Real numbers encompass all rational and irrational numbers. Ordering them on a number line visually represents their magnitude. Numbers to the right are greater than numbers to the left. This helps in comparing and understanding the relative values of different numbers, including decimals, fractions, and even $\pi$ or $\sqrt{2}$. A number line extends infinitely in both positive and negative directions.
Placing real numbers accurately on a number line requires converting them to a common form, usually decimals, to make comparisons easier. Understanding the concept of absolute value, which is the distance from zero, is also essential when working with negative numbers.
Match the term to its correct definition:
| Term | Definition |
|---|---|
| 1. Real Number | A. The distance of a number from zero. |
| 2. Rational Number | B. A line representing numbers geometrically. |
| 3. Irrational Number | C. Any number that can be expressed as a fraction $\frac{p}{q}$, where p and q are integers and q ≠ 0. |
| 4. Absolute Value | D. A number that cannot be expressed as a fraction and has a non-repeating, non-terminating decimal representation. |
| 5. Number Line | E. Any number that can be found on the number line; includes both rational and irrational numbers. |
Match the numbers with the letters!
Complete the following paragraph with the correct words:
When ordering real numbers on a number line, numbers to the _______ are always _______ than numbers to the _______. The number _______ is the point of origin. _______ numbers are located to the left of zero.
Explain in your own words how ordering real numbers on a number line can help you compare the values of different fractions and decimals.
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