The concept of decimals

### 1.1. Knowledge to remember

1.1.1. The concept of decimals

**a) **

1 dm or \(\frac{1}{10}\)m is also written as 0.1m.

1cm or \(\frac{1}{100}\) m is also written as 0.01m

1mm or \(\frac{1}{1000}\) m is also written as 0.001m

The decimals \(\frac{1}{10}\), \(\frac{1}{100}\), \(\frac{1}{1000}\) are written as 0.1; 0.01; 0.001.

0.1 reads as: zero a comma; 0.1 = \(\frac{1}{10}\)

0.01 reads as: zero comma zero one; 0.01 = \(\frac{1}{100}\)

0.001 reads as: zero zero zero zero; 0.001 = \(\frac{1}{1000}\)

The numbers 0.1; 0.01; 0.001 is called a decimal number.

**b) **

5 dm or \(\frac{5}{10}\)m is also written as 0.5m.

7cm or \(\frac{7}{100}\) m is also written as 0.07m

9mm or \(\frac{9}{1000}\) m is also written as 0.009m

The decimals \(\frac{5}{10}\), \(\frac{7}{100}\), \(\frac{9}{1000}\) are written as 0.1; 0.01; 0.001.

0.5 reads as: zero a comma; 0.5 = \(\frac{5}{10}\)

0.07 reads as: zero comma zero one; 0.07 = \(\frac{7}{100}\)

0.001 reads as: zero zero zero one; 0.009 = \(\frac{9}{1000}\)

The numbers 0.5; 0.07; 0.009 is called decimal.

c)

2m 7dm or 2\(\frac{7}{10}\) m is written as 2.7 m; 2.7 reads as: two point seven meters

8m56cm or 8\(\frac{56}{100}\) m is written as 8.56m; 8.56m reads as: eighty seventy-six meters.

0m195mm or 0m and \(\frac{195}{1000}\)m is written as 0.195m;

0.195m reads: zero point one hundred and ninety five meters.

Numbers: 2.7; 8.56; 0.195 is also a decimal

Each decimal number has two parts: the integer part and the decimal part, which are separated by commas.

The digits to the left of the comma belong to the integer part, the digits to the right of the comma belong to the decimal part.

Example 1:

Example 2:

### 1.1.2. Decimal concept (continued)

square meter | dm | cm | mm |

2 | 7 | ||

8 | 5 | 6 | |

0 | first | 9 | 5 |

- 2m 7dm or \(2\frac{7}{{10}}\)m is written as 2.7 m;

2.7 reads as: two point seven meters.

- 8m 56cm or \(8\frac{56}{{100}}\)m is written as 8.56m;

8.56m read as: eight point fifty six meters.

- 0m 195mm or 0m and \(\frac{{195}}{{1000}}\)m is written as 0.195m;

0.195m reads: zero point one hundred and ninety five meters.

Numbers: 2.7 ; 8.56 ; 0.195 is also a decimal.

*Each decimal number has two parts: the integer part and the decimal part, which are separated by commas.*

*The digits to the left of the comma belong to the integer part, the digits to the right of the comma belong to the decimal part.*

**Example 1:**

Example 2:

### 1.2. Solve textbook exercises pages 34, 35

**Lesson 1 Textbook page 34**

Read decimal fractions and decimals on the lines of the number line:

a)

b)

**Solution guide:**

a) One-tenth (no point one)

Two tenths (no point two)

Three-tenths (no point three)

…………………………

Eight tenths (no point eight)

Nine tenths (no point nine)

b)

One percent (zero point not one )

Two percent (zero point not two)

…………………………

Eight percent (zero point zero eight)

Nine percent (zero point not nine).

Lesson 2 Textbook page 35

Fill in the correct decimal places (according to the pattern)

a) 7dm =\(\frac{7}{{10}}\)m = 0.7m b) 9cm = \(\frac{9}{{100}}\)mm = 0.09m

5dm =\(\frac{5}{{10}}\)mm = … m 3cm = \(\frac{3}{{100}}\)mm = … m

2mm = \(\frac{2}{{1000}}\)mm = … m 8mm = \(\frac{8}{{1000}}\)mm = … m

4g = \(\frac{4}{{1000}}\)mkg = … kg 6g = \(\frac{6}{{1000}}\)mkg = … kg

*Solution guide:*

a) 7dm =\(\frac{7}{{10}}\)m = 0.7m b) 9cm = \(\frac{9}{{100}}\)mm = 0.09m

5dm =\(\frac{5}{{10}}\)mm = 0.5 m 3cm = \(\frac{3}{{100}}\)mm = 0.03 m

2mm = \(\frac{2}{{1000}}\)mm = 0.002 m 8mm = \(\frac{8}{{1000}}\)mm = 0.008 m

4g = \(\frac{4}{{1000}}\)mkg = 0.004 kg 6g = \(\frac{6}{{1000}}\)mkg = 0.006 kg

Lesson 3 Textbook page 35

Fill in the blanks with the appropriate decimals and decimals (according to the pattern):

*Solution guide:*

### 1.3. Solution of textbook exercises page 37

Lesson 1 Textbook page 37

Read each of the following decimals:

9.4 ; 7.98 ; 25,477 ; 206,075 ; 0.307

*Solution guide:*

– 9.4 : Nine point four.

– 7.98 : Seven point ninety-eight.

– 25,477 : Twenty-five point four hundred and seventy-seven.

– 206,075 : Two hundred and six points zero hundred and seventy-five.

– 0.307 : No point three hundred and seven.

Lesson 2 Textbook page 37

Write the following mixed numbers as decimals and then read the numbers:

\(5\frac{9}{{10}};82\frac{{45}}{{100}};810\frac{{225}}{{1000}}\)

*Solution guide:*

Lesson 3 Textbook page 37

Write the following decimal numbers as decimal fractions:

0.1 ; 0.02 ; 0.004 ; 0.095

*Solution guide:*

\(\begin{array}{l}

0.1 = \frac{1}{{10}}\\

0.02 = \frac{2}{{100}}\\

0.004 = \frac{4}{{1000}}\\

0.095 = \frac{{95}}{{1000}}

\end{array}\)

.

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