COMPARING AND ORDERING DECIMALS

Problem 1 :

Place the following numbers in order from least to greatest :

-8.2, 0.4, -2 1/2, 2.4

Solution :

-8.2, 0.4, -2 1/2, 2.4

Converting 2  1/2 as decimal, we get -2.5. Now comparing and arranging can be done.

-8.2, 0.4, -2.5, 2.4

Arranging from least to greatest :

-8.2 < -2 1/2 < 0.4 < 2.4

Problem 2 :

Place a >, <, or = symbol on each line to compare the rational numbers below.

(i) 1.2  ___8/4  (ii) 6.05  ____6.05

Solution :

(i) 1.2 ____8/4

Simplifying 8 by 4, we get 2. So, 1.2 is lesser.

1.2 < 2

(ii) 6.05  _____6.05

Comparing 6.05 and 6.05, they both are same.

6.05 = 6.05

Problem 3 :

Place the following numbers in order from greatest to least :

0.5, -5 1/9, -7.1, 0.9

Solution :

0.5, -5 1/9, -7.1, 0.9

0.5, -5.5, -7.1, 0.9

0.9 > 0.5 > -5 1/9 > -7.1

Problem 4 :

Place a >, <, or = symbol on each line to compare the rational numbers below.

(i) 8.5 _____ 10/5  (ii) 10.2  _____10

Solution :

(i) 8.5 ____10/5

Dividing 10 and 5, we get 2. Comparing 8.5 and 2, 8.5 is greater.

8.5 ____ 2

8.5 > 2

(ii) 10.2 ____10

10.2 is greater than 10

10.2 > 10

Problem 5 :

Place the following numbers in order from least to greatest :

-2.4, -3 3/9, 9.5, 0.2

Solution :

-2.4, -3 3/9, 9.5, 0.2

-2.4, -3.3, 9.5, 0.2

-3 3/9 < -2.4 < 0.2 < 9.5

Problem 6 :

Place a >, <, or = symbol on each line to compare the rational numbers below.

(i) 1.4___-14/7  (ii) 6.8 _____ 8.6

Solution :

(i) 1.4 ____-14/7

Simplifying 14 and 7, we get 2. Comparing positive and negative values, positive value is greater.

1.4 ___-2

1.4 > -2

(ii) 6.8 ____8.6

6.8 < 8.6

Problem 7 :

Place the following numbers in order from greatest to least :

7.4, -4 5/10, 0.2, -7.4

Solution :

7.4, -4 5/10, 0.2, -7.4

7.4, -4.5, 0.2, -7.4

7.4 > 0.2 > -4.5 > -7.4

Problem 8 :

Place the following numbers in order from least to greatest :

-34/4, 4, 0.7, -9.3

Solution :

-8 2/4, 4, 0.7, -9.3

-34, 4, 0.7, -9.3

-9.3 < -34/4 < 0.7 < 4

Problem 9 :

Place the following numbers in order from greatest to least :

0.3, 3.3, -3.3, -3

Solution :

0.3, 3.3, -3.3, -3

3.3 > 0.3 > -3 >-3.3

Problem 10 :

Place a >, <, or = symbol on each line to compare the rational numbers below.

(i)  8.5 ____-8.5   (ii) 0.2 ___0.5

Solution :

(i) 8.5 ____-8.5

Comparing positive and negative values, always positive value is greater.

8.5 > -8.5

(ii) 0.2 ___0.5

0.2 < 0.5

Problem 11 :

Which of these numbers is the smallest?

a) 0.5       b)  0.0501      c)  0.051      d)  0.499       e) 0.49

Solution :

By converting each decimals into like decimals, the comparision can be made easier. By comparing the options given, the maximum number of digits after the decimal is 4.

• 0.5 = 0.5000
• 0.0501 = 0.0501
• 0.051 = 0.0510
• 0.499 = 0.4990
• 0.49 = 0.4900

Comparing the above decimals, 0.0501 is the smallest. So, option b is correct.

Problem 12 :

Which of these fractions is equal to 0.8?

a) 1/8     b) 4/5      c)  0.8/10    d)  8/100     e)  5/4

Solution :

To convert 0.8 as fraction, we have to multiply both numerator and denominator by 10.

= 0.8 x 10/10

= 8/10

= 4/5

Option b is correct.

Problem 13 :

A bag of rice contains 360 g. A special offer packet contains an extra 15%. Work out how much extra rice is in the special offer packet.

A bag of sugar contains 250 g. A special offer packet contains an extra 50% Work out how much extra sugar is in the special offer packet.

Which packet consist of more quantity ?

Solution :

Original quantity of rice in the bag = 360 g

After including 15% extra, quantitty of rice in the new bag = (100 + 15)% of 360

= 115% of 360

= 1.15 x 360

= 414 grams

Original quantity of sugar in the bag = 250 g

After including 15% extra, quantitty of sugar in the new bag = (100 + 50)% of 250

= 150% of 250

= 1.5 x 250

= 375 grams 

Comparing these two, quantity of rice is greater.

Problem 14 :

Mark all numbers that are bigger than 0.45

0.5, 0.6, 0.4, 0.08, 0.404

Solution :

0.5, 0.6, 0.4, 0.08, 0.404

Converting each decimals into like decimals,

0.500, 0.600, 0.400, 0.080, 0.404

0.500 and 0.600 are greater than 0.45

Problem 15 :

Which is larger?

a) 78%     b) 3/4     c) 0.74     d) 5/6

Solution :

a) 78% = 78/100 ==> 0.78

b)  3/4 = 0.75

c)  0.74 = 0.74

d)  5/6 = 0.83

Comparing the decimals we have, 0.83 is greater. Then 5/6 is the greater.

Problem 16 :

Which is larger?

a) 35%     b) 18/50     c) 0.375      d) 22/60

Solution :

a) 35% = 35/100 ==> 0.35

b) 18/50

= 18/50 x 2/2

= 36/100

= 0.36

c) 0.375

d) 22/60 = (11/3) x (1/10)

= 3.66 x 1/10

= 0.366

0.375 is greater. Then option c is correct.