← Back to the Scientific Notation worksheet
Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Standards: 8.EE.A.3, 8.EE.A.4 · Level: Grade 8
Problem 1 Large numbers
(a) The point moves 6 places left: 6.3 × 106. (b) 2 places: 4.8 × 102. (c) 10 places: 5.2 × 1010.
(a) 6.3 × 106 (b) 4.8 × 102 (c) 5.2 × 1010
Problem 2 Small numbers
(a) The point moves 4 places right: 4 × 10−4. (b) 5 places: 7.15 × 10−5. (c) 2 places: 6.2 × 10−2.
(a) 4 × 10−4 (b) 7.15 × 10−5 (c) 6.2 × 10−2
Problem 3 Back to standard form
(a) Move the point 5 places right: 390,000. (b) Move 3 places left: 0.00804. (c) 7 places right: 12,000,000.
(a) 390,000 (b) 0.00804 (c) 12,000,000
Problem 4 Is it scientific notation?
(a) 45 is not below 10: 4.5 × 104. (b) 0.7 is below 1: 7 × 104. (c) Correct. (d) 10 is not below 10: 1 × 103.
(a) no, 4.5 × 104 (b) no, 7 × 104 (c) yes (d) no, 1 × 103
Problem 5 Calculator notation
(a) 3.2E5 means 3.2 × 105 = 320,000. (b) 7.5E−3 means 7.5 × 10−3 = 0.0075. (c) Replace × 10 by E: 9.1E−6.
(a) 320,000 (b) 0.0075 (c) 9.1E−6
Problem 6 Follow the decimal point
The point travels 4 places right, so the exponent is −4. The coefficient is 5.8.
5.8 × 10−4
Problem 7 Order small numbers
Compare exponents first. The −3 numbers are smaller: 4.2 < 5, so 4.2 × 10−3 < 5 × 10−3. Then 1.1 × 10−2 < 3.9 × 10−2. In decimals: 0.0042, 0.005, 0.011, 0.039.
4.2 × 10−3, 5 × 10−3, 1.1 × 10−2, 3.9 × 10−2
Problem 8 Multiply
(a) 3 · 2.5 = 7.5 and 4 + 3 = 7: 7.5 × 107. (b) 4 · 6 = 24 and −3 + 5 = 2, so 24 × 102 = 2.4 × 103.
(a) 7.5 × 107 (b) 2.4 × 103
Problem 9 Divide
(a) 8.4 ÷ 2.1 = 4 and 9 − 4 = 5: 4 × 105. (b) 9 ÷ 3 = 3 and −2 − (−6) = 4: 3 × 104.
(a) 4 × 105 (b) 3 × 104
Problem 10 Add and subtract
(a) Rewrite 2.6 × 104 as 0.26 × 105. Then 3.4 + 0.26 = 3.66. (b) Rewrite 4 × 10−4 as 0.4 × 10−3. Then 7.1 − 0.4 = 6.7.
(a) 3.66 × 105 (b) 6.7 × 10−3
Problem 11 How many times as much
Divide: (6 × 107) ÷ (2 × 104) = 3 × 103.
3 × 103 = 3,000 times as many
Problem 12 Town and city
(3 × 105) ÷ (6 × 104) = 0.5 × 101 = 5. Check: 300,000 ÷ 60,000 = 5.
5 times as large
Problem 13 Which is larger?
The exponent 6 is greater than 5, and both coefficients are between 1 and 10, so 7.2 × 106 is larger. Standard form: 7,200,000 and 950,000.
7.2 × 106 is larger
Problem 14 Choosing a unit
0.000007 = 7 × 10−6 meter. Since 10−6 meter is 1 micrometer, the width is 7 micrometers.
7 × 10−6 m = 7 micrometers
Problem 15 Radio signal delay
Time = distance ÷ speed = (7.2 × 107) ÷ (1.8 × 105). Since 7.2 ÷ 1.8 = 4 and 7 − 5 = 2, time = 4 × 102 = 400 seconds. And 400 s = 6 min 40 s.
4 × 102 seconds = 6 minutes 40 seconds
Problem 16 Data center storage
(2.4 × 1012)(5 × 103) = 12 × 1015. Since 12 is not below 10, this is 1.2 × 1016.
1.2 × 1016 bytes
Problem 17 Hair and paper
(1 × 10−4) ÷ (8 × 10−5) = 0.125 × 101 = 1.25. Check: 0.0001 ÷ 0.00008 = 1.25.
1.25 times as thick
Problem 18 Country and state
3.3 ÷ 5.5 = 0.6 and 8 − 6 = 2, so 0.6 × 102 = 6 × 101. Check: 330,000,000 ÷ 5,500,000 = 60.
60 times as large
Problem 19 Concert revenue
65 = 6.5 × 101. Multiply: (4 × 105)(6.5 × 101) = 26 × 106 = 2.6 × 107. In dollars: $26,000,000.
2.6 × 107 dollars = $26,000,000
Problem 20 Bacteria colony
Colony: (1 × 10−12)(2.5 × 109) = 2.5 × 10−3 gram. Rice ÷ colony: (2.5 × 10−2) ÷ (2.5 × 10−3) = 1 × 101 = 10.
2.5 × 10−3 gram; the rice grain is 10 times as heavy