Question 1

What is a recurring decimal in Mathematics?

Accepted Answer

A recurring decimal, also known as a repeating decimal, is a decimal number that has digits that repeat infinitely. For example, 0.333... is a recurring decimal where the digit '3' repeats indefinitely. In the IB MYP Mathematics curriculum, understanding recurring decimals is essential for grasping the concept of rational numbers.

Question 2

How can I convert a recurring decimal into a fraction?

Accepted Answer

To convert a recurring decimal into a fraction, you can use algebraic methods. For example, for the recurring decimal 0.666..., let x = 0.666... Multiply both sides by 10 to get 10x = 6.666... Subtract the original equation from this new equation to get 9x = 6, hence x = 6/9, which simplifies to 2/3. This method is part of the IB MYP Mathematics curriculum, helping students understand the relationship between decimals and fractions.

Question 3

Why do some decimals repeat and others do not?

Accepted Answer

Decimals repeat when they represent rational numbers that cannot be expressed as a finite decimal. This occurs because the division of the numerator by the denominator results in a remainder that eventually repeats. Non-repeating decimals are typically irrational numbers, which cannot be expressed as a simple fraction. Understanding this distinction is crucial in the IB MYP Mathematics curriculum under the Number topic.

Question 4

What is the difference between a terminating and a recurring decimal?

Accepted Answer

A terminating decimal is a decimal that ends after a finite number of digits, such as 0.75. In contrast, a recurring decimal has one or more repeating digits that continue indefinitely, like 0.777... Recognizing the difference between these types of decimals is important in the IB MYP Mathematics curriculum, as it helps students classify numbers accurately.

Question 5

How do recurring decimals relate to rational numbers?

Accepted Answer

Recurring decimals are directly related to rational numbers because every recurring decimal can be expressed as a fraction, which is the definition of a rational number. This relationship is a key concept in the IB MYP Mathematics curriculum, as it helps students understand the nature of numbers and their representations in different forms.

Recurring Decimals

Short Notes - Recurring Decimals

Study Notes & Exam Tips

Recurring Decimals — frequently asked questions