Positive and negative numbers and zero - Examples, Exercises and Solutions

Let's begin by marking F and 0 on the number line

We can thus determine that:

$F=0$

Therefore, the distance is 0 steps.

We first mark the letter C on the number line and then proceed towards the letter H:

Note that the distance between the two letters is 5 steps.

One might think that as a consequence of the displacement on the axis being towards the negative domain, the result is also negative.

However it is important to keep in mind that here we are referring to the distance.

Distance can never be negative.

Even if the displacement is towards the negative domain, the distance is an existing value.

We first mark the letter D on the number line and then proceed towards the letter K:

Note that the distance between the two letters is 7 steps.

Let's begin by marking the letter J on the number line and then proceeding towards the letter D:

Note that the distance between the two letters is 6 steps

One might think that because there are numbers on the axis that go into the negative domain, that the result must also negative.

However it is important to keep in mind that here we are asking about distance.

Distance can never be negative.

Even if we move towards or from the domain of negativity, distance is an existing value (absolute value).

We can think of it as if we were counting the number of steps, and it doesn't matter if we start from five or minus five, both are 5 steps away from zero.

We first mark the letter I on the number line and then proceed towards the letter E:

Note that the distance between the two letters is 4 steps.

Let's begin by marking the letter D on the number line and then proceeding towards the letter I:

Note that the distance between the two letters is 5 steps

If we draw a number line, we can see that to the right of zero are positive numbers, and to the left of zero are negative numbers:

Therefore, the answer is correct.

If we draw a number line, we can see that the number minus 6 is located to the left of the number 2:

Therefore, the answer is not correct.

Indeed, both forms are identical since a number without a sign will be positive, as in the case of 3.98

If there is a plus sign before the number, the number is necessarily positive, as in the case of +3.98

Therefore, the answer is correct.

In mathematics, numbers are categorized as either positive or negative, and this is denoted using a sign. For example, positive numbers might include a "+" sign on the left (though it's often omitted), such as $+3$ or simply $3$, whereas negative numbers require a "-" sign, such as $-3$.

The placement of the sign is crucial for properly understanding the value and meaning of the number. The sign is always placed to the left of the number when it comes to expressing signed numbers on the number line, or anywhere formally outside of a context where postfix notation is specifically used (e.g., for programming or algorithmic purposes).

Therefore, the provided statement "The sign is always written to the left of the number" is indeed True.

The sign cannot be omitted as it determines whether the number will be negative or positive.

The answer is indeed correct, any positive number to the right of zero is inevitably greater than zero.

The answer is incorrect because neative 3 is greater than negative 4:

-4 < -3