Understanding Scientific Notation

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Questions and Answers

Which of the following represents the correct format for expressing a quantity in scientific notation?

  • $a \times 10^n$, where 0 < a < 10 and n is a positive integer
  • $a \times 10^n$, where 1 ≤ a < 10 and n is an integer (correct)
  • $a \times 10^n$, where a > 1 and n is a negative integer
  • $a \times 10^n$, where a ≥ 1 and n is any real number

Convert 0.00028 into scientific notation.

  • $2.8 \times 10^{-5}$
  • $2.8 \times 10^{-4}$ (correct)
  • $2.8 \times 10^{4}$
  • $2.8 \times 10^{5}$

What does the term 'entidades elementales' refer to in the context of chemistry?

  • Complex organic molecules
  • Mixtures of different chemical compounds
  • Fundamental particles such as atoms, molecules, and ions (correct)
  • Large structures in organic chemistry

When using a scientific calculator, which function is typically used to enter numbers in scientific notation?

<p>EXP (C)</p> Signup and view all the answers

Evaluate: $\frac{10^4}{10^4}$.

<p>1 (B)</p> Signup and view all the answers

Simplify the expression: $(7.5 \times 10^9) \times (4.932 \times 10^{-4})$

<p>3.70 \times 10^6 (A)</p> Signup and view all the answers

Calculate: $(3.971 \times 10^8) \times (1.7 \times 10^{-8})$

<p>6.7507 (B)</p> Signup and view all the answers

What is the result of $(5.908 \times 10^{24}) \times (8.9 \times 10^{-10})$ in scientific notation?

<p>5.25812 \times 10^{15} (C)</p> Signup and view all the answers

What is the result of $(1.903 \times 10^5) \times (9.5 \times 10^{-5})$?

<p>18.0785 (B)</p> Signup and view all the answers

If a population is reported as $8.0 \times 10^9$ people, how would you express this number in standard notation?

<p>8,000,000,000 (B)</p> Signup and view all the answers

What is the order of operations that needs to be followed while using scientific notation?

<p>Multiply coefficients, then add exponents (B)</p> Signup and view all the answers

How would you represent $2.8 \times 10^{-4}$g using scientific calculator?

<p>2.8 [EXP] (-) 4 (D)</p> Signup and view all the answers

Approximately, how many entities elementary are in 2 moles?

<p>$1.204 \times 10^{24}$ (D)</p> Signup and view all the answers

Which one of the followings is a limitation of using scientific notation?

<p>It may introduce rounding errors if not handled correctly (D)</p> Signup and view all the answers

Why is using scientific notation important in scientific field?

<p>It allows for easier handling of extremely large or small numbers. (B)</p> Signup and view all the answers

If Avogadro's number are $6.02 \times 10^{23}$, approximately how many entities elemenatry are in 0.5 mol?

<p>$3.01 \times 10^{23}$ entities (A)</p> Signup and view all the answers

Which one of the followings is an advantage of using degree mode (Deg) on a scientific calculator?

<p>Calculates trigonometric functions with angles measured in degrees (C)</p> Signup and view all the answers

Why is important to set the Mode in Deg when using a scientific calculator?

<p>It ensures that trigonometric calculations results are interpreted correctly in degrees (D)</p> Signup and view all the answers

How did the scientific notation changed scientific practices?

<p>Enabled scientists to perform calculations with extremely large or small numbers in a simple way (A)</p> Signup and view all the answers

Complete: In scientific notation, the decimal point is placed after the first ___ digit.

<p>Significant (C)</p> Signup and view all the answers

Flashcards

Scientific Notation

A way to express very large or very small numbers as a number between 1 and 10 multiplied by a power of 10.

1 mole

Avogadro's number, representing the number of entities (atoms, molecules, ions, etc.) in one mole of a substance.

Calculator Use

It simplifies calculations with very large or small numbers. Use the EXP button.

10^n / 10^n

Any number divided by itself equals 1.

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Study Notes

  • Scientific notation expresses any quantity: $a \times 10^n$
  • Where $a$ is greater or equal to 1
  • And $a$ is less than 10
  • Where $n$ is an integer that can be positive or negative
  • Example: 8,000,000,000.0 inhabitants is written as 8.0 x 10^9 inhabitants
  • 1 mol = 6.02 x 10^23 elemental entities, like atoms, molecules, ions, etc.
  • 2 x 6.02 x 10^23 = 1.204 x 10^24

Calculator Scientific Notation Usage

  • For 8.0 x 10^9, enter 8, then EXP, then 9 on the calculator.
  • To solve 6.02 x 10^23 - 8.0 x 10^9, the second term is negligible: 6.02 x 10^23 - 6.02 x 10^20 = 6.01398 x 10^23
  • Example calculations:
  • (1.5 x 10^9) x (4.932 x 10^-4) = 7,398
  • (3.971 x 10^3) x (1.7 x 10^-3) = 6.7507
  • (5.908 x 10^24) x (8.9 x 10^-16) = 5.25872 x 10^9
  • (7.903 x 10^3) x (9.5 x 10^-5) = 78.0785
  • 10^4 / 10^4 = 10^(4-4) = 1

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