1.08 Identifying and representing integers
Consider the point on the number line.
What number is represented by the point on the number line?
Is the number positive, negative or neither?
State the integer that the point furthest to the left on the number line lies on:
State whether each of the following numbers is an integer:
State the integer that the point is plotted on for each of the following number lines:
Plot the following integers on a number line:
Determine whether the following statements are true or false:
- 15 can be written as 15.
6 is equal to 6.
7 can be written as -7.
-10 is equal to -10.
-20 can be written as -20.
-8 is equal to 8.
1 can be written as 1.
Zero is neither positive nor negative.
Describe how to tell if two integers on a number line are opposites.
The integers 3 and - 3 are plotted on the following number line:
Determine whether the following statements are true or false:
3 and - 3 appear on opposite sides of 0, but are not the same distance from 0.
3 and - 3 are the same distance from 0, but do not have the same value.
3 and - 3 are the same distance from 0, and have the same value.
Plot the number 8 on a number line.
On the same number line, plot the other number which is the same distance from 0 as the number 8.
State the number plotted in part (b).
Consider the integer 19.
State its opposite.
True or False: "The opposite of a number is always greater than the number itself."
Plot the opposite of the number 6 on a number line.
On the same number line, plot the opposite of -6.
True or False: "The opposite of the opposite of a number is the original number itself."
State the integer that is the opposite of forty five.
State the integer that is the opposite of the opposite of the following integers:
Which value represents spending \$33: +33 or -33?
State whether the following situations could represent the number - 14:
A weight gain of 14 \text{ kg}.
Walking down 14 flights of stairs.
A tree grew 14 \text{ cm} in a month.
The temperature dropped 14 \degree \text{F} overnight.
A loss of \$ 14.
A distance of 14 \text{ m} above sea level.
A withdrawal of \$14 in a bank account.
The amount of harvest decreased by 14 \text{ kg} this year.
Write an integer to represent each of the following statements:
A price rise of \$17.
A loss of \$176.
A temperature drop of 5 \degree \text{F}.
58 \degree \text{F} above 0 \degree \text{F}.
An elevation of 980 \text{ ft}.
Bob grew by 9 \text{ cm} last year.
There are 14 more people at a school this year than last year.
Buffy deposited \$ 100 to his account.
State the integer that represents the opposite of the following:
Descending 9 floors.
A weight loss of 14 \text{ kg}.
Depositing \$75 in to a bank account.
A distance of 320 \text{ ft} below sea level.
A weight gain of 8 \text{ kg}.
Ascending 10 floors.
Withdrawing \$145 from a bank account.
A profit of \$650.
At high tide, the water level was 5 \text{ ft} above a marker and at low tide, the water level was 5 \text{ ft} below the marker. Plot the high and low tide measure on a number line.
The temperature over a day rose and fell. It ended up 0 \degree \text{F} from where it started at the beginning of the day. Is the temperature lower, higher, or exactly the same as it was at the beginning of the day?
Consider the following statement: "Arriving 18 minutes late."
State the opposite of "Arriving 18 minutes late".
Suppose "Arriving 18 minutes late" is represented by the number 18. State the integer that should represent its opposite.
A gain of \$300 can be represented by the integer 300.
State the opposite of this situation.
State the integer that represents your answer in part (a).
A temperature of 8 \degree \text{F} below zero can be represented by the integer - 8.
State the integer that represents the opposite of this temperature.
A temperature drop of 17 \degree \text{F} can be represented by the integer - 17.
State an integer that represents the opposite of a temperature drop of 17 \degree \text{F}.
State an integer that represents the opposite of the opposite of a temperature drop of 17\degree \text{F}.
A mountain peak is measured to have a height of 5000 \text{ m} above sea level. An ocean trench is found that is the same distance below sea level.
If the height above sea level of the mountain peak is represented by the number 5000, state the integer that represents the location of the trench.
In this scenario, state what the integer 0 represents.