What is a Non-Repeating Decimal to Fraction Conversion?

S3-SA4-0457

Grade Level:

Class 6

AI/ML, Data Science, Physics, Economics, Cryptography, Computer Science, Engineering

Definition

What is it?

Converting a non-repeating decimal to a fraction means changing a decimal number that stops after a few digits (like 0.75) into a simple fraction (like 3/4). These decimals are also called 'terminating decimals' because they terminate or end. We learn how to write these numbers as a ratio of two whole numbers.

Simple Example

Quick Example

Imagine you scored 0.8 out of 1 in a quick quiz at school. This 0.8 is a non-repeating decimal. To convert it to a fraction, you can think of it as 8 parts out of 10. So, 0.8 becomes 8/10, which simplifies to 4/5. It's like saying you got 4 out of 5 marks if the quiz was scaled.

Worked Example

Step-by-Step

Let's convert 0.625 to a fraction.

Step 1: Write the decimal as a fraction with 1 in the denominator. So, 0.625 = 0.625/1.
---Step 2: Count the number of digits after the decimal point. In 0.625, there are three digits (6, 2, 5).
---Step 3: Multiply both the numerator and the denominator by 10 raised to the power of the number of decimal places. Since there are 3 decimal places, we multiply by 10^3 = 1000. So, (0.625 * 1000) / (1 * 1000).
---Step 4: This gives us 625/1000.
---Step 5: Now, simplify the fraction by finding the greatest common divisor (GCD) of the numerator and denominator. Both 625 and 1000 can be divided by 25. 625 / 25 = 25, and 1000 / 25 = 40. So, we have 25/40.
---Step 6: We can simplify further. Both 25 and 40 can be divided by 5. 25 / 5 = 5, and 40 / 5 = 8. So, we have 5/8.
---Answer: Therefore, 0.625 converted to a fraction is 5/8.

Why It Matters

Understanding decimals and fractions is crucial in many fields. Data scientists use them to analyze information, engineers use them for precise measurements in building bridges or designing circuits, and even economists use them to calculate percentages and growth rates. This skill is a building block for advanced math and science.

Common Mistakes

MISTAKE: Not simplifying the fraction to its lowest terms. For example, converting 0.5 to 5/10 and stopping there. | CORRECTION: Always simplify the fraction by dividing the numerator and denominator by their greatest common factor until no further division is possible. 5/10 simplifies to 1/2.

MISTAKE: Incorrectly counting the number of decimal places. For example, thinking 0.25 has one decimal place instead of two. | CORRECTION: Carefully count all digits after the decimal point. 0.25 has two digits (2 and 5) after the decimal, so you multiply by 100.

MISTAKE: Forgetting to multiply both the numerator and the denominator by the same power of 10. | CORRECTION: Remember that to keep the value of the fraction the same, whatever you multiply the top (numerator) by, you must also multiply the bottom (denominator) by.

Practice Questions

Try It Yourself

QUESTION: Convert 0.4 to a fraction. | ANSWER: 2/5

QUESTION: Convert 0.35 to a fraction. | ANSWER: 7/20

QUESTION: An auto-rickshaw driver covered 12.75 km. Express 12.75 as a mixed fraction. | ANSWER: 12 and 3/4

MCQ

Quick Quiz

Which of these fractions is equivalent to 0.125?

2026-01-04T00:00:00.000Z

2026-01-08T00:00:00.000Z

2026-01-10T00:00:00.000Z

2026-01-02T00:00:00.000Z

The Correct Answer Is:

0.125 has three decimal places, so it is 125/1000. Dividing both by 125 gives 1/8. Options A, C, and D are incorrect conversions.

Real World Connection

In the Real World

When you buy vegetables at the market, the shopkeeper might weigh 0.75 kg of tomatoes. To understand this in terms of parts, you can think of it as 3/4 of a kilogram. Similarly, in sports like cricket, strike rates or economy rates are often given as decimals, which can be understood better as fractions.

Key Vocabulary

Key Terms

DECIMAL: A number that includes a decimal point, showing parts of a whole | FRACTION: A number representing a part of a whole, written as a numerator over a denominator | TERMINATING DECIMAL: A decimal number that has a finite number of digits after the decimal point (it stops) | NUMERATOR: The top number in a fraction, showing how many parts are being considered | DENOMINATOR: The bottom number in a fraction, showing the total number of equal parts

What's Next

What to Learn Next

Great job learning about converting non-repeating decimals! Next, you can explore 'Converting Repeating Decimals to Fractions'. This will help you understand how to handle decimals that go on forever, which is an exciting step in your math journey!