D1-L13 Decimals Practice : Notation, Place Value, Compare and Order

DECIMAL NUMBERS – D1                      Date/Time:               Tutor:

(Part 1) Revise (20mins)                                        Start Time:                 

1. Notation and Place Value, Comparing and Ordering of Decimals (up to 3 d.p) 

2. Comparing and Ordering Decimals, Using Number Lines

3. Conversion of Decimals and Fractions

(Part2) Practice (45 mins)                                      Start Time:

Express each decimal as a fraction or a mixed number in its simplest form

1.  0.4 =         

2.  1.6 =                     

Express each fraction or mixed number as a decimal.

3.   ¼ = 

4.  3/8 = 

Express each fraction or mixed number as a decimal.

5.  4 ½ = 

6.  2 2/5 = 

7.  Which is the greatest?

         3.5,       2.8,       3.04,      4.4

8.  Which is the smallest?

         64.049,      68.123,       65.408,       67.637

9. Arrange these numbers in decreasing order.

         6.606,        6.66,           6.6,             6.066

Round each decimal to 2 decimal places.

10.   8.123

11.   2.367

12.  99.999  

13.   In the number pattern below, what is the missing number in the box? (6/p1/18f)
         9.25,     9.55,      9.85, ?  ,     10.45

14. Express 0.15 as a fraction in the simplest form. (7/p1/18f)

(1)  3/10

(2)  3/15

(3)  3/20
(4)  3/25               

                                                                                                    

15*.  Round off 70.171 to the nearest tenth.

16.* Which digit in 68.57 is in the tenth place?

17*. In the number line below, what is the number indicated by the arrow?

                

(1) 9.88 

(2) 10.05 

(3) 10.15 

(4) 10.42                                                                                                        (           )

18.  In 356.174, what does the digit 7 stand for? (1/p1/18s)

(1) 7 thousandths

(2) 7 hundredths

(3) 7 tenths

(4) 7 tens                                                                                                       (           )

19.  Which one of the following numbers is the largest? (4/p1/18s)

(1) 0.8

(2) 0.72

(3) 0.098

(4) 0.605                                                                                                        (           )

20.  Simon’s height is 1.85 m. Round off his height to the nearest tenth. (19/p1/18s)

Answer Keys

1.   2/5
2.   1 2/5
3.    0.25
4.    0.375
5.   4.5
6.   2.4
7.   4.4
8.   64.049
9.   6.66, 6.606, 6.6, 6.066
10.  8.12
11.  3.37
12.  1.00
13.  3
14.  3
15.  7.02
16.  5
17.  102
18.  2
19.  1
20.  1.9m

D2 Decimals : Ordering and Comparing Decimals, Using Number Lines

ORDERING AND COMPARING DECIMALS

Comparing Decimals

Example

Which number is bigger: 0.43 or 0.403?

Looking at the digits, 403 seems bigger than 43. But, it is not!

Method

Step1: Draw the place_Value_tables and put the numbers

th	h	o	.	t	h	th
		0	.	4	3
		0	.	4	0	2

Step2: Put 0 into the empty square

th	h	o	.	t	h	th
		0	.	4	3	0
		0	.	4	0	2

                             =    3 bigger

Step3: Compare the first column on the left. If the digits are equal, move to next number until the bigger number

            0.43 is bigger than 0.402

Example

Which number is smaller: 8.003 or 8.01?

Method

Step1: Draw the placeValuetable and put the numbers

th	h	o	.	t	h	th
		8	.	0	0	3
		8	.	0	1

Step2: Put 0 into the empty square

th	h	o	.	t	h	th
		8	.	0	0	3
		8	.	0	1	0

             =      =    0 is smaller

Step3: Compare the first column on the left. If the digits are equal, move to next number until the required smaller number.

             8.003 is smaller than 8.01

Ordering Decimals

Ascending order is arranging the numbers from the Smallest to the Biggest numbers

Ascending order:     1.01, 2.01, 3.01, 4.01

Descending order is arranging the numbers from the Biggest to the Smallest numbers.

                                    5.2, 4,2 , 3.2, 1.2

            Descending -> Down => from big to small

Example

Put the 1.517, 1.57, 1.08 and 0.8 in ascending order

Method

Step1: Draw the placeValueTable and put the numbers

th	h	o	.	t	h	th
		1	.	5	1	7
		1	.	5	7
		1	.	0	8
		0	.	8

Step2: Put 0 into the empty square

th	h	o	.	t	h	th
		1	.	5	0	7	3
		1	.	5	7	0	4
		1	.	0	8	0	2
		0	.	8	0	0	1

            (1)    (2) (3) (4) number

Step3: Compare the first column on the left. If the digits are equal, move to next number until the required smallest number (for Ascending), write number

                        0.8 , 1.08, 1.517, 1.57

Example

Put the 0.402, 1.2, 0.41, 0.375 in descending order.

Method

Step1: Draw the placeValueTable and put the numbers

th	h	o	.	t	h	th
		0	.	4	0	2
		1	.	2
		0	.	4	1
		0	.	3	7	5

Step2: Put 0 into the empty square

th	h	o	.	t	h	th
		0	.	4	3	2	3
		1	.	2	0	0	4
		0	.	4	1	0	2
		0	.	3	7	5	1

Step3: Compare the first column on the left. If the digits are equal, move to next number until the required biggest number (for descending), write number

                        1.2, 1.432, 0.410, 0.375

Using Number Line

Example

What are the values A, B and C?

Method(count blank spaces)

Step1: Find the interval value between 2 known number (1.0 and 1.5).

           Count number of blanks: 5 blanks / ‘spaces’ between 1.0 and 1.5  

Each marker = 1.5 -1.0 / 5 = 0.5/5 = 0.1

 => 1.0 + 0.1 = 1.1 for first marker

Step2: Put in the marker

             1.0 + 0.1=1.1, 1.1+0.1 = 1.2, …

Step3: Answer

            A = 1.2 , B = 1.8 and C = 2.4

Example

What are the values of A and B?

Method (marker + 1)

Step1: Find the interval value between 2 known number (1.0 and 2.0).

           - Count number of marker I between the 2 numbers, and ADD 1

            - 4 marker + 1 = 5

Each marker = 2.0 -2.0 / 5 = 1.0/5 = 0.2

=> 1.0 + 0.2 = 1.2 for first marker

Step2: Put in the marker

             1.0 + 0.2, 1.2+0.2, …

Step3: Answer

            A = 1.6, B = 1.2

~~ the end ~~~ :)