the result of multiplying (2.5 × 10¹⁰) and (3.5 × 10⁻⁷) is 8.8.10³ (cause the result must have 2 significant number)
Further Explanation
Significant numbers are numbers obtained from the measurement results of exact numbers and the last number estimated
In scientific notation, all numbers are displayed before the big order is called significant numbers
the scientific notation can be described as:
a, ... x 10ⁿ
a, ... called an important number
10ⁿ is called a big order
Rules for significant numbers in general:
- 1. all non-zero numbers are significant numbers
- 2. a zero which is located between two non-zero numbers including a significant number
- 3. all zeros are located in the final row written behind the decimal point include significant number
- 4. zero decimal point is not significant number
In the question it is known that (2.5 × 10¹⁰) and (3.5 × 10⁻⁷) both have a significant number in a row 2.5 and 3.5
so that it meets the rule of significant numbers which is multiplication of 2 significant number produces numbers that have the fewest significant numbers, So the multiplication of the two will produce 2 significant number
So that we do the significant number then proceed a big order
- 1. Multiplication of significant number2.5 x 3.5 = 8.75
- 2. a big order multiplication 10¹⁰ x 10⁻⁷ = 10¹⁰⁻⁷ = 10³
So the result = 8.75.10³
Because the result must have 2 significant number , the result is 8.8.10³ (8.75 we round up)
Learn more
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