Use your calculator to determine the answer to the following calculation:
1.0×10−154.2×10−7

Results of operations count: -1539 or 2.4 .10⁻⁹ (two significant figure)

Calculating operations in mathematics consist of the operations of addition, subtraction, division, and multiplication.

In one arithmetic operation can have all four operations above, which are called mixed arithmetic operations

We must know the order in which the arithmetic operations must be done first.

The order of the process follows the PEMDAS system, namely: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.

So:

In the following calculation 1.0 × 10−154.2 × 10−7

1. we prioritize the multiplication operation from the left then after that the subtraction operation, we get:

= 10 - 1542 - 7

= - 1539

2. If it is considered that the problem is a division of rank numbers(scientific notation)

1.0 × 10⁻¹⁵ : 4.2 × 10⁻⁷

then we use principles in rank operations

General properties of numbers:

• 1. aᵇ x aⁿ = aᵇ⁺ⁿ

• 2. aᵇ: aⁿ = aᵇ⁻ⁿ, a ≠ 0

• 3. a⁻ᵇ = 1 / aᵇ, a ≠ 0

• 4. (aᵇ) ⁿ = aᵇⁿ

• 5.

aⁿ: rank number

Then the solution:

We divide the principal numbers first and then the rank numbers, then we multiply the results of the two operations

1. division of principal numbers

1: 4.2 = 0.238

2. division of rank numbers

10⁻¹⁵: 10⁻⁷ = 10⁻⁸

Both of the result we multiply becomes:

0.238 .10⁻⁸, in the form of scientific notation becomes:

2.38 .10⁻⁹ or

2.4 .10⁻⁹ (two significant figure)

rank number

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 a composite number

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Keywords: scientific notation, rank number, significant figure, PEMDAS

56 moles of   lieter in chemistry

answer : (a) volume of the gas = 8.67 ×   l

                (b) second virial coefficient b = -1.21226 l/mole

solution :   given,     t = 300k

                                p = 20atm

                                z = 0.86

                                n = 8.2 mmoles = 8.2 × moles

                                r =   0.082 l atm/k/mol

        find,     (a) volume of gas   and (b) second virial coefficient b at 300k.

formula used :            

                          and            

(a)            

                    = \times 0.082\times 300}{20}[/tex]

                    = 8.67 ×   l

(b)      

                    = (0.00867-1) × 8.659

                    = - 8.5839 l/mole