Compare two decimals

### 1.1. Knowledge to remember

**a) **

**Example 1;** Compare 8.1m and 7.9m

We can write: 8.1m = 81dm

7.9m = 79dm

We have: 81dm > 79dm (81 > 79 because in tens there are 8>7)

ie: 8.1m > 7.9m

So: 8.1 > 7.9 (the integer part has 8 > 7)

- Of two decimals with different integer parts, the decimal with the larger integer part is larger.

**b)**

**Example 2:** Compare 35.7m and 35,698m

We see that 35.7m and 35.698m have the same integer part, we compare to the decimal part:

The decimal part of 35.7m is \(\frac{7}{10}\)m = 7dm = 700mm

The decimal part of 35.698m is \(\frac{698}{1000}\)m = 698mm

That 700mm > 698mm

so: \(\frac{7}{10}\)m > \(\frac{698}{1000}\)m

Therefore: 35.7m > 35.698m

So 35.7 > 35,698 (integer parts are equal, tenths have 7>6)

- Of two decimals with equal integer parts, the decimal with the larger tenths is the greater number.

**c)**

- To compare two decimal numbers we can do the following:
- Compare the integer parts of those two numbers like comparing two natural numbers, the decimal number with the larger integer part is the larger number
- If the integer part of the two numbers are equal, then we compare the decimal, from tenths, hundredths, thousandths…to the same row, which decimal has digits in The larger the corresponding row, the larger the number.
- If the integer and decimal parts of two numbers are equal, then the two numbers are equal

**For example: **2001,2 > 1999,7 (because 2001 > 1999)

78.469 < 78.5 (because equal integer parts in the tenths have 4<5)

### 1.2. Solution of textbook exercises page 42

**Lesson 1 Textbook page 42**

Compare two decimals:

a) 48.97 and 51.02

b) 96.4 and 96.38

c) 0.7 and 0.65

**Solution guide:**

a) We have 48 < 51 so 48.97 < 51.02

b) Comparing the integer part, we have 96 = 96 and in the tenth row there are 4 > 3 so 96.4 > 96.38

c) Comparing the integer part we have 0 = 0 and in the tenth row there are 7 > 6 so 0.7 > 0.65

Lesson 2 Textbook page 42

Write the following numbers in order from smallest to largest:

6,375; 9.01; 8.72; 6,735; 7.19

*Solution guide:*

Comparing the integer part of the given numbers we have: 6 < 7 < 8 < 9

Compare two numbers with the same integer part of 6 as 6.375 and 6.735. In the tenths we have: 3 < 7, so 6.375 < 6.735

So: 6.375 < 6.735 < 7.19 < 8.72 < 9.01

The numbers in order from smallest to largest are:

6,375; 6,735; 7.19; 8.72; 9.01.

Lesson 3 Textbook page 42

Write the following numbers in order from largest to smallest:

0.32; 0.197; 0.4; 0.321; 0.187

*Solution guide:*

The given numbers all have an integer part of 0 .

Comparing the tenths of the numbers we have: 1 < 3 < 4

Compare two numbers with the same tenth of 1 as 0.197 and 0.187. In the percentile we have: 9 > 8, so 0.197 > 0.187

The two numbers 0.32 and 0.321 have the same tenth of 33 and the percentile of 2; in the thousandths we have 0 < 1 (we can write 0.32 = 0.320). Hence 0.321 > 0.32 .

So: 0.4 > 0.321 > 0.32 > 0.197 > 0.187

The numbers arranged in order from largest to smallest are:

0.4; 0.321; 0.32; 0.197; 0.187.

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