1.10 Absolute values and number lines
Consider the number line below:
How far is the number 3 from 0?
Now, state the value of |3|.
How far is the number - 7 from 0?
Now, state the value of |-7|.
Describe what the absolute value of - 5 represents on a number line.
Write down all the numbers that have a value of:
Evaluate the following:
\left| - 3 \right|
\left| - 155 \right|
\left|3341\right|
\left| - 4.2 \right|
\left|6.4\right|
\left|\dfrac{6}{13}\right|
\left| - \dfrac{10}{19} \right|
State whether the following are smaller than |-39|:
-42
|-40|
|-10|
20
35
|25|
|-41|
-35
State whether the following are greater than |12|:
|-10|
|-15|
20
|-30|
|15|
|-18|
11
-17
Evaluate each of these numbers and order the results, from smallest to largest.
\left|28\right|,\, \left|15\right|,\, \left|23\right|
\left| - 33 \right|,\,\left| - 11 \right|,\, \left| - 22 \right|
\left|21\right|,\, \left| - 7 \right|,\, \left| - 49 \right|,\, \left|40\right|
\left|3.8\right|,\, \left| - 0.7 \right|,\, \left|7\right|,\, \left| - 9 \right|
If |a|=6, what values could a be equal to? Explain your answer.
Find the possible values of x for each of the following:
Identify the sign, \lt, \gt or =, that should appear between each pair of numbers to make each statement true:
\vert 9 \vert \, ⬚ \, \vert - 2\vert
\vert - 7 \vert \, ⬚ \, \vert 7\vert
\vert -9 \vert \, ⬚ \, \vert 0\vert
\vert - 7 \vert \, ⬚ \, \vert- 10 \vert
35 \, ⬚ \, \vert - 50 \vert
- \vert 29 \vert \, ⬚ \, - \vert 74 \vert
\vert -45 \vert \, ⬚ \, \vert 22 \vert
\vert -1 \vert \, ⬚ \, - \vert 30 \vert
Today, Santiago has a peak temperature of 36.4 \degree\text{C}, while Minneapolis has a peak temperature of -10.8 \degree\text{C}.
Which city had the least peak temperature today?
Which city's peak temperature is closer to the freezing point (0 \degree \text{C})?
Amelia has a bank account balance of - \$16.60. Marge has a bank account balance of - \$53.30.
Who has a bigger debt?
Who's account balance is further from a \$0 balance?