9 Questions
¿Qué representa el número en notación científica $5.2 \times 10^{4}$ en forma decimal?
$52,000$
Si tenemos $3 \times 10^{-2}$ y $4 \times 10^{-3}$, ¿cuál es el resultado de multiplicar estos dos números en notación científica?
$12 \times 10^{-6}$
¿Cuál es el resultado de dividir $8 \times 10^{5}$ entre $4 \times 10^{2}$ en notación científica?
$2 \times 10^{3}$
Si se suman $7.2 \times 10^{3}$ y $6.5 \times 10^{4}$ en notación científica, ¿cuál es el resultado?
$7.65 \times 10^{5}$
Si tenemos $9.8 \times 10^{6}$ y $1.5 \times 10^{3}$, ¿cuál es el resultado de restar estos dos números en notación científica?
$9.8 \times 10^{3}$
¿Cuál es el resultado de multiplicar $2.4 \times 10^{-4}$ por $5 \times 10^{2}$ en notación científica?
$1.2 \times 10^{-2}$
Si se divide $6.3 \times 10^{8}$ entre $9 \times 10^4$ en notación científica, ¿cuál es el resultado?
$7 \times 10^{3}$
Si se suman $4.1 \times 10^5$ y $5.8 \times 10^3$ en notación científica, ¿cuál es el resultado?
$4.15 \times 10^6$
¿Cuál es el resultado de dividir $1.8 \times 10^7$ entre $3 \times 10^3$ en notación científica?
$0.6 \times 10^4$
Study Notes
Understanding Scientific Notation
Scientific notation is a handy tool used in math and science to represent very large or very small numbers in a compact manner. Instead of writing out the entire numeral, including any leading zeros, we use an exponent to denote the position of the decimal point relative to its usual location in everyday decimal form.
For instance, the number (10^{11}) (read as 'ten raised to the power of eleven') represents (1,!000,!000,!000,!000) in regular decimal form.
Conversely, (\frac{1}{10^{11}}) (which means ‘divide by ten raised to the power of eleven’) corresponds to (0.00000000001).
The beauty of scientific notation lies in its simplicity. Large numbers become manageable, while tiny quantities becomes easier to grasp. Furthermore, performing addition, subtraction, multiplication, and division operations on these numbers is far simpler due to the consistent placement of the decimal points.
Here's a quick guide to working with scientific notation:
- Move the decimal point appropriately to obtain a number between 1 and 10.
- Count the number of positions the decimal was moved.
- Use the exponent as the value of the counted positions.
- Ensure consistency when dealing with negative signs; for example, ((-2.0)\times 10^{-2}=-0.02) but ((-2.0)\times 10^{+2}=20).
Mastering scientific notation empowers you to handle vast ranges of sizes—from the smallest known particles to the scale of galaxies—with ease.
Learn the principles and advantages of using scientific notation for representing large and small numbers efficiently in math and science. Discover how to convert between regular decimal form and scientific notation, and how to perform operations like addition, subtraction, multiplication, and division with ease.
Make Your Own Quizzes and Flashcards
Convert your notes into interactive study material.
Get started for free
