To solve this, you need to convert units.

How are m² and dm² related?

First imagine 1 m. Divide 1m into 10 pieces. One of these parts is then 1 dm long.

Now form a square with a side length of 1 m and inside a square with a side length of 1 dm.

The large square has an area of 1 m² and the small square has an area of 1 dm².

How many square**decimeter** then fit into a square**meter**? 100 red boxes fit into the large square: With units: 100 dm² are 1 m².

Image: Schöningh Verlag (Reinhild Kassing)

### All units at a glance

If you do that with the square for dm² and m² for all units of area, you get:

1 km² $$ = $$ 100 ha

1 ha $$ = $$ 100 a

1 a $$ = $$ 100 m²

1 m² $$ = $$ 100 dm²

1 dm² $$ = $$ 100 cm²

1 cm² $$ = $$ 100 mm²

There are two ways to convert area units:

- Option 1: With the value board
- Option 2: With the conversion number

### The place value table

A place value table is the best way to help you with conversions.

For areas, the value table looks like this:

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

Example: 2203 dm² in the place value table

You can write the numbers in 3 different ways:

- 2203 dm²
- mixed spelling: 22 m² 3 dm²
- with decimal point: 22.03 m²

*kapiert.de*can do more:

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and tests - individual classwork trainer
- Learning manager

### Possibility 1: Convert with a place value table

**Example 1:** Convert 7 km² to m².

Enter the 7 for the units of km².

Fill in zeros up to the units of m².

Read from: 7 km² $$ = $$ 7,000,000 m².

Finished!

You can also read:

7 km² $$ = $$ 700 ha and 7 km² $$ = $$ 70,000 a.

### The other way around

**Example 2:** Convert 6000 cm² to dm².

Enter the 6000 cm².

Start from the right with the units of cm².

Cross out zeros until you get to dm².

Read from: 6000 cm² $$ = $$ 60 dm²

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

Memorize the value table for units of area:

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.

### Option 2: With conversion number

The great thing is: For areas, all conversion numbers between neighboring units are 100!

Excerpt from the chain of units:

1 m² $$ = $$ 100 dm² $$ = $$ 10000 cm² $$ = $$ 1000000 mm²

Most of the time you don't need hectares and ares. These are the most common units:

Now come the 2 examples precalculated with the conversion number.

*kapiert.de*can do more:

- interactive exercises

and tests - individual classwork trainer
- Learning manager

### Step sequence for conversion

**Example 1:** Convert 7 km² to m².

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

One m² is smaller than one km².

- 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. Find the conversion number.

1 km² $$ = $$ 100 ha; 1 ha $$ = $$ 100 a; 1 a $$ = $$ 100 m²

100$$*$$100$$*$$100 $$=$$ 1 000 000Calculate.

7 $$*$$ 1 000 000 $$=$$ 7 000 000

So 7 km² $$ = $$ 7,000,000 m²

For the fast:

The conversion figure is 100 $$ * $$ 100 $$ * $$ 100. That means: append 6 zeros.

So: 7 km² $$ = $$ 7,000,000 m².

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

### The other way around

**Example 2:** Convert 6000 cm² to dm².

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

One m² is smaller than one km².

- 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 larger, so divide. Find the conversion number.

The units are adjacent, so 100.

Calculate.

6000 : 100 $$=$$ 60

6000 cm² $$ = $$ 60 dm²

For the fast:

You convert to the next larger unit. That is, you take away two zeros.

So: 6000 cm² $$ = $$ 60 dm²

- Determine whether the unit you are looking for is the larger or the smaller unit.
- Determine whether you are multiplying or dividing by the conversion number.
- Larger into smaller unit: numerical value becomes larger, so multiply
- Smaller into larger unit: numerical value becomes smaller, so divide

- Find the conversion number.
- Calculate.

### With a comma

For some conversions you need a point number.

**Example 1:** Convert 510 dm² to m².

Enter the 510 at dm². Start from the right at the ones.

Put a comma after the 5 because you are supposed to convert to m².

Read from: 510 dm² $$ = $$ 5.10 m² (5.1 m² is also correct).

Or in the mixed notation: 5 m² 10 dm².

Everything in one line: 510 dm² $$ = $$ 5.10 m² $$ = $$ 5 m² 10 dm².

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.

*kapiert.de*can do more:

- interactive exercises

and tests - individual classwork trainer
- Learning manager

### Continue with a comma

**Example 2:** Convert 0.05 m² to cm².

Enter 0.05 m² in the place value table. The units of m² are in front of the comma.

Delete the comma and add zeros until you get to cm².

Read from: 0.05 m² $$ = $$ 500 cm².

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

### Calculate with units of area

You can add or subtract areas. Only one thing is important: all surface areas must be in the same unit.

**Example:** Calculate 2453 dm² $$ + $$ 20 m².

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

Convert 20 m² to dm².

20 m² $$ = $$ 2000 dm²Do the math.

2453 dm² $$ + $$ 20 m² $$ = $$ 2453 dm² $$ + $$ 2000 dm² $$ = $$ 4453 dm²

If you calculate with units of area:

- Convert all information into a unit, in such a way that you have no point numbers.
- Do the math.

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