Practical examples of writing very small numbers in scientific notation.

📚 Quick Study Guide

• 🔢 Scientific notation expresses numbers as $a \times 10^b$, where $1 \le |a| < 10$ and $b$ is an integer.
• 🔬 For very small numbers, the exponent $b$ is negative. It indicates how many places to move the decimal point to the left to get the original number.
• 💡 To convert a small number to scientific notation: Move the decimal point until you have a number between 1 and 10. Count how many places you moved the decimal. If you moved it to the right, the exponent will be negative.
• 📝 Example: 0.0005 becomes $5 \times 10^{-4}$ because you move the decimal 4 places to the right.
• 🧪 Another Example: 0.00000321 becomes $3.21 \times 10^{-6}$ because you move the decimal 6 places to the right.

Practice Quiz

1. What is 0.000015 written in scientific notation?
   1. $1.5 \times 10^{-5}$
   2. $1.5 \times 10^{5}$
   3. $15 \times 10^{-6}$
   4. $0.15 \times 10^{-4}$
2. Express 0.0042 in scientific notation.
   1. $4.2 \times 10^{-3}$
   2. $4.2 \times 10^{3}$
   3. $42 \times 10^{-4}$
   4. $0.42 \times 10^{-2}$
3. What is the scientific notation for 0.0000008?
   1. $8 \times 10^{-7}$
   2. $8 \times 10^{7}$
   3. $8 \times 10^{-6}$
   4. $0.8 \times 10^{-8}$
4. Convert 0.0000901 to scientific notation.
   1. $9.01 \times 10^{-5}$
   2. $9.01 \times 10^{5}$
   3. $90.1 \times 10^{-6}$
   4. $0.901 \times 10^{-4}$
5. Express 0.000000056 in scientific notation.
   1. $5.6 \times 10^{-8}$
   2. $5.6 \times 10^{8}$
   3. $56 \times 10^{-9}$
   4. $0.56 \times 10^{-7}$
6. What is 0.000123 in scientific notation?
   1. $1.23 \times 10^{-4}$
   2. $1.23 \times 10^{4}$
   3. $12.3 \times 10^{-5}$
   4. $0.123 \times 10^{-3}$
7. Convert 0.000004 to scientific notation.
   1. $4 \times 10^{-6}$
   2. $4 \times 10^{6}$
   3. $4 \times 10^{-5}$
   4. $0.4 \times 10^{-5}$