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Scientific Notation: Classroom Packet

Grade 8 Algebra: Writing Numbers in Scientific Notation

Name: ______________________Date: ____________Score: ____ / 8

Level 1

Large whole numbers

  1. 1. Write in scientific notation:
    50005000
  2. 2. Write in scientific notation:
    72 00072\,000
  3. 3. Write in scientific notation:
    300 000300\,000
  4. 4. Write in scientific notation:
    4 500 0004\,500\,000
  5. 5. Write in scientific notation:
    860860
  6. 6. Write in scientific notation:
    91 000 00091\,000\,000
  7. 7. Write in scientific notation:
    620 000620\,000
  8. 8. Write in scientific notation:
    2 300 000 0002\,300\,000\,000

Answer Key

Level 1

  1. 1. 5×1035 \times 10^3
  2. 2. 7.2×1047.2 \times 10^4
  3. 3. 3×1053 \times 10^5
  4. 4. 4.5×1064.5 \times 10^6
  5. 5. 8.6×1028.6 \times 10^2
  6. 6. 9.1×1079.1 \times 10^7
  7. 7. 6.2×1056.2 \times 10^5
  8. 8. 2.3×1092.3 \times 10^9

Grade 8 Algebra: Writing Numbers in Scientific Notation

Name: ______________________Date: ____________Score: ____ / 8

Level 2

Small decimals

  1. 1. Write in scientific notation:
    0.0040.004
  2. 2. Write in scientific notation:
    0.060.06
  3. 3. Write in scientific notation:
    0.000570.00057
  4. 4. Write in scientific notation:
    0.30.3
  5. 5. Write in scientific notation:
    0.00000820.0000082
  6. 6. Write in scientific notation:
    0.0001090.000109
  7. 7. Write in scientific notation:
    0.00910.0091
  8. 8. Write in scientific notation:
    0.000000060.00000006

Answer Key

Level 2

  1. 1. 4×10−34 \times 10^{-3}
  2. 2. 6×10−26 \times 10^{-2}
  3. 3. 5.7×10−45.7 \times 10^{-4}
  4. 4. 3×10−13 \times 10^{-1}
  5. 5. 8.2×10−68.2 \times 10^{-6}
  6. 6. 1.09×10−41.09 \times 10^{-4}
  7. 7. 9.1×10−39.1 \times 10^{-3}
  8. 8. 6×10−86 \times 10^{-8}

Grade 8 Algebra: Writing Numbers in Scientific Notation

Name: ______________________Date: ____________Score: ____ / 8

Level 3

Mixed numbers and non-standard form

  1. 1. Write in scientific notation:
    34×10534 \times 10^5
  2. 2. Write in scientific notation:
    0.6×1040.6 \times 10^{4}
  3. 3. Write in scientific notation:
    250×10−6250 \times 10^{-6}
  4. 4. Write in scientific notation:
    0.075×10−20.075 \times 10^{-2}
  5. 5. Write in scientific notation:
    6 020 000 0006\,020\,000\,000
  6. 6. Write in scientific notation:
    0.00000004050.0000000405
  7. 7. Write in scientific notation:
    0.48×1070.48 \times 10^{7}
  8. 8. Write in scientific notation:
    5200×10−95200 \times 10^{-9}

Answer Key

Level 3

  1. 1. 3.4×1063.4 \times 10^6
  2. 2. 6×1036 \times 10^3
  3. 3. 2.5×10−42.5 \times 10^{-4}
  4. 4. 7.5×10−47.5 \times 10^{-4}
  5. 5. 6.02×1096.02 \times 10^9
  6. 6. 4.05×10−84.05 \times 10^{-8}
  7. 7. 4.8×1064.8 \times 10^6
  8. 8. 5.2×10−65.2 \times 10^{-6}

Grade 8 Algebra: Converting to Standard Form

Name: ______________________Date: ____________Score: ____ / 8

Level 1

Positive exponents

  1. 1. Write in standard form:
    3×1043 \times 10^4
  2. 2. Write in standard form:
    6.1×1026.1 \times 10^2
  3. 3. Write in standard form:
    2.45×1052.45 \times 10^5
  4. 4. Write in standard form:
    9×1069 \times 10^6
  5. 5. Write in standard form:
    1.8×1031.8 \times 10^3
  6. 6. Write in standard form:
    7.07×1077.07 \times 10^7
  7. 7. Write in standard form:
    4.6×1014.6 \times 10^1
  8. 8. Write in standard form:
    3.002×1043.002 \times 10^4

Answer Key

Level 1

  1. 1. 30 00030\,000
  2. 2. 610610
  3. 3. 245 000245\,000
  4. 4. 9 000 0009\,000\,000
  5. 5. 18001800
  6. 6. 70 700 00070\,700\,000
  7. 7. 4646
  8. 8. 30 02030\,020

