Question

Explain the importance of scientific notation. Why is it necessary even when using calculators or computers? Provide three real-world examples where scientific notation is used, how it is used, and why. Finally, post three facts that include information about extremely large or small numbers that require scientific notation.

A) Scientific notation is primarily used for complex calculations.
B) Scientific notation is only necessary in manual calculations.
C) Scientific notation is unnecessary in modern technology.
D) Scientific notation is essential for simplifying numerical expressions.

Answer 1

Scientific notation is important because it allows us to express very large or very small numbers conveniently. It is necessary even when using calculators or computers to simplify complex calculations. Examples include distance measurement, atomic mass, and population size.

Step-by-step explanation:

Scientific Notation in Mathematics

Scientific notation is important because it allows us to express very large or very small numbers in a convenient and standardized format. It is necessary even when using calculators or computers because it simplifies complex calculations and avoids the potential for errors due to working with extremely large or small numbers directly.

Real-world Examples of Scientific Notation

1. Distance Measurement: The distance from Earth to the Sun is about 150,000,000,000 meters. In scientific notation, this distance is expressed as 1.5 x 1011 meters.
2. Atomic Mass: The mass of a hydrogen atom is approximately 0.00000000000000000000000167 grams. In scientific notation, this mass is written as 1.67 x 10-24 grams.
3. Population Size: The world population is approximately 7,700,000,000 people. In scientific notation, this number is represented as 7.7 x 109 people.

Facts about Extremely Large or Small Numbers

1. One fact about extremely large numbers is that there are estimated to be about 100,000,000,000 stars in the Milky Way galaxy.
2. One fact about extremely small numbers is that a nanometer is one billionth of a meter, making it a commonly used unit for measuring the size of atoms and molecules.
3. Another fact about extremely small numbers is that a femtosecond is one quadrillionth of a second, and it is used to measure incredibly short time intervals in fields like laser physics.