What is Writing a Remainder as a Decimal?

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Grade Level:

Class 3

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Definition

What is it?

Writing a remainder as a decimal means continuing a division problem even after you get a remainder. Instead of stopping, you add a decimal point and zeros to the dividend, then keep dividing to get a more precise answer, often with decimal places.

Simple Example

Quick Example

Imagine you have 7 laddoo and want to share them equally among 2 friends. Each friend gets 3 laddoo, and you have 1 laddoo left over. If you want to share that last laddoo too, you can cut it in half, giving each friend 0.5 laddoo more. So, 7 divided by 2 is 3.5.

Worked Example

Step-by-Step

Let's divide 15 by 4 and write the remainder as a decimal.

1. First, perform normal division: 15 divided by 4.

2. 4 goes into 15 three times (3 x 4 = 12). Subtract 12 from 15, which leaves a remainder of 3.

3. Now, to write the remainder as a decimal, add a decimal point (.) and a zero (0) to 15, making it 15.0. Also add a decimal point to your quotient (3.), making it 3.

4. Bring down the 0. Now you are dividing 30 by 4.

5. 4 goes into 30 seven times (7 x 4 = 28). Write 7 after the decimal point in the quotient, making it 3.7.

6. Subtract 28 from 30, which leaves a remainder of 2.

7. Add another zero to 15.0, making it 15.00, and bring down this new 0. Now you are dividing 20 by 4.

8. 4 goes into 20 five times (5 x 4 = 20). Write 5 after the 7 in the quotient, making it 3.75. Subtract 20 from 20, leaving a remainder of 0.

So, 15 divided by 4, with the remainder written as a decimal, is 3.75.

Why It Matters

This concept is super important for getting exact measurements and calculations in science, finance, and even daily life. Scientists use it for precise measurements, engineers for building accurate structures, and even you when calculating percentages for your exam marks or sharing bills accurately.

Common Mistakes

MISTAKE: Stopping at the whole number remainder and not continuing the division. For example, saying 7 divided by 2 is 3 remainder 1. | CORRECTION: Add a decimal point and zeros to the dividend and continue dividing until the remainder is zero or you reach a desired number of decimal places.

MISTAKE: Forgetting to add the decimal point in the quotient when adding it to the dividend. | CORRECTION: As soon as you add a decimal point to the dividend (e.g., from 7 to 7.0), immediately add a decimal point to your answer (e.g., from 3 to 3.).

MISTAKE: Misplacing the decimal point in the final answer. | CORRECTION: Ensure the decimal point in the quotient is directly above the decimal point in the dividend, aligning the place values correctly.

Practice Questions

Try It Yourself

QUESTION: Divide 9 by 2 and write the remainder as a decimal. | ANSWER: 4.5

QUESTION: A 25-meter rope needs to be cut into 4 equal pieces. How long will each piece be, expressed as a decimal? | ANSWER: 6.25 meters

QUESTION: You have Rs. 50 and want to buy 3 identical pens. If each pen costs Rs. 16, how much change will you get back, expressed as a decimal if you divide the remaining amount by 3? (Hint: First find total cost, then change, then divide change by 3). | ANSWER: Rs. 0.666... (approximately 0.67)

MCQ

Quick Quiz

What is 11 divided by 4, with the remainder written as a decimal?

2 remainder 3

2.75

2.3

3.25

The Correct Answer Is:

When 11 is divided by 4, it's 2 with a remainder of 3. To continue as a decimal, add a decimal and zero (11.0). 30 divided by 4 is 7 with remainder 2. Add another zero (11.00). 20 divided by 4 is 5. So, 2.75.

Real World Connection

In the Real World

When you buy vegetables at a market, and the vendor weighs 1.5 kg of potatoes, that '0.5' comes from writing a remainder as a decimal. Or when you calculate your average marks for 5 subjects and get 85.6, that decimal part is crucial for knowing your exact performance.

Key Vocabulary

Key Terms

REMAINDER: The amount left over after dividing one number by another | DECIMAL POINT: A symbol (.) used to separate the whole number part from the fractional part of a number | DIVIDEND: The number being divided | QUOTIENT: The result obtained when one number is divided by another | DIVISION: The process of splitting a number into equal parts.

What's Next

What to Learn Next

Great job understanding this! Next, you can explore 'Rounding Decimals'. This will teach you how to simplify long decimal answers to a more manageable number of decimal places, which is very useful in real-world calculations.