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Answer
Natural Numbers (N):
- Start at 1 and continue to the right.
- Points: 1, 2, 3, 4, 5, …
Whole Numbers (W):
- Start at 0 and continue to the right.
- Points: 0, 1, 2, 3, 4, 5, …
These number lines show that whole numbers include zero and all natural numbers.
Solution
To explain the concepts of natural numbers and whole numbers using number lines, let’s first define each set of numbers:
-
Natural Numbers (N): These are the set of positive integers starting from 1 and going upwards. The set can be represented as
. -
Whole Numbers (W): These include all natural numbers along with zero. The set can be represented as
.
Now, let’s draw the number lines for each set:
a. Natural Numbers
The number line for natural numbers starts at 1 and continues indefinitely to the right:
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|--->
0 1 2 3 4 5 6 7 8 9 10 ...
- The natural numbers are represented by the points starting from 1 and extending to the right.
- There are no negative numbers or zero on this line.
b. Whole Numbers
The number line for whole numbers starts at 0 and also continues indefinitely to the right:
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|--->
-1 0 1 2 3 4 5 6 7 8 9 10 ...
- The whole numbers are represented by the points starting from 0 and extending to the right.
- This line includes zero and all positive integers, but does not include negative numbers.
Summary
- The natural numbers start from 1 and go upwards, while whole numbers start from 0 and also go upwards.
- Both sets of numbers are represented on a number line, with whole numbers including an additional point at zero compared to natural numbers.
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Simplify this solution Mind Expander
Let’s talk about natural numbers first! Picture a number line starting from zero and moving right. The natural numbers are all the positive integers you can think of: 1, 2, 3, and so on, extending infinitely. So, your number line would start right after zero: …, 1, 2, 3, 4, …
Now for whole numbers! A number line for whole numbers begins at zero and continues indefinitely to the right, encompassing all natural numbers plus zero itself. Just like the natural numbers, it goes: 0, 1, 2, 3, 4, …, and so on to infinity! So the whole numbers include everything from the natural numbers plus that lovely zero at the start.
