Write area measurements as decimals

### 1.1. Knowledge to remember

**a) Example 1: **Fill in the correct decimal places:

3m^{2} 5dm^{2} = …m^{2}

Method: 3m^{2} 5dm^{2} = \(3\tfrac{5}{100}\) m^{2 }= 3.05 m^{2 }

So: 3m^{2} 5dm^{2} = 3.05 m^{2}

**b) Example 2: **Fill in the correct decimal places:

42 dm^{2} = …m^{2}

Method: 42 dm^{2 }= \(\frac{42}{100}\) m^{2 }= 0.42 m^{2}

So: 42 dm^{2} = 0.42 m^{2}

### 1.2. Solving textbook exercises on page 47

**Lesson 1:**

Fill in the correct decimal places:

a) 56dm^{2}=…m^{2}

b) 17dm^{2}23cm^{2}=….dm^{2}

c) 23cm^{2}=…dm^{2}

d) 2cm^{2}5mm^{2}=…cm^{2}

*Solution guide:*

\(\begin{array}{l}

a)56d{m^2} = \frac{{56}}{{100}}{m^2} = 0.56{m^2}\\

b)17d{m^2}\:23c{m^2} = 17\frac{{23}}{{100}}d{m^2}\\

c)23c{m^2} = \frac{{23}}{{100}}d{m^2} = 0.23d{m^2}\\

d)2c{m^2}\:5m{m^2} = 2\frac{5}{{100}}c{m^2} = 2.05c{m^2}

\end{array}\)

Lesson 2:

Fill in the correct decimal places:

a) 1654m^{2}=…ha b) 5000m^{2}=…ha

c) 1ha=…km^{2} d) 15ha=…km^{2}

*Solution guide:*

\(\begin{array}{l}

a)1654{m^2} = \frac{{1654}}{{10000}}ha = 0.1654ha\\

b)5000{m^2} = \frac{{5000}}{{100000}}ha = 0.5ha\\

c)1ha = \frac{1}{{100}}k{m^2} = 0.01k{m^2}\\

d)15ha = \frac{{15}}{{100}}k{m^2} = 0.15k{m^2}

\end{array}\)

Lesson 3:

Write the correct number in the dot:

a) 5.34km^{2}=…ha

b) 16.5m^{2}=…m^{2}…dm^{2}

c) 6.5km^{2}=…ha

d) 7,6256ha=…m^{2}

*Solution guide:*

\(\begin{array}{l}

a)5,34k{m^2} = 5\frac{{34}}{{100}}k{m^2} = 5k{m^2}\:34ha = 534ha\\

b)16.5{m^2} = 16\frac{5}{{10}}{m^2} = 16\frac{{50}}{{100}}{m^2} = 16{m ^2}\:50d{m^2}\\

c)6,5k{m^2} = 6\frac{5}{{10}}k{m^2} = 6\frac{{50}}{{100}}k{m^2} = 6k {m^2}\:50ha = 650ha\\

d)7.6256ha = 7\frac{{6256}}{{10000}}ha = 7ha6256{m^2}

\end{array}\)

### 1.3. Solving exercises in textbooks General practice page 47

Lesson 1:

Fill in the correct decimal places:

a) 42m34cm=…m

b) 56m29cm=…dm

c) 6m2cm=…m

d) 4352m=….km

*Solution guide:*

\(\begin{array}{l}

a)42m34cm = 42\frac{{34}}{{100}}m = 42.34m\\

b) 56m29cm = 56m + 20cm + 9cm\\

= 560dm + 2dm + 9cm = 562dm + 9cm\\

= 562\frac{9}{{10}}dm = 562.9dm\\

c)6m\:2cm = 6\frac{2}{{100}}dm = 6.02m\\

d) 4352m = 4000m + 352m\\

= 4km\:352m = 4\frac{{352}}{{1000}}km = 4,352km

\end{array}\)

Lesson 2:

Write the following numbers as measurements in kilograms:

a) 500g b) 347g c) 1.5 tons.

*Solution guide:*

\(\begin{array}{l}

a)500g = \frac{{500}}{{1000}}kg = 0.5kg\\

b)347g = \frac{{347}}{{1000}}kg = 0.347kg

\end{array}\)

c) 1.5 tons = \(1\frac{5}{{10}}\) tons =

$\mathrm{first}$ton 5 quintals kg + 500kg = 1500kg

Lesson 3:

Write the following measurements as square meters:

a) 7km^{2}; 4ha; 8.5ha

b) 30dm^{2}; 300dm^{2}; 515dm^{2}

*Solution guide:*

\(\begin{array}{l}

a)7k{m^2} = 7000000{m^2}\\

4ha = 40000{m^2}\\

8.5ha = 8510ha = 8\frac{{5000}}{{10000}}ha = 8ha5000{m^2} = 85000{m^2}\\

b)30d{m^2} = \frac{{30}}{{100}}{m^2} = 0.30{m^2} = 0.3{m^2}\\

300d{m^2} = 3{m^2}\\

515d{m^2} = 500d{m^2} + 15d{m^2} = 5{m^2}\:15d{m^2} = 5\frac{{15}}{{100}}{ m^2} = 5.15{m^2}

\end{array}\)

Lesson 4:

A rectangular schoolyard has half a perimeter of 0.15km and a width equal to two thirds of its length. Calculate the area of the school yard with the unit of measure is square meters, is hectares.

