Brüche als Dezimalzahl und Prozent
About this app
Ein Hunderterfeld zeigt, wie ein Bruch zur Dezimalzahl und zu Prozent wird: Erweitern auf Zehntel, Hundertstel und Tausendstel, schriftlich teilen mit Restleiter bis zur Periode (1/3 = 0,3 periodisch) und Vergleichen mit zwei Feldern, Stellenwerttafel und Zahlenstrahl (0,25 < 0,3). Mit Übungsaufgaben.
With explain mode: an AI tutor walks you through the app, points out what matters in the scene and answers your questions.
How a fraction becomes a decimal
There are two ways. First, expand: if the simplified denominator goes into 10, 100 or 1000, you expand to tenths, hundredths or thousandths, for example 3/4 = 75/100 = 0.75. Second, divide: you divide the numerator by the denominator with long division. If the remainder becomes 0, the decimal terminates. If a remainder comes back, everything repeats from there and the decimal recurs, for example 1/3 = 0.3 recurring. Percent means hundredths: 0.75 is 75%.
What the app shows
A hundred square made of ten strips of ten small squares; the coloured area is the fraction. When you expand, new lines cut the square into tenths, hundredths and thousandths, and the area reshapes with the same size until it consists of whole parts or visibly does not fit. When you divide, a remainder ladder appears: each remainder is shown as a strip, and an arc marks the remainder that comes back. A place value chart, a percent bar and, for comparing, a number line complete the picture.
Try it yourself
Set numerator and denominator or drag the handle on the percent bar. Expand 1/4 step by step and see why tenths do not fit but hundredths do. Divide 1/7 and watch the six different remainders before 1 comes back. Compare 0.25 with 0.3 and 1/4 with 0.4 in two squares. The Practice panel offers short tasks with three answers; after each answer the square shows why it is right or not.
Frequently asked questions
- How do you convert a fraction to a decimal?
- Either expand the fraction to tenths, hundredths or thousandths, if the simplified denominator goes into 10, 100 or 1000, or divide the numerator by the denominator. 1/4 = 25/100 = 0.25; 1/3 = 1 ÷ 3 = 0.333… = 0.3 recurring.
- When does a decimal recur?
- When long division never leaves remainder 0. Because there are only finitely many possible remainders, one of them comes back, and from then on digits and remainders repeat. This happens exactly when the simplified denominator has a prime factor other than 2 and 5.
- Why is 0.25 smaller than 0.3?
- Decimals are compared place by place from the left. 0.3 = 0.30, and in the tenths place it is 2 against 3. In a hundred square 0.25 is only 25 small squares, but 0.3 is 30. More decimal places do not mean a larger value.
- What can I try in the app?
- Set fractions with denominators up to 50, expand to tenths, hundredths and thousandths, use long division until the digits recur, compare two numbers in hundred squares, a place value chart and a number line, and solve short practice tasks with instant feedback.
Subject: Bruchrechnung (Klasse 6)
More from Bruchrechnung (Klasse 6)
- Bruch-Werkstatt: Was ein Bruch bedeutet
- Brüche addieren und subtrahieren
- Brüche dividieren: Wie oft passt es hinein?
- Brüche multiplizieren mit kreuzweisem Kürzen
- Brüche multiplizieren: Anteil vom Anteil
- Brüche vergleichen und ordnen
- Bruchteile von Mengen und Größen
- Dividieren mit dem Kehrwert
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