Question

Express in scientific notation. Make sure your answer has the same number of significant figures as the starting value. (1.8 x 10-2) ÷ (9 x 102) = _____

Answer 1

Answer : The answer is, $0.2\times 10^{-4}$

Explanation :

Scientific notation : It is defined as the way or representation of expressing the number that are too big or too small that is written in the decimal form. That means always written in the power of 10 form.

For example : 8000 is written as, $8.0\times 10^3$  in this notation, the significant figure is, 1 but $0.8\times 10^4$  in this notation, the significant figures are, 2

The given problem are :

$\frac{1.8\times 10^{-2}}{9\times 10^2}=0.2\times 10^{-4}$

According to the divide and multiplication rules of scientific figures, the final answer is only as precise as the value with the least number of significant figures.

Hence, the answer is, $0.2\times 10^{-4}$

Answer 2

The result of division (1.8 x 10⁻²) ÷ (9 x 10²) is 2.10⁻⁵ (cause the result must have 1 significant number)

Further Explanation

Significant numbers are obtained from measurement results of exact numbers and the last number estimated

This is called significant numbers

The scientific notation can be described as:

a, ... x 10ⁿ

where the power of n is an integer, and the coefficient a is a real number

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 of the include significant number

• 4. zero decimal point is the not significant number

• 5. In multiplication and division of important numbers, the final results look at the least number of significant numbers.

In the question, it is known that

(1.8 x 10⁻²) ÷ (9 x 10²) has 2(1.8) and 1(9) significant numbers, so the division of both produces 1 significant number

So that we did the significant number then proceed with rank number

• 1. Division of siginificant numbers

1.8: 9 = 0.2

• 2. Division of rank numbers

10⁻²: 10² = 10⁻⁴

So the result = 0.2.10⁻⁴

In the form of scientific notation, it becomes: 2.10⁻⁵

The result has one significant number, which is number 2

Learn more

the number of significant figures

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the result of multiplying of significant numbers

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Compute 4,659 × 104−2.14 × 104.

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Keywords: the scientific notation, significant number