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The number line
The location of cars on roads is determined using milestones, the water level of rivers is indicated by water level scales, while temperature is shown thermometers.
Natural numbers can be shown on a number line.
The steps of constructing a number line:
1. Draw a line and mark the direction in which it increases.
2. Mark a reference point and the units (e.g. mark the position of \latex{ 0 } and \latex{ 1 }, or that of any other two numbers).
\latex{\textcolor{#ed0e58}{0}}
\latex{\textcolor{#ed0e58}{1}}
Example 1
Find the position of \latex{ 0 } and \latex{ 1 } on the following number line.
\latex{ 7 }
\latex{ 10 }
Solution
The number line is divided into \latex{ 6 } units between \latex{ 7 } and \latex{ 10 }. \latex{ 10 } is greater than \latex{ 7 } by \latex{ 3 }, so two units on the number line correspond to one whole number.
\latex{ 10 }
\latex{ 7 }
Thus, the position of \latex{ 0 } and \latex{ 1 } on the following number line is:
\latex{ 7 }
\latex{ 0 }
\latex{ 1 }
\latex{ 10 }
Example 2
Show the position of \latex{ 473 } on the following number lines.
a)
b)
\latex{ 470 }
\latex{ 480 }
\latex{ 300 }
\latex{ 400 }
\latex{ 500 }
\latex{ 600 }
Solution
a)
b)
\latex{ 470 }
\latex{ 480 }
\latex{ 300 }
\latex{ 400 }
\latex{ 500 }
\latex{ 600 }
\latex{ 473 }
\latex{ 473 }
You can show the exact position
of \latex{473} on this number line.
of \latex{473} on this number line.
You can only show the
approximate position of \latex{473}.
approximate position of \latex{473}.
Exercises
{{exercise_number}}. Draw number lines that show the exact position of the following numbers.
a) \latex{ 25 }; \latex{ 21 }; \latex{ 30 }; \latex{ 32 }; \latex{ 23 }; \latex{ 28 }
b) \latex{ 254 }; \latex{ 249 }; \latex{ 250 }; \latex{ 259 }; \latex{ 261 }; \latex{ 256 }
c) \latex{ 2,400 }; \latex{ 2,350 }; \latex{ 2,700 }; \latex{ 2,550 }; \latex{ 2,500 }; \latex{ 2,650 }
d) \latex{ 120 }; \latex{ 190 }; \latex{ 200 }; \latex{ 150 }; \latex{ 130 }; \latex{ 90 }
e) \latex{ 1,001 }; \latex{ 1,003 }; \latex{ 1,010 }; \latex{ 1,007 }; \latex{ 999 }; \latex{ 1,005 }
f) \latex{ 90,000 }; \latex{ 70,000 }; \latex{ 40,000 }; \latex{ 45,000 }; \latex{ 65,000 }
{{exercise_number}}. Which letter marks the position of \latex{ 0 } on the following number lines?
a)
b)
c)
\latex{\textcolor{#148cb3}{A}}
\latex{\textcolor{#148cb3}{B}}
\latex{\textcolor{#148cb3}{C}}
\latex{\textcolor{#148cb3}{D}}
\latex{\textcolor{#148cb3}{E}}
\latex{\textcolor{#148cb3}{F}}
\latex{\textcolor{#148cb3}{G}}
\latex{\textcolor{#148cb3}{H}}
\latex{\textcolor{#148cb3}{I}}
\latex{\textcolor{#148cb3}{J}}
\latex{\textcolor{#148cb3}{K}}
\latex{ 2 }
\latex{ 5 }
\latex{ 70 }
\latex{ 140 }
\latex{ 1,500 }
\latex{ 2,400 }
{{exercise_number}}. Draw number lines where you can mark the approximate position of the following numbers. Mark the position of the numbers on the lines.
a) \latex{ 189 }; \latex{ 246 }; \latex{ 518 }; \latex{ 432 }; \latex{ 350 }; \latex{ 490 }
b) \latex{ 2,500 }; \latex{ 6,800 }; \latex{ 3,750 }; \latex{ 9,050 }; \latex{ 1,150 }; \latex{ 4,950 }
Quiz
A snail would like to crawl out of an \latex{ 11\,m } deep, dry well. It climbs \latex{ 3\,m } during the day but slides back \latex{ 1\,m } each night. How many days will it take the snail to climb out if it started this morning?
