What is Truncation?

S8-SA2-0168

Grade Level:

Class 8

AI/ML, Data Science, Research, Journalism, Law, any domain requiring critical thinking

Definition

What is it?

Truncation is the process of shortening something by removing parts from the end. In mathematics, it means reducing the number of digits after the decimal point without rounding. You simply cut off the extra digits.

Simple Example

Quick Example

Imagine your mobile data usage shows 1.789 GB. If your phone app only displays data up to two decimal places without rounding, it will show 1.78 GB. The '9' is simply cut off, not rounded up or down.

Worked Example

Step-by-Step

Let's truncate the number 7.3482 to two decimal places.

1. Identify the number: 7.3482
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2. Identify the desired number of decimal places: two decimal places.
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3. Locate the second digit after the decimal point: '4'.
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4. Remove all digits that come after the desired decimal place. In this case, remove '8' and '2'.
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5. The remaining number is 7.34.
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Answer: 7.34

Why It Matters

Truncation is crucial in computer science, data science, and engineering when precise calculations are not always needed, or when memory needs to be saved. For example, AI algorithms might truncate less important data points to speed up processing. It helps engineers manage data size and ensures systems don't crash due to too much information.

Common Mistakes

MISTAKE: Confusing truncation with rounding. | CORRECTION: Truncation always cuts off digits, never changing the last kept digit based on the next digit. Rounding adjusts the last digit up or down.

MISTAKE: Applying truncation to whole numbers. | CORRECTION: Truncation primarily applies to decimal parts of numbers. For whole numbers, it's usually about shortening text or data strings, not numerical values.

MISTAKE: Thinking truncation always results in a smaller number. | CORRECTION: While it often makes the number smaller (e.g., 5.78 to 5.7), if the original number was negative (e.g., -5.78 to -5.7), the truncated number is actually larger (closer to zero).

Practice Questions

Try It Yourself

QUESTION: Truncate 12.567 to one decimal place. | ANSWER: 12.5

QUESTION: A cricket player's average score is 34.1234. If the scoreboard truncates averages to two decimal places, what will be displayed? | ANSWER: 34.12

QUESTION: Truncate the number -9.8765 to two decimal places. | ANSWER: -9.87

MCQ

Quick Quiz

Which of the following describes truncation?

Always rounding up to the nearest whole number.

Cutting off digits after a certain decimal place without rounding.

Rounding to the nearest even number.

Adding zeros to the end of a number.

The Correct Answer Is:

Truncation specifically means to cut off digits after a certain point, ignoring the value of the next digit for rounding. Options A, C, and D describe different operations.

Real World Connection

In the Real World

When you check your bank balance on a UPI app like PhonePe or Google Pay, sometimes very long decimal values for interest calculations are truncated for display, showing only two decimal places (rupees and paise). Similarly, in stock market apps, share prices might be truncated to save space and simplify viewing, even if the actual price has more decimal places for precise trading.

Key Vocabulary

Key Terms

DECIMAL PLACE: The position of a digit after the decimal point | ROUNDING: Adjusting a number up or down to a nearby value | DIGIT: A single symbol used to make numbers (0-9) | PRECISION: The level of detail in a measurement or calculation

What's Next

What to Learn Next

Now that you understand truncation, explore 'Rounding Numbers'. Rounding is another way to simplify numbers but it considers the next digit, which is a key difference from truncation. Learning both will give you a complete picture of how numbers are simplified.