Real World Examples of Scientific Notation in Action

📚 Quick Study Guide

🔢 Scientific Notation: A way of expressing numbers that are too big or too small to be conveniently written in decimal form. It's written as $a \times 10^b$, where 1 ≤ |a| < 10 and b is an integer.
• 🌌 Large Numbers: Used to represent astronomical distances (e.g., the distance to stars) and the size of the universe.
• 🔬 Small Numbers: Used to represent the size of atoms, the mass of subatomic particles, and wavelengths of light.
• ➕ Addition/Subtraction: Numbers must have the same exponent to be added or subtracted directly.
• ✖️ ➗ Multiplication/Division: Multiply/divide the $a$ values and add/subtract the $b$ (exponent) values.
• 💡 Calculator Use: Most calculators have an 'EE' or 'EXP' button for entering scientific notation.

🧪 Practice Quiz

1. What is the approximate distance to the Andromeda Galaxy (2,500,000 light-years) expressed in scientific notation, given that 1 light-year is approximately $9.461 \times 10^{15}$ meters?
1. $2.36 \times 10^{22}$ m
2. $2.36 \times 10^{16}$ m
3. $2.37 \times 10^{22}$ m
4. $2.40 \times 10^{16}$ m
2. The mass of an electron is approximately 0.00000000000000000000000000000091093837 kg. What is this mass in scientific notation?
1. $9.109 \times 10^{-31}$ kg
2. $9.109 \times 10^{31}$ kg
3. $9.1 \times 10^{-30}$ kg
4. $9.0 \times 10^{-31}$ kg
3. A computer can perform $4.5 \times 10^{9}$ calculations per second. How many calculations can it perform in 60 seconds? Express your answer in scientific notation.
1. $2.7 \times 10^{10}$
2. $2.7 \times 10^{9}$
3. $2.7 \times 10^{11}$
4. $2.7 \times 10^{8}$
4. The population of a city is 3,400,000. Express this number in scientific notation.
1. $3.4 \times 10^{6}$
2. $3.4 \times 10^{-6}$
3. $34 \times 10^{5}$
4. $0.34 \times 10^{7}$
5. The wavelength of a certain color of light is 0.00000055 meters. Express this wavelength in scientific notation.
1. $5.5 \times 10^{-7}$ m
2. $5.5 \times 10^{7}$ m
3. $5.5 \times 10^{-6}$ m
4. $55 \times 10^{-8}$ m
6. What is $(2 \times 10^{5}) \times (3 \times 10^{3})$? Express the answer in scientific notation.
1. $6 \times 10^{8}$
2. $5 \times 10^{8}$
3. $6 \times 10^{15}$
4. $5 \times 10^{2}$
7. What is $(8 \times 10^{6}) / (2 \times 10^{2})$? Express the answer in scientific notation.
1. $4 \times 10^{4}$
2. $4 \times 10^{8}$
3. $1.6 \times 10^{8}$
4. $4 \times 10^{3}$