Question

learn order rational numbers
to order rational numbers, follow these steps:

1. write each number in the same form. since there may be mixed numbers or fractions, it may be better to write all of the numbers as decimals.
2. use the signs of the numbers, place value, or a number line to compare the numbers.
3. order the values from least to greatest or greatest to least.

to order the set of numbers: {\frac{1}{4}, -0.375, -\frac{11}{50}, 0.3}, graph each number on a number line. the least value is farthest to the left and the greatest value is farthest to the right.
number line with -1, -0.75, -0.5, -0.25, 0, 0.25, 0.5, 0.75, 1; -0.375, -\frac{11}{50} marked between -0.5 and -0.25; \frac{1}{4}, 0.3 marked between 0 and 0.5
so, the set of numbers in order from least to greatest is
____________________ and from greatest to least is
____________________
____________________
example 4 order sets of rational numbers
order the set \\{-2.46, -2\frac{22}{25}, -2\frac{1}{10}\\}\\) from least to greatest.
step 1 write the mixed numbers as decimals.
-2.46 = -2.46 \quad -2\frac{22}{25} = \square \quad -2\frac{1}{10} = \square
step 2 graph the numbers on a number line.
number line with -3.00, -2.90, -2.80, -2.70, -2.60, -2.50, -2.40, -2.30, -2.20, -2.10, -2.00; -2\frac{22}{25} marked near -2.90; -2.46 marked near -2.45; -2\frac{1}{10} marked near -2.10
so, the set of numbers in order from least to greatest is -2\frac{22}{25}, -2.46, -2\frac{1}{10}.
check
order the set \\{2.12, -2.1, 2\frac{1}{10}, -2\frac{1}{5}\\}\\) from least to greatest.
show your work here
go online you can complete an extra example online.

Explanation:

Step1: Convert mixed numbers to decimals

First, convert \(2\frac{1}{10}\) and \(-2\frac{1}{5}\) to decimals.
For \(2\frac{1}{10}\), we know that \(\frac{1}{10}=0.1\), so \(2\frac{1}{10}=2 + 0.1 = 2.1\).
For \(-2\frac{1}{5}\), \(\frac{1}{5}=0.2\), so \(-2\frac{1}{5}=-(2 + 0.2)=-2.2\).
The given numbers are \(2.12\), \(-2.1\), \(2.1\) (from \(2\frac{1}{10}\)), and \(-2.2\) (from \(-2\frac{1}{5}\)).

Step2: Order the negative numbers

Among the negative numbers \(-2.2\) and \(-2.1\), since \(-2.2 < -2.1\) (because in negative numbers, the larger the magnitude, the smaller the number).

Step3: Order the positive numbers

Among the positive numbers \(2.1\) and \(2.12\), we have \(2.1 < 2.12\) (since \(2.1 = 2.10\) and \(2.10 < 2.12\)).

Step4: Combine and order all numbers

Now, combining the ordered negative and positive numbers, we get the order from least to greatest as: \(-2\frac{1}{5}\) (which is \(-2.2\)), \(-2.1\), \(2\frac{1}{10}\) (which is \(2.1\)), \(2.12\).

Answer:

\(-2\frac{1}{5}\), \(-2.1\), \(2\frac{1}{10}\), \(2.12\)