Use your calculator to determine the answer to the following calculation: 1.0×10−154.2×10−7
2 answers:
Results of operations count: -1539 or 2.4 .10⁻⁹ (two significant figure)
<h3>Further explanation</h3>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:
- 1. If there are parentheses, then do it first
- 2. multiplication and division operations have the same degree, so it is done from the left first
- 3. operations of addition and subtraction calculations also have the same degree so that it can be done from the left first
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)
<h3>Learn more</h3>rank number
a composite number
Keywords: scientific notation, rank number, significant figure, PEMDAS
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