# What is 1 6 0 3

### Decimal fraction through decimal fraction

Hm, you can divide a decimal fraction by a natural number. Something like: $$ 6.16: 4 = 1.54 $$

But what about this: $$ 0.035: 0.07 $$

Decimal fraction divided by a decimal fraction ??

Here you can use a very important math recipe: You lead the problem back to a known problem that you can already solve.

Change the problem so that you divide by a natural number, but the result does not change! You can do this by multiplying both numbers by a tens so that the second number (the divisor) no longer has a decimal point.

Multiply so that a 7 comes out at 0.07.

So both numbers **times 100**.

That makes:

$$3,5:7$$

You can already do that. Divide as if there were no commas and then use the sample to think about where the comma has to go in the result.

$$3,5:7=0,5$$

So:

$$0,035:0,07=0,5$$

Don't worry, because you have multiplied both numbers (dividend or divisor) by the same number, both tasks will have the same result.

So **divide** you a decimal fraction by a decimal fraction:

- Multiply both numbers by the same tens so that the divisor (the 2nd number) becomes a natural number.
- Divide “normal”. If you exceed the decimal point on the left when calculating, you put the decimal point in the result.

The result of the “new” task is the result of the original task.

Don't forget: The trick with the number ten and the same result only works when dividing!

You multiply a decimal fraction by a decimal number by adding the decimal point to the number of zeros **To the right** backward. Sometimes you have to add zeros to the decimal fraction.

Why is that possible ???

If you multiply the dividend and divisor by the same number and then divide, the ratio stays the same. This is how you see it better:

- 4 : 2 = 2
- 40 : 20 = 2
- 8 : 4 = 2

### Divide in writing

If the numbers get unwieldy, do the math in writing.

$$0,252:0,06$$

Multiply so that at 0.06 you get 6.

So both numbers **times 100**.

$$0,252*100=25,2$$

$$0,06*100=6$$

The new task: $$ 25.2: 6 = $$

So the following applies: $$ 0.252: 0.06 = 4.2 $$

You multiply a decimal fraction by a decimal number by adding the decimal point to the number of zeros **To the right** backward. Sometimes you have to add zeros to the decimal fraction.

### Another example

$$0,0056:0,7$$

A natural number should be used in place of 0.7. Multiply by 10.

$$0,0056*10=0,056$$

$$0,7*10=7$$

$$0,0056:0,7=0,008$$

You can always try the inverse calculation.

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