Write length measurements as decimals

### 1.1. Knowledge to remember

**a) Example 1: **Put the appropriate decimal in the dot:

6m4dm = …m

How to do: 6m4dm = \(6\tfrac{4}{10}\)m = 6.4m

So: 6m 4dm = 6.4m

**b) Example 2:** Put the appropriate decimal in the dot:

3m 5cm = …m

Method: 3m 5cm = \(3\tfrac{5}{100}\)m = 3.05m

so: 3m 5cm = 3.05m

### 1.2. Solution of textbook exercises page 44

**Lesson 1 of the textbook page 44:**

Fill in the correct decimal places:

a) 8m6dm=…m b) 2dm2cm=…dm

c) 3cm7cm=…m d) 23m13cm=…m

*Solution guide:*

a) \(8m\:6dm = 8\frac{6}{{10}}m = 8.6m\)

b) \(2dm\:2cm = 2\frac{2}{{10}} = 2,2dm\)

c) \(3m\:7cm = 3\frac{7}{{100}} = 3.07m\)

d) \(23m\:13cm = 23\frac{{13}}{{100}} = 23.13m\)

Lesson 2 Textbook page 44:

Write the number of the following measurements as decimals:

a) The unit of measurement is meters:

3m4dm; 2m5cm; 21m36cm

b) The unit of measurement is decimeter:

8dm7cm; 4dm32mm; 73mm.

*Solution guide:*

\(\begin{array}{l}

a)3m\:4dm = 3\frac{4}{{10}}m = 3.4m\\

2m\:5cm = 2\frac{5}{{100}}m = 2.05m\\

21m\:36cm = 21\frac{{36}}{{100}}m = 21.36m

\end{array}\)

\(\begin{array}{l}

b)8dm\:7cm = 8\frac{7}{{10}}dm = 8.7dm\\

4dm\:32mm = 4\frac{{32}}{{100}}dm = 4.32dm\\

73mm = \frac{{73}}{{100}}dm = 0.73dm

\end{array}\)

Lesson 3 Textbook page 44:

Put the appropriate decimal in the dot:

a) 5km302m=…km b) 5km75m=…km c) 302m=…km

*Solution guide:*

a) \(5km\:302m = 5\frac{{302}}{{1000}}km = 5,302km\)

b) \(5km\:75m = 5\frac{{75}}{{1000}}km = 5,075km\)

c) \(302m = \frac{{302}}{{1000}}km = 0.302km\)

1.3. Solving exercises in the textbook Practice page 45

Lesson 1 of the textbook page 45:

Put the appropriate decimal in the dot:

a) 35m23cm=…m

b) 51dm3cm=…dm

c) 14m7cm=….m

*Solution guide:*

\(\begin{array}{l}

a)35m\:23cm = 35\frac{{23}}{{100}}m = 35.23m\\

b)51dm3cm = 51\frac{3}{{10}}dm = 51.3dm\\

c)14m\:7cm = 14\frac{7}{{100}}m = 14.07m.

\end{array}\)

Lesson 2 Textbook page 45:

Put the appropriate decimal in the dot:

315cm=…m 234cm=…m

506cm=…m 34dm=…m

Model: 315cm = 3.15m.

Method: 315cm = 300cm + 15cm = 3m15cm

\( = 3\frac{{15}}{{100}}m = 3.15m\)

*Solution guide:*

\(\begin{array}{l}

234cm = 200cm + 34cm = 2m\:34cm = 2\frac{{34}}{{100}}m = 2.34m\\

506cm = 500cm + 6cm = 5m\:6cm = 5\frac{6}{{100}}m = 5.06m\\

34dm = \frac{{34}}{{10}}m = 3.4m

\end{array}\)

Lesson 3 Textbook page 45:

Write the following measurements as decimals in kilometers:

a) 3km245m b) 5km34m c) 307m.

*Solution guide:*

\(\begin{array}{l}

a)3km\:245m = 3\frac{{245}}{{1000}}km = 3,245km\\

b)5km\:34m = 5\frac{{34}}{{1000}}km = 5,034km\\

c)307m = \frac{{307}}{{1000}}km = 0.307km

\end{array}\)

Lesson 4 Textbook page 45:

Write the correct number in the dot:

a) 12.44m=…m…cm; b) 7.4dm=…dm…cm;

c) 3.45km=…mm; d) 34.3km=…m

*Solution guide:*

\(\begin{array}{l}

a)12.44m = 12\frac{{44}}{{100}}m = 12m\:44cm\\

b)7.4dm = 7\frac{4}{{10}}dm = 7dm\:4cm\\

c)3.45km = 3,450km = 3\frac{{450}}{{1000}}km = 3km450m = 3450m\\

d)34.3km = 34,300km = 34\frac{{300}}{{1000}}km = 34km300m = 34300m

\end{array}\)

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