mozaMedical by Mozaik Education

Length

\latex{ 1 } \latex{ fathom }

\latex{ 1 } \latex{ foot }

\latex{ 1 } \latex{ span }

Early units of length were closely related to the human body (\latex{ fathom }, \latex{ foot }, \latex{ span }, etc.).

When people established trade relationships with other cultures, the standardisation of the units of measurement became necessary. Today, most countries use the units of measurement adopted during the French Revolution at the end of the \latex{ 1700s }. The basic unit of length was defined as the forty-millionth part of the Paris meridian, that is, \latex{ 1 } \latex{ metre }.

Measuring certain lengths in \latex{ metres } might result in too large or too small values. Thus, it is a good idea to introduce other units as well.

\latex{ 1 } \latex{ kilometre }

\latex{ 1 } \latex{ metre }

\latex{ 1 } \latex{ millimetre }

\latex{ 1 } \latex{ centimetre }

\latex{ 1 } \latex{ decimetre }

The units of length:

\latex{1\; \textcolor{#e3004f}{mm} \lt 1\; \textcolor{#e3004f}{cm} \lt 1\; \textcolor{#e3004f}{dm} \lt 1\; \textcolor{#e3004f}{m} \lt 1\;\textcolor{#e3004f}{km}}

\latex{10\;mm = 1 \;cm \;\;\;\;\;10 \;cm = 1 \;dm\;\;\;\;\; 10 \;dm = 1 \;m \;\;\;\;\;1,000 \;m = 1\; km}

\latex{1\;km\;=\;1,000\;m\;=\;10,000\;dm\;=\;100,000\;cm\;=\;1,000,000\;mm}

\latex{\times1,000}

\latex{\times10}

Exercises

{{exercise_number}}. Estimate first, then measure

a) the height of the letter \latex{ E } in the title above;
b) the length of the row of dots above;
c) the thickness of a maths book;
d) the height of your maths book’s front cover;
e) the width of your maths book’s front cover.

{{exercise_number}}. Measure your span. How many spans long is a desk? Measure the length of the desk in \latex{ centimetres } as well.

{{exercise_number}}. Draw the sole of your shoe on a paper, then measure its \latex{ perimeter }.

{{exercise_number}}. Eve told her mother: "Dad and I both measured our desks, and we each got \latex{ 5 } spans." Whose desk is longer, and by how much if Eve’s span is \latex{ 15\,cm } and her father’s span is \latex{ 25\,cm ?}

{{exercise_number}}. The ant can only measure in \latex{ millimetres }, the mouse in \latex{ centimetres }, the rabbit in \latex{ decimetres } and the elephant in \latex{ metres }. Convert the following amounts into their units. (For an ant, \latex{ 5\, dm\,4\,cm = 500\,mm + 40\,mm = 540\,mm }.)

a) \latex{ 3\,m\, 4\,cm }
b) \latex{ 67\,cm\,8 \,mm }
c) \latex{ 9\,m\,78 \,mm }
d) \latex{ 13\,m\,57 \,cm }

a) \latex{ 5,000\,mm }
b) \latex{ 48\,dm\,6\, cm }
c) \latex{ 2\,m\,87 \,cm }
d) \latex{ 13\,m\,25 \,cm }

a) \latex{ 6,700\,mm }

b) \latex{ 3\,m\,90 \,cm }

c) \latex{ 12\,m\,70 \,cm }
d) \latex{ 27\,m\,430\,cm }

a) \latex{ 300\,cm }
b) \latex{ 5,900\,cm }
c) \latex{ 5\,m\,400 \,cm }
d) \latex{ 40\,m\,700\,cm }

{{exercise_number}}. This traffic sign is before a bridge. Can the cars with the following heights cross the bridge?

a) \latex{ 328\,cm }

c) \latex{ 2,270\,mm }

e) \latex{ 1\,m\,89\,cm }

g) \latex{ 3\,m\,25\,cm }

b) \latex{ 250\,cm }
d) \latex{ 1,187\,cm }
f) \latex{ 2\,m\,110\,cm }
h) \latex{ 2\,m\,96\,cm } (→)

{{exercise_number}}. Which one is greater?

a) \latex{ 16\,mm } or \latex{ 2\,cm }

b) \latex{ 28\,km } or \latex{ 5,600\,m }

c) \latex{ 5,670\,cm } or \latex{ 48\,m }

d) \latex{ 1,867\,m } or \latex{ 1 } and a half \latex{ km }

{{exercise_number}}. Choose the most probable answer.

a) The width of a newspaper: \latex{ 30\,mm }, \latex{ 30\,cm }, \latex{ 3\,km }.
b) The height of a basketball player: \latex{ 1\,km }, \latex{ 100\,cm }, \latex{ 2,000 \,mm }.
c) The length of a new pencil: \latex{ 19\,mm }, \latex{ 19\,cm }, \latex{ 56\,cm }.
d) The length of a shopping trip: \latex{ 5\,mm }, \latex{ 5\,cm }, \latex{ 5\,km }.
e) The length of a hand on a wristwatch: \latex{ 20\,cm }, \latex{ 12\,mm }, \latex{ 5\,cm }.

{{exercise_number}}. Arrange the following cities in ascending order according to their distance from the Equator: Budapest, Rome, Prague, Helsinki.

{{exercise_number}}. Which of the following units would an astronomer, a surveyor, a mason, a carpenter and a keysmith use most often?

\latex{ centimetre }, \latex{ kilometre }, one-tenth of a \latex{ millimetre }, \latex{ millimetre }, \latex{ metre }

{{exercise_number}}. Arrange the birds in descending order according to their wingspan.

\latex{ 195\,cm }

Grey heron

\latex{ 63\,cm }

Scops owl

\latex{ 49\,cm }

Bee-eater

\latex{ 110\,cm }

Black-headed gull

{{exercise_number}}. A part of a \latex{ 10 }-\latex{ m }-long measuring tape has been ripped off. In a long jump competition, this tape was used to measure the distances by placing the \latex{ 10\,cm } mark at the starting point. According to the tape, Zack jumped \latex{ 380\,cm }. How far did he actually jump?

{{exercise_number}}.

a) Only the \latex{ 0 } and the \latex{ 6\,cm } marks are visible on an old ruler. At least how many marks should be added to the ruler so you can measure every \latex{ centimetre } between \latex{ 0 } and \latex{ 6 }?

b) Only the \latex{ 0 } and the \latex{ 12\,cm } marks are visible on a ruler. At least how many marks should be added to the ruler so you can measure every \latex{ centimetre } between \latex{ 0 } and \latex{ 12 }?

Quiz

A tailor has a \latex{ 16 }-\latex{m}-long roll of fabric. He cuts off \latex{ 2 } \latex{metres} every day. On which day will he cut off the last piece of fabric?

Mathematics 5.

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