Przeliczanie jednostek długości $1\mathrm{cm}=10\mathrm{mm}$ $1\text{dm}=10\mathrm{cm}$ $1\text{m}=10\text{dm},1\text{m}=100\mathrm{cm}$ $1\mathrm{km}=1000\text{m}$

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a)

Wyrazimy podane długości w milimetrach.

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$5\mathrm{cm}=5\cdot 1\mathrm{cm}=5\cdot 10\mathrm{mm}=\underline{\underline{50\mathrm{mm}}}$

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$13\mathrm{cm}=13\cdot 1\mathrm{cm}=13\cdot 10\mathrm{mm}=\underline{\underline{130\mathrm{mm}}}$

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$100\text{dm}=100\cdot \underline{1\text{dm}}=100\cdot \underline{10\mathrm{cm}}=100\cdot \underline{10\cdot 1\mathrm{cm}}=100\cdot \underline{10\cdot 10\mathrm{mm}}=\underline{\underline{10000\mathrm{mm}}}$

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$3\text{dm}=3\cdot 1\text{dm}=3\cdot 10\mathrm{cm}=30\mathrm{cm}=30\cdot 1\mathrm{cm}=30\cdot 10\mathrm{mm}=\underline{\underline{300\mathrm{mm}}}$

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$15\text{m}=15\cdot 1\text{m}=15\cdot 100\text{cm}=15000\text{cm}=15000\cdot 1\mathrm{cm}=15000\cdot 10\mathrm{mm}=\underline{\underline{150000\mathrm{mm}}}$

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$1\mathrm{km}=1000\text{m}=1000\cdot 1\text{m}=1000\cdot \underline{100\mathrm{cm}}=1000\cdot \underline{100\cdot 1\mathrm{cm}}=1000\cdot \underline{100\cdot 10\mathrm{mm}}=\underline{\underline{1000000\mathrm{mm}}}$

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b)

Wyrazimy podane długości w centymetrach.

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Skoro

$10\mathrm{mm}=1\text{cm}$

to

$40\mathrm{mm}=4\cdot 10\mathrm{mm}=4\cdot 1\mathrm{cm}=\underline{\underline{4\mathrm{cm}}}$

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$34\text{dm}=34\cdot 1\text{dm}=34\cdot 10\mathrm{cm}=\underline{\underline{340\mathrm{cm}}}$

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$80\text{dm}=80\cdot 1\text{dm}=80\cdot 10\mathrm{cm}=\underline{\underline{800\mathrm{cm}}}$

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$5\text{m}=5\cdot 1\text{m}=5\cdot 100\mathrm{cm}=\underline{\underline{500\mathrm{cm}}}$

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$16\text{m}=16\cdot 1\text{m}=16\cdot 100\mathrm{cm}=\underline{\underline{1600\mathrm{cm}}}$

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$3\mathrm{km}=3\cdot 1\mathrm{km}=3\cdot \underline{1000\text{m}}=3\cdot \underline{1000\cdot 1\text{m}}=3\cdot \underline{1000\cdot 100\mathrm{cm}}=\underline{\underline{300000\mathrm{cm}}}$

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c)

Wyrazimy podane długości w decymetrach.

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Skoro

$100\mathrm{mm}=1\text{dm}$

to

$1000\mathrm{mm}=\underline{\underline{10\text{dm}}}$

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Skoro

$10\mathrm{cm}=1\text{dm}$

to

$30\mathrm{cm}=3\cdot 10\mathrm{cm}=3\cdot 1\text{dm}=\underline{\underline{3\text{dm}}}$

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Skoro

$10\mathrm{cm}=1\text{dm}$

to

$350\mathrm{cm}=35\cdot 10\mathrm{cm}=35\cdot 1\text{dm}=\underline{\underline{35\text{dm}}}$

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$6m=6\cdot 1m=6\cdot 10\mathrm{dm}=\underline{\underline{60\text{dm}}}$

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$24m=24\cdot 1m=24\cdot 10\mathrm{dm}=\underline{\underline{240\text{dm}}}$

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$79\mathrm{km}=79\cdot 1\mathrm{km}=79\cdot \underline{1000\text{m}}=79\cdot \underline{1000\cdot 1\text{m}}=79\cdot \underline{1000\cdot 10\mathrm{dm}}=\underline{\underline{790000\mathrm{dm}}}$

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d)

Wyrazimy podane długości w metrach. 