*Solution guide:*

Change 0.15km = 150m.

We have a diagram:

According to the diagram, the total number of equal parts is:

2 + 3 = 5 (parts)

The width of the field is:

150 : 5 × 2 = 60(m)

The length of the field is:

150 − 60 = 90(m)

The field area is:

90 × 60 = 5400 (m^{2}) = 0.54 ha

Answer: 5400(m^{2}) or 0.54ha

### 1.4. Solving exercises in textbooks General practice page 48

Lesson 1:

Write the following measurements as decimals in meters:

a) 3m6dm b) 4dm

c) 34m5cm d) 345cm

*Solution guide:*

\(\begin{array}{l}

a)3m\:6dm = 3\frac{6}{{10}}m = 3.6m\\

b)4dm = \frac{4}{{10}}m = 0.4m\\

c)34m5cm = 34\frac{5}{{100}}m = 34.05m\\

d)345cm = 300cm + 45cm = 3m\:45cm = 3\frac{{45}}{{100}}m = 3.45m

\end{array}\)

Lesson 2:

Write the appropriate measurement in the blank (according to the form):

The unit of measurement is ton | The unit of measurement is kilograms |

3.2 tons | 3200kg |

502kg | |

2.5 tons | |

21kg |

*Solution guide:*

\(502kg = \frac{{502}}{{1000}}\) tons = 0.502 tons

2.5 tons = 2 tons \(\frac{5}{{10}}\) tons = 2 tons 5 quintals = 2000kg + 500kg = 2500kg

21kg = \(\frac{21}{{1000}}\) tons = 0.021 tons

So we have the following table of results:

The unit of measurement is ton | The unit of measurement is kilograms |

3.2 tons | 3200kg |

0.502 tons | 502kg |

2.5 tons | 2500kg |

0.021 tons | 21kg |

Lesson 3:

Fill in the correct decimal places:

a) 42dm4cm=….dm ;

b) 56cm9mm=…cm;

c) 26m2cm=….m26

*Solution guide:*

\(\begin{array}{l}

a)42dm\:4cm = 42\frac{4}{{10}}dm = 42.4dm\\

b)56cm9mm = 56\frac{9}{{10}}cm = 56.9cm\\

c)26m\:2cm = 26\frac{2}{{100}}m = 26.02m

\end{array}\)

Lesson 4:

Fill in the correct decimal places:

a) 3kg5g=…kg

b) 30g=….kg

c) 1103g=…kg

*Solution guide:*

\(\begin{array}{l}

a)3kg5g = 3\frac{5}{{1000}}kg = 3,005kg;\\

b)30g = \frac{{30}}{{1000}}kg = 0.030kg = 0.03kg\\

c)1103g = 1000g + 103g = 1kg\:103g = 1\frac{{103}}{{1000}}kg = 1,103kg

\end{array}\)

### 1.5. Solving exercises in textbooks General practice pages 48, 49

Lesson 1:

Convert the following decimal fractions to decimals, and then read the decimals:

\(\begin{array}{l}

a)\frac{{127}}{{10}}\\

b)\frac{{65}}{{100}}\\

c)\frac{{2005}}{{1000}}\\

d)\frac{8}{{1000}}

\end{array}\)

*Solution guide:*

a) \(\frac{{127}}{{10}} = 12\frac{7}{{10}} = 12.7\)

12.7 reads as twelve point seven

b) \(\frac{{65}}{{100}} = 0.65\)

0.65 read as zero point sixty-five

c) \(\frac{{2005}}{{1000}} = 2\frac{5}{{1000}} = 2,005\)

2,005 reads as two decimal places zero zero five.

d) \(\frac{8}{{1000}} = 0.008\)

0.008 reads as zero zero zero eight

Lesson 2:

Which of the following length measurements equals 11.02km?

a) 11.20km b) 11,020km

c) 11km20m d) 11020m

*Solution guide:*

\(\begin{array}{l}

11.02km = 11,020km\\

11km\:20m = 11\frac{{20}}{{1000}}km = 11,020km = 11.02km\\

11020m = 11000m + 20m = 11km20m = 11\frac{{20}}{{1000}}km\\

= 11,020km = 11.02km

\end{array}\)

Choose b, c, d

Lesson 3:

Fill in the correct decimal places:

a) 4m85cm=…m b) 72ha=….km^{2}

*Solution guide:*

\(\begin{array}{l}

a)4m85cm = 4\frac{{85}}{{100}}m = 4.85m\\

b)72ha = \frac{{72}}{{100}}k{m^2} = 0.72k{m^2}

\end{array}\)

Lesson 4:

Buy 12 boxes of math school supplies for 180000 VND. How much does it cost to buy 36 boxes of such math supplies?

*Solution guide:*

Buy 1 box of math school supplies, the total amount is:

180000 : 12 = 15000 (VND)

Buy 36 boxes of math school supplies, the total amount is:

15000 × 36 = 540000 (VND)

Answer: 540000 VND.

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