Fractions to Decimals: Repeating and Recurring Practice for Class 5

For Class 5 students, the simplest way to convert a fraction to a decimal is to divide the numerator by the denominator. You continue dividing, adding zeros after the decimal point, until the division ends (terminating decimal) or a pattern of repeating numbers appears (repeating decimal).

For example, to convert 2/3:

• Divide 2 by 3.
• Since 2 is smaller than 3, add a decimal point and a zero to make it 20.
• 20 divided by 3 is 6 with a remainder of 2.
• When you bring down another zero, it becomes 20 again, which shows the digit '6' will keep repeating.
• Therefore, 2/3 as a decimal is 0.666...

Some fractions create repeating decimals because their denominator has prime factors other than 2 or 5. When you divide the numerator by such a denominator, the division process never terminates, and the remainders start to repeat in a cycle, which in turn causes the digits in the quotient to repeat in a pattern.

The fraction 5/6 as a repeating decimal is 0.8333.... When you use long division to divide 5 by 6, the digit 8 appears after the decimal point, followed by the digit 3 which repeats infinitely. This is an example of a recurring decimal where only part of the decimal sequence repeats.

The key difference is that a terminating decimal ends after a certain number of digits, while a repeating (or recurring) decimal has one or more digits that continue repeating forever in a pattern.

• Terminating Decimals: Result from fractions whose denominators, in simplest form, have only prime factors of 2 and 5 (e.g., 1/4 = 0.25).
• Repeating Decimals: Result from fractions whose denominators have prime factors other than 2 or 5 (e.g., 1/3 = 0.333...).

You can show that a decimal is repeating by using bar notation, where a bar (or vinculum) is placed over the digit or group of digits that repeat. This is a shorter and more precise way than writing the digits with dots.

• For 0.333..., you would write 0.3̅.
• For 0.8333..., where only the 3 repeats, you write 0.83̅.
• For 0.121212..., you write 0.12̅.

To convert a mixed number to a decimal, you first convert the fractional part into a decimal and then add it to the whole number part.

For example, to convert 2 1/3:

• First, handle the fraction 1/3. Convert it to a decimal by dividing 1 by 3, which gives 0.333...
• Next, add the whole number 2 to this decimal.
• The final result is 2 + 0.333... = 2.333...

This worksheet helps Class 5 students build several important maths skills that are crucial for understanding fractions and decimals. Key skills developed include:

• Long Division: Provides essential practice with the division method used for fraction to decimal conversion.
• Pattern Recognition: Helps students visually identify and understand recurring decimal patterns.
• Number Sense: Improves the conceptual understanding of the relationship between fractions and their decimal representations.
• Calculation Confidence: Boosts confidence in performing multi-step problems accurately.

Yes, this Class 5 Maths worksheet on converting fractions to repeating decimals is designed to be easily printable as a free PDF download. It also comes with a complete answer key, which allows parents and teachers to quickly check the solutions for all practice problems.

You can spot a repeating pattern by carefully observing the remainders during the long division process. When a remainder repeats itself for the first time, the digits in your answer (the quotient) will also start to repeat in the same sequence from that point on, creating the recurring decimal pattern.