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Decimal numbers on the number line
Decimal numbers can also be shown on a number line. In the following image, you can see that the scale of the number line must be adjusted according to accuracy. Showing \latex{ 80.35 } on a number line:
How we show \latex{ 80.35 }:
How we show \latex{ 80 }:
How we show \latex{ 80.3 }:
\latex{ 80 }
\latex{ 0 }
\latex{ 10 }
\latex{ 20 }
\latex{ 30 }
\latex{ 40 }
\latex{ 50 }
\latex{ 60 }
\latex{ 70 }
\latex{ 81.0 }
\latex{ 80 }
\latex{ 90 }
\latex{ 100 }
\latex{ 90 }
\latex{ 89 }
\latex{ 88 }
\latex{ 87 }
\latex{ 86 }
\latex{ 85 }
\latex{ 84 }
\latex{ 83 }
\latex{ 82 }
\latex{ 81 }
\latex{ 80 }
\latex{ 80.3 }
\latex{ 80.0 }
\latex{ 80.1 }
\latex{ 80.2 }
\latex{ 80.35 }
\latex{ 80.4 }
\latex{ 80.5 }
\latex{ 80.6 }
\latex{ 80.7 }
\latex{ 80.8 }
\latex{ 80.9 }
\latex{ 80.3 }
Example 1
The results of the \latex{ 60 }-\latex{ metre } dash were the following:
Dan \latex{ 12.2 } \latex{ s }; Frank \latex{ 11.7 } \latex{ s }; Matt \latex{ 11.4 } \latex{ s }; Victor \latex{ 13.8 } \latex{ s } and Rob \latex{ 13.2 } \latex{ s }.
Show the results of each athlete on a number line. What was their order?
Show the results of each athlete on a number line. What was their order?
Solution
Since the results fall between \latex{ 11 } and \latex{ 14 } seconds, it is enough to show the part of the number line between \latex{ 11 } and \latex{ 14 }. The results are accurate to one-tenth of a second, so the units must be divided into \latex{ 10 } equal parts.
\latex{ 11 }
\latex{ 12 }
\latex{ 13 }
\latex{ 14 }
\latex{ 13.8 }
\latex{ 13.2 }
\latex{ 12.2 }
\latex{ 11.7 }
\latex{ 11.4 }
The number line shows you that the order of the athletes was Matt, Frank, Dan, Rob, and Victor.
Example 2
Where are the numbers
a) greater than \latex{ 1.2 };
b) not greater than \latex{ 4.7 };
c) not smaller than \latex{ 1.2 } and smaller than \latex{ 4.7 } on a number line?
Solution
\latex{\textcolor{#17A5DE}{\square\leq 4.7.}} \latex{ 4.7 } is part of the blue set.
a)
b)
c)
\latex{\textcolor{#ED145A}{1.2\lt \square. }} \latex{ 1.2 } is not part of the red set.
\latex{\textcolor{#09A04F}{1.2\leq \square \lt 4.7.}} \latex{ 1.2 } is part of the green set; however, \latex{ 4.7 } is not.
\latex{ 1 }
\latex{ 2 }
\latex{ 3 }
\latex{ 4 }
\latex{ 5 }
\latex{ 1 }
\latex{ 2 }
\latex{ 4 }
\latex{ 3 }
\latex{ 5 }
\latex{ 1 }
\latex{ 2 }
\latex{ 3 }
\latex{ 4 }
\latex{ 5 }
\latex{ 1.2 }
\latex{ 4.7 }
\latex{ 4.7 }
\latex{ 1.2 }
Exercises
{{exercise_number}}. Mark the numbers on a number line.
A = zero and five tenths
B = one and two tenths
C = two and twenty-five one-hundredths
D = four and three tenths
E = three and fifty one-hundredths
{{exercise_number}}. Show the following decimals on a number line.
a) \latex{ A } = \latex{ 52.8 }; \latex{ B }= \latex{ 51.9 }; \latex{ C } = \latex{ 53.7 }; \latex{ D } = \latex{ 53.3 }; \latex{ E } = \latex{ 53 }; \latex{ F } = \latex{ 51.7 }
b) \latex{ G } = \latex{ 3.193 }; \latex{ H } = \latex{ 3.211 }; \latex{ I } = \latex{ 3.208 }; \latex{ J } = \latex{ 3.199 }; \latex{ K } = \latex{ 3.19 }; \latex{ L }= \latex{ 3.2 }
c) \latex{ M } = \latex{ 0.297 }; \latex{ N } = \latex{ 0.304 }; \latex{ O } = \latex{ 0.29 }; \latex{ P } = \latex{ 0.311 }; \latex{ Q } = \latex{ 0.308 }; \latex{ R } = \latex{ 0.3 }
b) \latex{ G } = \latex{ 3.193 }; \latex{ H } = \latex{ 3.211 }; \latex{ I } = \latex{ 3.208 }; \latex{ J } = \latex{ 3.199 }; \latex{ K } = \latex{ 3.19 }; \latex{ L }= \latex{ 3.2 }
c) \latex{ M } = \latex{ 0.297 }; \latex{ N } = \latex{ 0.304 }; \latex{ O } = \latex{ 0.29 }; \latex{ P } = \latex{ 0.311 }; \latex{ Q } = \latex{ 0.308 }; \latex{ R } = \latex{ 0.3 }
{{exercise_number}}. Show the following decimals on a number line. Mark the decimals whose place cannot be shown accurately.
A = \latex{ 11.4 }
B = \latex{ 12.36 }
C = \latex{ 10.92 }
D = \latex{ 11.500 }
E = \latex{ 12.25 }
F = \latex{ 10.99 }
{{exercise_number}}. Show the position of the decimals that are members of the following sets.
a) \latex{2\lt \textcolor{#09A04F}{\square} \leq 3}
b) \latex{1.2 \leq \textcolor{#ED145A}{\triangle} \leq 1.3}
c) \latex{0.12\lt \textcolor{#17A5DE}{\bigcirc} \lt 0.13}
{{exercise_number}}. Show on a number line the decimals that are
a) greater than \latex{ 2.8 };
b) not smaller than \latex{ 2.8 };
c) less than \latex{ 5.3 };
d) not greater than \latex{ 5.3 };
e) greater than \latex{ 0.7 } but not greater than \latex{ 3.5 }.
Quiz
What mathematical symbol should be used between \latex{ 5 } and \latex{ 6 } so the resulting number is greater than \latex{ 5 } and less than \latex{ 6 }?
