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Bruch-zu-Dezimal-Rechner

Schritt für Schritt Brüche in Dezimalzahlen umwandeln

Der Rechner wandelt den gegebenen (echten oder unechten) Bruch oder die gemischte Zahl in eine Dezimalzahl um (eventuell mit Wiederholungen oder wiederkehrenden Zahlen), wobei die Schritte angezeigt werden.

Enter a fraction or

If you don't need a mixed number, leave the left cell empty.
If you need a negative fraction, write the minus sign in the left cell.

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please contact us.

Solution

Your input: convert 390042 into a decimal.

Write the problem in the special format:

92.8571428571428423900

Step 1

How many 42's are in 3? The answer is 0.

Write down the calculated result in the upper part of the table.

Now, 3042=30=3.

Bring down the next digit of the dividend.

0092.8571428571428423900.00000000000009000.000000000000lll0.lll39.

Step 2

How many 42's are in 39? The answer is 0.

Write down the calculated result in the upper part of the table.

Now, 39042=390=39.

Bring down the next digit of the dividend.

0092.8571428571428423900.00000000000009000.000000000000lll0.lll39.9000.000000000000lll0.lll390.

Step 3

How many 42's are in 390? The answer is 9.

Write down the calculated result in the upper part of the table.

Now, 390942=390378=12.

Bring down the next digit of the dividend.

0092.8571428571428423900.00000000000009000.000000000000lll0.lll39.9000.000000000000lll0.lll390.9000.000000000000lll378.lll120.

Step 4

How many 42's are in 120? The answer is 2.

Write down the calculated result in the upper part of the table.

Now, 120242=12084=36.

Bring down the next digit of the dividend.

0092.8571428571428423900.00000000000009000.000000000000lll0.lll39.9000.000000000000lll0.lll390.9000.000000000000lll378.lll120.900.0000000000000lll84.lll36.0

Step 5

How many 42's are in 360? The answer is 8.

Write down the calculated result in the upper part of the table.

Now, 360842=360336=24.

Bring down the next digit of the dividend.

0092.8571428571428423900.00000000000009000.000000000000lll0.lll39.9000.000000000000lll0.lll390.9000.000000000000lll378.lll120.900.0000000000000lll84.lll36.000.0000000000000lll33.6lll2.40

Step 6

How many 42's are in 240? The answer is 5.

Write down the calculated result in the upper part of the table.

Now, 240542=240210=30.

Bring down the next digit of the dividend.

0092.8571428571428423900.00000000000009000.000000000000lll0.lll39.9000.000000000000lll0.lll390.9000.000000000000lll378.lll120.900.0000000000000lll84.lll36.000.0000000000000lll33.6lll2.400.0000000000000lll2.10lll300

Step 7

How many 42's are in 300? The answer is 7.

Write down the calculated result in the upper part of the table.

Now, 300742=300294=6.

Bring down the next digit of the dividend.

0092.8571428571428423900.00000000000009000.000000000000lll0.lll39.9000.000000000000lll0.lll390.9000.000000000000lll378.lll120.900.0000000000000lll84.lll36.000.0000000000000lll33.6lll2.400.0000000000000lll2.10lll3000000000000000lll294lll60

Step 8

How many 42's are in 60? The answer is 1.

Write down the calculated result in the upper part of the table.

Now, 60142=6042=18.

Bring down the next digit of the dividend.

0092.8571428571428423900.00000000000009000.000000000000lll0.lll39.9000.000000000000lll0.lll390.9000.000000000000lll378.lll120.900.0000000000000lll84.lll36.000.0000000000000lll33.6lll2.400.0000000000000lll2.10lll3000000000000000lll294lll6000000000000lll42lll180

Step 9

How many 42's are in 180? The answer is 4.

Write down the calculated result in the upper part of the table.

Now, 180442=180168=12.

Bring down the next digit of the dividend.

0092.8571428571428423900.00000000000009000.000000000000lll0.lll39.9000.000000000000lll0.lll390.9000.000000000000lll378.lll120.900.0000000000000lll84.lll36.000.0000000000000lll33.6lll2.400.0000000000000lll2.10lll3000000000000000lll294lll6000000000000lll42lll18000000000000lll168lll120

Step 10

How many 42's are in 120? The answer is 2.

Write down the calculated result in the upper part of the table.

Now, 120242=12084=36.

Bring down the next digit of the dividend.

