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.
Solution
Your input: convert 390042 into a decimal.
Write the problem in the special format:
−92.857142857142842−3900
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, 3−0⋅42=3−0=3.
Bring down the next digit of the dividend.
−0092.857142857142842−39↓00.0000000000000−9000.000000000000lll0.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, 39−0⋅42=39−0=39.
Bring down the next digit of the dividend.
−0092.857142857142842−390↓0.0000000000000−9000.000000000000lll0.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, 390−9⋅42=390−378=12.
Bring down the next digit of the dividend.
−0092.857142857142842−3900↓.0000000000000−9000.000000000000lll0.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, 120−2⋅42=120−84=36.
Bring down the next digit of the dividend.
−0092.857142857142842−3900.0↓000000000000−9000.000000000000lll0.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, 360−8⋅42=360−336=24.
Bring down the next digit of the dividend.
−0092.857142857142842−3900.00↓00000000000−9000.000000000000lll0.lll39.−9000.000000000000lll0.lll390.−9000.000000000000lll378.lll120.−900.0000000000000lll84.lll36.0−00.0000000000000lll33.6lll2.40
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, 240−5⋅42=240−210=30.
Bring down the next digit of the dividend.
−0092.857142857142842−3900.000↓0000000000−9000.000000000000lll0.lll39.−9000.000000000000lll0.lll390.−9000.000000000000lll378.lll120.−900.0000000000000lll84.lll36.0−00.0000000000000lll33.6lll2.40−0.0000000000000lll2.10lll300
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, 300−7⋅42=300−294=6.
Bring down the next digit of the dividend.
−0092.857142857142842−3900.0000↓000000000−9000.000000000000lll0.lll39.−9000.000000000000lll0.lll390.−9000.000000000000lll378.lll120.−900.0000000000000lll84.lll36.0−00.0000000000000lll33.6lll2.40−0.0000000000000lll2.10lll300−0000000000000lll294lll60
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, 60−1⋅42=60−42=18.
Bring down the next digit of the dividend.
−0092.857142857142842−3900.00000↓00000000−9000.000000000000lll0.lll39.−9000.000000000000lll0.lll390.−9000.000000000000lll378.lll120.−900.0000000000000lll84.lll36.0−00.0000000000000lll33.6lll2.40−0.0000000000000lll2.10lll300−0000000000000lll294lll60−00000000000lll42lll180
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, 180−4⋅42=180−168=12.
Bring down the next digit of the dividend.
−0092.857142857142842−3900.000000↓0000000−9000.000000000000lll0.lll39.−9000.000000000000lll0.lll390.−9000.000000000000lll378.lll120.−900.0000000000000lll84.lll36.0−00.0000000000000lll33.6lll2.40−0.0000000000000lll2.10lll300−0000000000000lll294lll60−00000000000lll42lll180−00000000000lll168lll120
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, 120−2⋅42=120−84=36.
Bring down the next digit of the dividend.
−0092.857142857142842−3900.0000000↓000000−9000.000000000000lll0.lll39.−9000.000000000000lll0.lll390.−9000.000000000000lll378.lll120.−900.0000000000000lll84.lll36.0−00.0000000000000lll33.6lll2.40−0.0000000000000lll2.10lll300−0000000000000lll294lll60−00000000000lll42lll180−00000000000lll168lll120−0000000000lll84lll360
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, 360−8⋅42=360−336=24.
Bring down the next digit of the dividend.
−0092.857142857142842−3900.00000000↓00000−9000.000000000000lll0.lll39.−9000.000000000000lll0.lll390.−9000.000000000000lll378.lll120.−900.0000000000000lll84.lll36.0−00.0000000000000lll33.6lll2.40−0.0000000000000lll2.10lll300−0000000000000lll294lll60−00000000000lll42lll180−00000000000lll168lll120−0000000000lll84lll360−000000000lll336lll240
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, 240−5⋅42=240−210=30.
Bring down the next digit of the dividend.
−0092.857142857142842−3900.000000000↓0000−9000.000000000000lll0.lll39.−9000.000000000000lll0.lll390.−9000.000000000000lll378.lll120.−900.0000000000000lll84.lll36.0−00.0000000000000lll33.6lll2.40−0.0000000000000lll2.10lll300−0000000000000lll294lll60−00000000000lll42lll180−00000000000lll168lll120−0000000000lll84lll360−000000000lll336lll240−00000000lll210lll300
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, 300−7⋅42=300−294=6.
Bring down the next digit of the dividend.
−0092.857142857142842−3900.0000000000↓000−9000.000000000000lll0.lll39.−9000.000000000000lll0.lll390.−9000.000000000000lll378.lll120.−900.0000000000000lll84.lll36.0−00.0000000000000lll33.6lll2.40−0.0000000000000lll2.10lll300−0000000000000lll294lll60−00000000000lll42lll180−00000000000lll168lll120−0000000000lll84lll360−000000000lll336lll240−00000000lll210lll300−0000000lll294lll60
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, 60−1⋅42=60−42=18.
Bring down the next digit of the dividend.
−0092.857142857142842−3900.00000000000↓00−9000.000000000000lll0.lll39.−9000.000000000000lll0.lll390.−9000.000000000000lll378.lll120.−900.0000000000000lll84.lll36.0−00.0000000000000lll33.6lll2.40−0.0000000000000lll2.10lll300−0000000000000lll294lll60−00000000000lll42lll180−00000000000lll168lll120−0000000000lll84lll360−000000000lll336lll240−00000000lll210lll300−0000000lll294lll60−00000lll42lll180
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, 180−4⋅42=180−168=12.
Bring down the next digit of the dividend.
−0092.857142857142842−3900.000000000000↓0−9000.000000000000lll0.lll39.−9000.000000000000lll0.lll390.−9000.000000000000lll378.lll120.−900.0000000000000lll84.lll36.0−00.0000000000000lll33.6lll2.40−0.0000000000000lll2.10lll300−0000000000000lll294lll60−00000000000lll42lll180−00000000000lll168lll120−0000000000lll84lll360−000000000lll336lll240−00000000lll210lll300−0000000lll294lll60−00000lll42lll180−00000lll168lll120
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, 120−2⋅42=120−84=36.
Bring down the next digit of the dividend.
−0092.857142857142842−3900.0000000000000↓−9000.000000000000lll0.lll39.−9000.000000000000lll0.lll390.−9000.000000000000lll378.lll120.−900.0000000000000lll84.lll36.0−00.0000000000000lll33.6lll2.40−0.0000000000000lll2.10lll300−0000000000000lll294lll60−00000000000lll42lll180−00000000000lll168lll120−0000000000lll84lll360−000000000lll336lll240−00000000lll210lll300−0000000lll294lll60−00000lll42lll180−00000lll168lll120−0000lll84lll360
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}