Question

7. Compare and order the following numbers:
9
5.2, -5.6666…, 3u9/10, √21

Answer 1

Step-by-step explanation:To compare and order the given numbers, examine each one:

1. 9: This is a whole number.

2. 5.2: This is a decimal number greater than 5.

3. -5.6666...: This is a repeating decimal, often written as -5.67 or rounded to -5.67.

4. 3⅘ or 3u9/10: This is a mixed number or fraction, equal to 3.9 or 3.90.

5. √21: This is the square root of 21, which is an irrational number, approximately equal to 4.5825.

To compare and order these numbers, we can follow these steps:

Step 1: Start by comparing the whole numbers (9, 5.2, -5.67, 3.9, and √21). The order from least to greatest is:

-5.67 < 3.9 < 5.2 < 9 < √21

Step 2: Next, compare the decimal numbers and fractions. We can convert the fraction 3⅘ or 3u9/10 to a decimal, which is 3.9.

The final order, from least to greatest, is:

-5.67 < 3.9 < 5.2 < 9 < √21

So, the correct order is -5.67, 3.9, 5.2, 9, and √21.

Answer 2

Answer: -5.6666..., 3u9/10, -17/3, 5.2, 9, √21

Explanation:

To compare and order the given numbers, let's start by organizing them in ascending order:

-5.6666..., 3u9/10, 5.2, 9, √21

First, let's compare -5.6666... and 3u9/10.

-5.6666... is a recurring decimal, which means it goes on forever. On the other hand, 3u9/10 is a fraction.

To compare these numbers, let's convert -5.6666... into a fraction. Let's call it x:

x = -5.6666...

Multiplying both sides of the equation by 10, we get:

10x = -56.6666...

Now, subtracting x from 10x, we have:

10x - x = -56.6666... - (-5.6666...)

9x = -51

Dividing both sides of the equation by 9, we find:

x = -51/9

Simplifying the fraction, we get:

x = -17/3

Comparing -17/3 and 3u9/10, we can see that -17/3 is smaller.

So, the order so far is:

-5.6666..., 3u9/10, -17/3, 5.2, 9, √21

Next, let's compare -17/3 and 5.2.

To compare these numbers, we can convert -17/3 into a decimal:

-17 ÷ 3 ≈ -5.6666...

Since -5.6666... is less than 5.2, the new order becomes:

-5.6666..., 3u9/10, -17/3, 5.2, 9, √21

Now, let's compare 5.2 and 9.

Since 5.2 is less than 9, the new order becomes:

-5.6666..., 3u9/10, -17/3, 5.2, 9, √21

Finally, let's compare 9 and √21.

√21 is an irrational number, meaning it cannot be expressed as a fraction or a terminating or repeating decimal. Comparing it with 9, we can't determine the exact order.

So, the final order is:

-5.6666..., 3u9/10, -17/3, 5.2, 9, √21