0092.8571428571428423900.00000000000009000.000000000000lll0.lll39.9000.000000000000lll0.lll390.9000.000000000000lll378.lll120.900.0000000000000lll84.lll36.000.0000000000000lll33.6lll2.400.0000000000000lll2.10lll3000000000000000lll294lll6000000000000lll42lll18000000000000lll168lll1200000000000lll84lll360

Step 11

How many 42's are in 360? The answer is 8.

Write down the calculated result in the upper part of the table.

Now, 360842=360336=24.

Bring down the next digit of the dividend.

0092.8571428571428423900.00000000000009000.000000000000lll0.lll39.9000.000000000000lll0.lll390.9000.000000000000lll378.lll120.900.0000000000000lll84.lll36.000.0000000000000lll33.6lll2.400.0000000000000lll2.10lll3000000000000000lll294lll6000000000000lll42lll18000000000000lll168lll1200000000000lll84lll360000000000lll336lll240

Step 12

How many 42's are in 240? The answer is 5.

Write down the calculated result in the upper part of the table.

Now, 240542=240210=30.

Bring down the next digit of the dividend.

0092.8571428571428423900.00000000000009000.000000000000lll0.lll39.9000.000000000000lll0.lll390.9000.000000000000lll378.lll120.900.0000000000000lll84.lll36.000.0000000000000lll33.6lll2.400.0000000000000lll2.10lll3000000000000000lll294lll6000000000000lll42lll18000000000000lll168lll1200000000000lll84lll360000000000lll336lll24000000000lll210lll300

Step 13

How many 42's are in 300? The answer is 7.

Write down the calculated result in the upper part of the table.

Now, 300742=300294=6.

Bring down the next digit of the dividend.

0092.8571428571428423900.00000000000009000.000000000000lll0.lll39.9000.000000000000lll0.lll390.9000.000000000000lll378.lll120.900.0000000000000lll84.lll36.000.0000000000000lll33.6lll2.400.0000000000000lll2.10lll3000000000000000lll294lll6000000000000lll42lll18000000000000lll168lll1200000000000lll84lll360000000000lll336lll24000000000lll210lll3000000000lll294lll60

Step 14

How many 42's are in 60? The answer is 1.

Write down the calculated result in the upper part of the table.

Now, 60142=6042=18.

Bring down the next digit of the dividend.

0092.8571428571428423900.00000000000009000.000000000000lll0.lll39.9000.000000000000lll0.lll390.9000.000000000000lll378.lll120.900.0000000000000lll84.lll36.000.0000000000000lll33.6lll2.400.0000000000000lll2.10lll3000000000000000lll294lll6000000000000lll42lll18000000000000lll168lll1200000000000lll84lll360000000000lll336lll24000000000lll210lll3000000000lll294lll6000000lll42lll180

Step 15

How many 42's are in 180? The answer is 4.

Write down the calculated result in the upper part of the table.

Now, 180442=180168=12.

Bring down the next digit of the dividend.

0092.8571428571428423900.00000000000009000.000000000000lll0.lll39.9000.000000000000lll0.lll390.9000.000000000000lll378.lll120.900.0000000000000lll84.lll36.000.0000000000000lll33.6lll2.400.0000000000000lll2.10lll3000000000000000lll294lll6000000000000lll42lll18000000000000lll168lll1200000000000lll84lll360000000000lll336lll24000000000lll210lll3000000000lll294lll6000000lll42lll18000000lll168lll120

Step 16

How many 42's are in 120? The answer is 2.

Write down the calculated result in the upper part of the table.

Now, 120242=12084=36.

Bring down the next digit of the dividend.

0092.8571428571428423900.00000000000009000.000000000000lll0.lll39.9000.000000000000lll0.lll390.9000.000000000000lll378.lll120.900.0000000000000lll84.lll36.000.0000000000000lll33.6lll2.400.0000000000000lll2.10lll3000000000000000lll294lll6000000000000lll42lll18000000000000lll168lll1200000000000lll84lll360000000000lll336lll24000000000lll210lll3000000000lll294lll6000000lll42lll18000000lll168lll1200000lll84lll360

Step 17

How many 42's are in 360? The answer is 8.

Write down the calculated result in the upper part of the table.

Now, 360-8 \cdot 42 = 360 - 336= 24.

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As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: \frac{3900}{42}=92.8 \overline{571428}

Answer: \frac{3900}{42}=92.8\overline{571428}