Can someone please explain this question? Order the following sets of rational numbers from least to greatest: A) 2 1/2, 2.333..., 2.51; 6000/29 B) 3.33; 577/154; 3.121212...; 3 5/8 C) 22; 32/11; 477/154; 2.7171... Here is my answer: A) 6000/29; 2.333...; 2.51; 2 1/2
B) 3.121212...; 3.33; 3.75; 3 5/8
C) 2.7171...; 2.91; 3.10; 22 Is this correct?
Here are my changes: A) 2.333...; 2 1/2; 2,51; 6000/29
B) 3.121212...; 3.33; 3 5/8; 577/154
Is this correct?
C) is the only correct one
in B) 3 5/8 = 3.625, clearly < than 3.75
in A) 6000/29 is clearly the largest, you have it as the smallest.
and 2 1/2 = 2.5
which is bigger, 2.51 or 2.5 ?
(which is more $2.51 or $2.50 ?)
yes
To order the sets of rational numbers from least to greatest, we can follow the following steps:
For Set A: {2 1/2, 2.333..., 2.51; 6000/29}
Step 1: Convert all the mixed numbers to improper fractions.
2 1/2 can be written as 5/2.
Step 2: Compare the fractions and decimals.
2.333... is approximately 2 and 1/3. Which is the same as 7/3.
2.51 can be written as 251/100.
Step 3: Arrange the fractions and decimals in ascending order.
So, the ordered set A would be: {6000/29, 7/3, 251/100, 5/2}
For Set B: {3.33; 577/154; 3.121212...; 3 5/8}
Step 1: Convert mixed numbers to improper fractions.
3 5/8 can be written as 29/8.
Step 2: Compare fractions and decimals.
3.121212... is a repeating decimal and is equivalent to 37/11.
Step 3: Arrange the fractions and decimals in ascending order.
So, the ordered set B would be: {37/11, 3.121212..., 3.33, 29/8}
For Set C: {22; 32/11; 477/154; 2.7171...}
Step 1: Convert mixed numbers to improper fractions.
22 remains as it is.
32/11 already in fraction form.
2.7171... is an approximation of a decimal and can be written as an irrational number.
Step 2: Compare fractions and decimals.
477/154 is already in fraction form.
Step 3: Arrange the fractions and decimals in ascending order.
So, the ordered set C would be: {32/11, 477/154, 2.7171..., 22}
Now, let's compare your answer with the explanations provided.
Set A: Your answer - {6000/29, 2.333..., 2.51, 2 1/2}
Explanation - {6000/29, 7/3, 251/100, 5/2} ... Correct!
Set B: Your answer - {3.121212..., 3.33, 3.75, 3 5/8}
Explanation - {37/11, 3.121212..., 3.33, 29/8} ... Not correct! You have an incorrect value for 3.75.
Set C: Your answer - {2.7171..., 2.91, 3.10, 22}
Explanation - {32/11, 477/154, irrational, 22} ... Not correct! You have incorrect values for 2.91 and 3.1.
Therefore, your answer for Set A is correct, but the answers for Sets B and C are not entirely correct.