Solved problems: ordering scientific notation from least to greatest

📚 Quick Study Guide

• 🔢 Compare the exponents first. The number with the smaller exponent is smaller. Example: $5.2 \times 10^3$ is smaller than $1.6 \times 10^5$.
• ⚖️ If the exponents are the same, compare the coefficients (the numbers before the $ \times 10^x$). The number with the smaller coefficient is smaller. Example: $2.5 \times 10^4$ is smaller than $6.8 \times 10^4$.
• ➕ If you have negative exponents, remember that the smaller the negative number, the larger its value. Example: $3.1 \times 10^{-2}$ is larger than $9.4 \times 10^{-5}$.
• 📝 Convert all numbers to the same exponent for easy comparison if needed. Example: To compare $3.2 \times 10^4$ and $1.2 \times 10^5$, convert the first to $0.32 \times 10^5$.
• 🧪 Always double-check your work to avoid simple errors!

Practice Quiz

1. Which of the following is the smallest number?
   1. $2.5 \times 10^3$
   2. $3.1 \times 10^2$
   3. $1.9 \times 10^4$
   4. $8.6 \times 10^1$
2. Order the following from least to greatest: $5.0 \times 10^{-3}$, $2.0 \times 10^{-5}$, $8.0 \times 10^{-4}$
   1. $2.0 \times 10^{-5} < 8.0 \times 10^{-4} < 5.0 \times 10^{-3}$
   2. $5.0 \times 10^{-3} < 8.0 \times 10^{-4} < 2.0 \times 10^{-5}$
   3. $8.0 \times 10^{-4} < 5.0 \times 10^{-3} < 2.0 \times 10^{-5}$
   4. $2.0 \times 10^{-5} < 5.0 \times 10^{-3} < 8.0 \times 10^{-4}$
3. Which number is the largest?
   1. $9.9 \times 10^{-2}$
   2. $1.0 \times 10^{-1}$
   3. $5.5 \times 10^{-3}$
   4. $2.2 \times 10^{-4}$
4. Arrange these numbers from least to greatest: $6.0 \times 10^7$, $6.0 \times 10^5$, $6.0 \times 10^6$
   1. $6.0 \times 10^7 < 6.0 \times 10^6 < 6.0 \times 10^5$
   2. $6.0 \times 10^5 < 6.0 \times 10^7 < 6.0 \times 10^6$
   3. $6.0 \times 10^5 < 6.0 \times 10^6 < 6.0 \times 10^7$
   4. $6.0 \times 10^6 < 6.0 \times 10^5 < 6.0 \times 10^7$
5. Which of the following is smaller than $4.0 \times 10^{-6}$?
   1. $5.0 \times 10^{-6}$
   2. $3.0 \times 10^{-5}$
   3. $2.0 \times 10^{-7}$
   4. $6.0 \times 10^{-7}$
6. Order from least to greatest: $7.0 \times 10^0$, $7.0 \times 10^{-1}$, $7.0 \times 10^1$
   1. $7.0 \times 10^0 < 7.0 \times 10^{-1} < 7.0 \times 10^1$
   2. $7.0 \times 10^{-1} < 7.0 \times 10^0 < 7.0 \times 10^1$
   3. $7.0 \times 10^1 < 7.0 \times 10^0 < 7.0 \times 10^{-1}$
   4. $7.0 \times 10^{-1} < 7.0 \times 10^1 < 7.0 \times 10^0$
7. Which of these is the largest?
   1. $1.2 \times 10^{-8}$
   2. $9.8 \times 10^{-9}$
   3. $5.6 \times 10^{-7}$
   4. $3.4 \times 10^{-6}$