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 40011 into a decimal.
Write the problem in the special format:
−36.363611−400
Step 1
How many 11's are in 4? The answer is 0.
Write down the calculated result in the upper part of the table.
Now, 4−0⋅11=4−0=4.
Bring down the next digit of the dividend.
−036.363611−40↓0.0000−000.000lll0.lll40.
Step 2
How many 11's are in 40? The answer is 3.
Write down the calculated result in the upper part of the table.
Now, 40−3⋅11=40−33=7.
Bring down the next digit of the dividend.
−036.363611−400↓.0000−000.000lll0.lll40.−000.000lll33.lll70.
Step 3
How many 11's are in 70? The answer is 6.
Write down the calculated result in the upper part of the table.
Now, 70−6⋅11=70−66=4.
Bring down the next digit of the dividend.
−036.363611−400.0↓000−000.000lll0.lll40.−000.000lll33.lll70.−00.0000lll66.lll4.0
Step 4
How many 11's are in 40? The answer is 3.
Write down the calculated result in the upper part of the table.
Now, 40−3⋅11=40−33=7.
Bring down the next digit of the dividend.
−036.363611−400.00↓00−000.000lll0.lll40.−000.000lll33.lll70.−00.0000lll66.lll4.0−0.0000lll3.3lll70
Step 5
How many 11's are in 70? The answer is 6.
Write down the calculated result in the upper part of the table.
Now, 70−6⋅11=70−66=4.
Bring down the next digit of the dividend.
−036.363611−400.000↓0−000.000lll0.lll40.−000.000lll33.lll70.−00.0000lll66.lll4.0−0.0000lll3.3lll70−0000lll66lll40
Step 6
How many 11's are in 40? The answer is 3.
Write down the calculated result in the upper part of the table.
Now, 40−3⋅11=40−33=7.
Bring down the next digit of the dividend.
−036.363611−400.0000↓−000.000lll0.lll40.−000.000lll33.lll70.−00.0000lll66.lll4.0−0.0000lll3.3lll70−0000lll66lll40−000lll33lll70
Step 7
How many 11's are in 70? The answer is 6.
Write down the calculated result in the upper part of the table.
Now, 70−6⋅11=70−66=4.
−036.363611−400.0000−000.000lll0.lll40.−000.000lll33.lll70.−00.0000lll66.lll4.0−0.0000lll3.3lll70−0000lll66lll40−000lll33lll70−00lll66lll4
As can be seen, the digits are repeating with some period, therefore it is a repeating (or recurring) decimal: 40011=36.¯36
Answer: 40011=36.¯36