Exercises: decimal numbers (mixed)

Which of both terms is larger? Calculate the solution and determine which is greater or whether the solutions are the same.

$0.2 \cdot 3 - {0.2}^{3}$ or $0.2 \cdot 3 - 0.3 \cdot 2$

For this task you need the following basic knowledge: Decimal numbers and Order of operations
For the first term, observe the order of operations (PEMDAS).
First, do the multiplication $0.2 \cdot 3$ : $0.2 \cdot 3 = 0.6$ .
Next, work out the exponential expression ${0.2}^{3}$ : ${0.2}^{3} = 0.008$ .
Finally, subtract, moving from left to right: $0.2 \cdot 3 - {0.2}^{3} = 0.6 - 0.008 = 0.592$
So, the first expression is equal to 0.592.
For the second expression, observe the order of operations (PEMDAS)
$0.2 \cdot 3$ has already been calculated for the first expression.
Multiply $0.3$ by $2$ : $0.3 \cdot 2 = 0.6$
Subtract, moving from left to right: $0.2 \cdot 3 - 0.3 \cdot 2 = 0$
So, clearly $0.2 \cdot 3 - {0.2}^{3} > 0.2 \cdot 3 - 0.3 \cdot 2$
$1.3 \cdot {3.1}^{2} + {2.2}^{3} \cdot 0.4$ or ${1.3}^{3} \cdot 3.1 + {2.2}^{2} \cdot 0.4$
For this task you need the following basic knowledge: Decimal numbers Order of operations (PEMDAS)
Expression 1
1) Exponential Expressions
${3.1}^{2} = 3.1 ･ 3.1 = 9.61$
${2.2}^{3} = 2.2 ･ 2.2 ･ 2.2 = 10.648$
2) Multiply
$1.3 ･ {3.1}^{2} = 1.3 ･ 9.61 = 12.493$
${2.2}^{3} ･ 0.4 = 10.648 ･ 0.4 = 4.2592$
3) Add
${1.3}^{3} ･ 3.1 + {2.2}^{2} ･ 0.4 = 12.493 + 4.2592 = 16.7522$
The first expression has been evaluated to 16.7522.
Expression 2:
1) Exponential Expressions
${1.3}^{3} = 1.3 ･ 1.3 ･ 1.3 = 2.197$
${2.2}^{2} = 2.2 ･ 2.2 = 4.84$
2) Multiply
${1.3}^{3} ･ 3.1 = 2.197 ･ 3.1 = 6.8107$
${2.2}^{2} ･ 0.4 = 4.84 ･ 0.4 = 1.936$
3) Add
${1.3}^{3} ･ 3.1 + {2.2}^{2} ･ 0.4 = 6.8107 + 1.936 = 8.7467$
The second expression has been evaluated to 8.7467
Finally, the values of the two expression have to be compared.
$16.7522 > 8.7467$
The first expression is the larger one.
As the order of operations must be observed, proceed as follows for each expression
evaluate the exponential expressions,
multiply by the respective decimal numbers,
add the two products to obtain the answer for the expression.

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