Clearing decimals, also known as decimal expansion or terminating decimals, refers to the process of converting a fraction into a decimal representation that ends after a finite number of digits. This can be done when the denominator of the fraction has only 2s or 5s as prime factors, or when it is a multiple of 25. Decimal expansion relies on the concept of place value, where each digit in the decimal representation represents a different power of 10. The process involves dividing the numerator by the denominator and expressing the remainder as a decimal fraction. This iterative division continues until the remainder becomes zero, indicating that the decimal representation has terminated.
Clearing Decimals: A Step-by-Step Guide
Clearing decimals involves separating the whole number part from the decimal part and making the resulting expression an integer. Here’s a detailed explanation of the process:
Step 1: Separate the Whole Number Part
- Identify the decimal point in the number.
- All digits to the left of the decimal point represent the whole number part.
Step 2: Multiply by 10^n
- Determine the number of decimal places in the number.
- Multiply the number by 10 raised to the power of the number of decimal places.
Step 3: Drop the Decimal Point
- Once you multiply the number by 10^n, the decimal point will shift n places to the right.
- Simply drop (remove) the decimal point from the resulting number.
Step 4: Calculate Final Result
- The resulting number is an integer that represents the cleared decimal.
Example:
Let’s clear the decimal 0.75:
- Whole number part: 0
- Number of decimal places: 2
- Multiply by 10^n: 0.75 x 10^2 = 75
- Drop the decimal point: 75
Therefore, the cleared decimal for 0.75 is 75.
Table of Examples:
| Decimal | Whole Number Part | Number of Decimal Places | Multiplied by 10^n | Cleared Decimal |
|---|---|---|---|---|
| 1.5 | 1 | 1 | 1.5 x 10^1 | 15 |
| 0.05 | 0 | 2 | 0.05 x 10^2 | 5 |
| 12.34 | 12 | 2 | 12.34 x 10^2 | 1234 |
| 0.875 | 0 | 3 | 0.875 x 10^3 | 875 |
1. Question: What is the process of clearing decimals?
Answer: Clearing decimals is the process of removing the decimal point and replacing it with a place value.
2. Question: What is the purpose of clearing decimals?
Answer: Clearing decimals is useful for converting decimals to integers so that they can be easily compared, added, subtracted, multiplied, and divided.
3. Question: What are the steps involved in clearing decimals?
Answer: The steps involved in clearing decimals include moving the decimal point to the right by the number of digits after the decimal point, multiplying the number by a power of ten, and removing the decimal point.
Well, there you have it, folks! Understanding how to clear decimals is like mastering a secret superpower that makes math a breeze. Remember, when it comes to decimals, all you need to do is shift the decimal point and adjust the number accordingly. It’s as simple as that. So next time you encounter a decimal problem, you’ll be able to tackle it with newfound confidence. Thanks for reading, and be sure to visit us again soon for more math-related adventures!