A number line shows the following numbers: −32, 0.5, 9–√, −2. Put them in the correct order on the number line.(2 points)
Wrong it goes
-3/2 --- -2 --- 0.5 --- 9 - √
-2 ---- -3/2 ------ 0.5 ------ √9
-32, -2, 0.5, 9-√
To put the numbers in the correct order on the number line, we need to arrange them from left to right.
The given numbers are:
−32
0.5
9–√
−2
Let's start by comparing the integers: −32 and −2. Since −32 is smaller than −2, we can put it to the left of −2 on the number line.
−32 -2
Next, we'll consider the decimal number: 0.5. Since 0.5 is between −32 and −2, we can place it in the middle of the number line.
−32 0.5 -2
Finally, we have the number 9–√. As the square root of any number is always positive, 9–√ will be greater than 0.5. Thus, we can place it to the right of 0.5 on the number line.
−32 0.5 -2 9–√
Therefore, the correct order on the number line is: −32, 0.5, −2, 9–√.
To put these numbers in the correct order on the number line, we need to understand how to compare and order numbers.
First, let's look at the given numbers: −32, 0.5, 9–√, −2.
To order numbers, we compare their values. Since these numbers include negative numbers and decimals, we need to consider their positions and values on the number line.
Step 1: Ordering Negative Numbers
On a number line, negative numbers are to the left of zero. So, let's compare −32 and −2. −32 is a smaller number than −2, so −32 will be placed to the left of −2 on the number line.
Number line so far: −32, −2
Step 2: Ordering Decimals
Now, let's compare 0.5 with the numbers we already have. 0.5 is a positive decimal and will be to the right of zero. Since we already have −2 to the right of −32, 0.5 will be placed between −2 and zero on the number line.
Number line so far: −32, −2, 0.5
Step 3: Ordering Radical Expressions
Now, let's consider the expression 9–√. To compare it with the numbers on the number line, we need to determine its value.
9–√ is an expression that represents a negative number because we have subtracted the square root from 9. The square root of a positive number is always positive. Therefore, 9–√ is less than zero.
Since we already have −32 to the left of zero on the number line, 9–√ will be placed to the left of −32.
Number line so far: 9–√, −32, −2, 0.5
Finally, we have placed all the given numbers on the number line in their correct order.
Number line: 9–√, −32, −2, 0.5