EVALUATE NUMERICAL EXPRESSIONS INVOLVING DECIMALS

Solve the problems below following the rules for order of operations.

Problem 1 :

12.2 × 9.4 - 2.68 + 1.6 ÷ 0.8

Solution :

Given 12.2 × 9.4 - 2.68 + 1.6 ÷ 0.8

= 12.2 × 9.4 - 2.68 + 1.6 ÷ 0.8 (Division)

= 12.2 × 9.4 - 2.68 + 2 (Multiplication)

= 114.68 - 2.68 + 2 (Subtraction)

= 112 + 2 (Addition)

= 114

Problem 2 :

9.6 + 3.6 - (0.4)²

Solution :

Given, 9.6 + 3.6 - (0.4)²

= 9.6 + 3.6 - (0.4)² (Exponents)

= 9.6 + 3.6 - 0.16(Addition)

= 13.2 - 0.16 (Addition)

= 13.04

Problem 3 :

(0.76 + 4.24) ÷ 0.25 + 8.6

Solution :

Given, (0.76 + 4.24) ÷ 0.25 + 8.6

= (0.76 + 4.24) ÷ 0.25 + 8.6 (Bracket)

= 5 ÷ 0.25 + 8.6 (Division)

= 20 + 8.6 (Addition)

= 28.6

Problem 4 :

(32.16 - 32.02)² ÷ (2.24 + 1.76)

Solution :

Given, (32.16 - 32.02)² ÷ (2.24 + 1.76)

= (32.16 - 32.02)² ÷ (2.24 + 1.76) (Bracket)

= (0.14)²  ÷ (2.24 + 1.76) (Exponents)

= 0.0196 ÷ (2.24 + 1.76) (Addition)

= 0.0196 ÷ 4 (Division)

= 0.0049

Problem 5 :

2.4 + (0.5)² - 0.35

Solution :

Given, 2.4 + (0.5)² - 0.35

= 2.4 + (0.5)² - 0.35 (Exponents)

= 2.4 + 0.25 - 0.35 (Addition)

= 2.65 - 0.35 (Subtraction)

= 2.3

Problem 6 :

(1.1)³ + 8.6 ÷ 2.15 - 0.086

Solution :

Given, (1.1)³ + 8.6 ÷ 2.15 - 0.086

= (1.1)³ + 8.6 ÷ 2.15 - 0.086 (Exponents)

= 1.331 + 8.6 ÷ 2.15 - 0.086 (Division)

= 1.331 + 4 - 0.086  (Subtraction)

= 1.331 + 3.914 (Addition)

= 5.245

Problem 7 :

(0.6)³ + (7 - 6.3) × 0.07

Solution :

Given, (0.6)³ + (7 - 6.3) × 0.07

= 0.216 + (7 - 6.3) × 0.07 (Exponents)

= 0.216 + (7 - 6.3) × 0.07 (Bracket)

= 0.216 + 0.7 × 0.07 (Multiplication)

= 0.216 + 0.049 (Addition)

= 0.265

Problem 8 :

(0.6)³ + (2.4)² + 18.6 ÷ 3.05 + 4.8

Solution :

Given, (0.6)³ + (2.4)² + 18.6 ÷ 3.05 + 4.8

= (0.6)³ + (2.4)² + 18.6 ÷ 3.05 + 4.8 (Exponents)

= 0.216 + + (2.4)² + 18.6 ÷ 3.05 + 4.8 (Exponents)

= 0.216 +  5.76 + 18.6 ÷ 3.05 + 4.8 (Division)

= 0.216 +  5.76 + 6.099 + 4.8 (Addition)

= 16.875