Question

use the space below to describe the process of converting and ordering real numbers. use the proficiency model to help you write your steps. to earn full credit, you must use the following vocabulary: descending, convert, decimal. here are some prompting questions: 1. how did you convert each number to a decimal? 2. what does descending order mean? 3. how did you put the numbers in descending order? 4. what strategies help you in this process? 5. explain the t - chart strategy. what is it used for? what are the labels?

Explanation:

Step1: Convert non - decimal real numbers

If the real number is a fraction, divide the numerator by the denominator. For example, if the number is $\frac{3}{4}$, then $3\div4 = 0.75$. If it is a square - root like $\sqrt{2}$, use a calculator to get an approximate decimal value ($\sqrt{2}\approx1.414$).

Step2: Define descending order

Descending order means arranging numbers from the largest value to the smallest value. For example, for the numbers 5, 3, 1, the descending order is 5, 3, 1.

Step3: Arrange decimal numbers

Compare the decimal numbers. Start by comparing the whole - number parts. If the whole - number parts are the same, compare the tenths place, then the hundredths place, and so on. For example, for 1.5 and 1.3, since 5>3 in the tenths place, 1.5>1.3.

Step4: T - chart strategy

A T - chart can be used to organize the original real numbers and their corresponding decimal conversions. Label one column "Original Number" and the other "Decimal Equivalent". Write each real number in the first column and its decimal conversion in the second column. This helps in visualizing the numbers and their values clearly for ordering.

Answer:

The process of converting real numbers to decimals involves division for fractions and approximation for roots. Descending order is from largest to smallest. To put numbers in descending order, compare decimal values. The T - chart strategy helps in organizing original numbers and their decimal equivalents for easier comparison and ordering.