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Możemy przeliczać jednostki, stosując schematy graficzne.

$700\cancel{0}\mathrm{mm}\underset{\begin{array}{c}\text{bo 10 mm}\\ \text{daje 1 cm}\end{array}}{\overset{:1\cancel{0}}{\to }}7\cancel{0}\cancel{0}\mathrm{cm}\underset{\begin{array}{c}\text{bo 100 cm}\\ \text{daje 1 m}\end{array}}{\overset{:1\cancel{0}\cancel{0}}{\to }}\underline{\underline{7\text{m}}}$

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$50\cancel{0}\cancel{0}\mathrm{cm}\underset{\begin{array}{c}\text{bo 100 cm}\\ \text{daje 1 m}\end{array}}{\overset{:1\cancel{0}\cancel{0}}{\to }}\underline{\underline{50\text{m}}}$

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$8\cancel{0}\mathrm{dm}\underset{\begin{array}{c}\text{bo 10 dm}\\ \text{daje 1 m}\end{array}}{\overset{:1\cancel{0}}{\to }}\underline{\underline{8\text{m}}}$

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$21\cancel{0}\mathrm{dm}\underset{\begin{array}{c}\text{bo 10 dm}\\ \text{daje 1 m}\end{array}}{\overset{:1\cancel{0}}{\to }}\underline{\underline{21\text{m}}}$

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$7\mathrm{km}\underset{\begin{array}{c}\text{bo 1 km}\\ \text{to 1000 m}\end{array}}{\overset{\cdot 1000}{\to }}\underline{\underline{7000\text{m}}}$

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$15\mathrm{km}\underset{\begin{array}{c}\text{bo 1 km}\\ \text{to 1000 m}\end{array}}{\overset{\cdot 1000}{\to }}\underline{\underline{15000\text{m}}}$

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e)

Wyrazimy podane długości w metrach. 

Jeśli tak nam wygodnie, możemy przeliczać jednostki, stosując schematy graficzne.

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$4800000\cancel{0}\mathrm{mm}\underset{\begin{array}{c}\text{bo 10 mm}\\ \text{daje 1 cm}\end{array}}{\overset{:1\cancel{0}}{\to }}48000\cancel{0}\cancel{0}\mathrm{cm}\underset{\begin{array}{c}\text{bo 100 cm}\\ \text{daje 1 m}\end{array}}{\overset{:1\cancel{0}\cancel{0}}{\to }}48\cancel{0}\cancel{0}\cancel{0}\text{m}\underset{\begin{array}{c}\text{bo 1000 m}\\ \text{daje 1 km}\end{array}}{\overset{:1\cancel{0}\cancel{0}\cancel{0}}{\to }}\underline{\underline{48\text{km}}}$

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$18000\cancel{0}\cancel{0}\mathrm{cm}\underset{\begin{array}{c}\text{bo 100 cm}\\ \text{daje 1 m}\end{array}}{\overset{:1\cancel{0}\cancel{0}}{\to }}18\cancel{0}\cancel{0}\cancel{0}\text{m}\underset{\begin{array}{c}\text{bo 1000 m}\\ \text{daje 1 km}\end{array}}{\overset{:1\cancel{0}\cancel{0}\cancel{0}}{\to }}\underline{\underline{18\text{km}}}$

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$54000\cancel{0}\mathrm{cm}\underset{\begin{array}{c}\text{bo 10 dm}\\ \text{daje 1 m}\end{array}}{\overset{:1\cancel{0}}{\to }}54\cancel{0}\cancel{0}\cancel{0}\text{m}\underset{\begin{array}{c}\text{bo 1000 m}\\ \text{daje 1 km}\end{array}}{\overset{:1\cancel{0}\cancel{0}\cancel{0}}{\to }}\underline{\underline{54\text{km}}}$

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$6\cancel{0}\cancel{0}\cancel{0}\text{m}\underset{\begin{array}{c}\text{bo 1000 m}\\ \text{daje 1 km}\end{array}}{\overset{:1\cancel{0}\cancel{0}\cancel{0}}{\to }}\underline{\underline{6\text{km}}}$