Grade 8 Algebra: Converting to Standard Form

Name: ______________________Date: ____________Score: ____ / 8

Level 2

Negative exponents

  1. 1. Write in standard form:
    4×10−24 \times 10^{-2}
  2. 2. Write in standard form:
    5.3×10−35.3 \times 10^{-3}
  3. 3. Write in standard form:
    8×10−18 \times 10^{-1}
  4. 4. Write in standard form:
    1.25×10−41.25 \times 10^{-4}
  5. 5. Write in standard form:
    6.9×10−66.9 \times 10^{-6}
  6. 6. Write in standard form:
    2.004×10−22.004 \times 10^{-2}
  7. 7. Write in standard form:
    7.1×10−57.1 \times 10^{-5}
  8. 8. Write in standard form:
    9.99×10−39.99 \times 10^{-3}

Answer Key

Level 2

  1. 1. 0.040.04
  2. 2. 0.00530.0053
  3. 3. 0.80.8
  4. 4. 0.0001250.000125
  5. 5. 0.00000690.0000069
  6. 6. 0.020040.02004
  7. 7. 0.0000710.000071
  8. 8. 0.009990.00999

Grade 8 Algebra: Converting to Standard Form

Name: ______________________Date: ____________Score: ____ / 8

Level 3

Comparing and ordering

  1. 1. Which is greater?:
    3×105  or  9×1043 \times 10^5 \;\text{or}\; 9 \times 10^4
  2. 2. Which is greater?:
    2.1×10−3  or  8×10−42.1 \times 10^{-3} \;\text{or}\; 8 \times 10^{-4}
  3. 3. Which is greater?:
    4.5×106  or  4.05×1064.5 \times 10^{6} \;\text{or}\; 4.05 \times 10^{6}
  4. 4. Order from least to greatest:
    6×102,  5×103,  7×10−16 \times 10^2,\; 5 \times 10^3,\; 7 \times 10^{-1}
  5. 5. Order from least to greatest:
    1.2×10−2,  9.8×10−3,  1.02×10−21.2 \times 10^{-2},\; 9.8 \times 10^{-3},\; 1.02 \times 10^{-2}
  6. 6. How many times greater is the first number?:
    8×107  than  2×1048 \times 10^7 \;\text{than}\; 2 \times 10^4
  7. 7. Which is greater?:
    5×10−2  or  5×10−35 \times 10^{-2} \;\text{or}\; 5 \times 10^{-3}
  8. 8. How many times greater is the first number?:
    6×105  than  3×10−16 \times 10^{5} \;\text{than}\; 3 \times 10^{-1}

Answer Key

Level 3

  1. 1. 3×1053 \times 10^5
  2. 2. 2.1×10−32.1 \times 10^{-3}
  3. 3. 4.5×1064.5 \times 10^{6}
  4. 4. 7×10−1, 6×102, 5×1037 \times 10^{-1},\, 6 \times 10^2,\, 5 \times 10^3
  5. 5. 9.8×10−3, 1.02×10−2, 1.2×10−29.8 \times 10^{-3},\, 1.02 \times 10^{-2},\, 1.2 \times 10^{-2}
  6. 6. 4×103=40004 \times 10^3 = 4000
  7. 7. 5×10−25 \times 10^{-2}
  8. 8. 2×1062 \times 10^6

Grade 8 Algebra: Multiplying and Dividing in Scientific Notation

Name: ______________________Date: ____________Score: ____ / 8

Level 1

Multiplying

  1. 1. Multiply. Write in scientific notation:
    (2×103)(3×104)(2 \times 10^3)(3 \times 10^4)
  2. 2. Multiply. Write in scientific notation:
    (4×102)(2×105)(4 \times 10^2)(2 \times 10^5)
  3. 3. Multiply. Write in scientific notation:
    (1.5×106)(3×102)(1.5 \times 10^6)(3 \times 10^2)
  4. 4. Multiply. Write in scientific notation:
    (3×10−2)(3×105)(3 \times 10^{-2})(3 \times 10^5)
  5. 5. Multiply. Write in scientific notation:
    (2.2×10−3)(4×10−1)(2.2 \times 10^{-3})(4 \times 10^{-1})
  6. 6. Multiply. Write in scientific notation:
    (1.1×104)(7×10−6)(1.1 \times 10^4)(7 \times 10^{-6})
  7. 7. Multiply. Write in scientific notation:
    (2×107)(4.5×101)(2 \times 10^{7})(4.5 \times 10^{1})
  8. 8. Multiply. Write in scientific notation:
    (3.1×10−4)(2×10−3)(3.1 \times 10^{-4})(2 \times 10^{-3})

Answer Key

Level 1

  1. 1. 6×1076 \times 10^7
  2. 2. 8×1078 \times 10^7
  3. 3. 4.5×1084.5 \times 10^8
  4. 4. 9×1039 \times 10^3
  5. 5. 8.8×10−48.8 \times 10^{-4}
  6. 6. 7.7×10−27.7 \times 10^{-2}
  7. 7. 9×1089 \times 10^8
  8. 8. 6.2×10−76.2 \times 10^{-7}

Grade 8 Algebra: Multiplying and Dividing in Scientific Notation

Name: ______________________Date: ____________Score: ____ / 8

Level 2

Dividing

  1. 1. Divide. Write in scientific notation:
    8×1062×102\dfrac{8 \times 10^6}{2 \times 10^2}
  2. 2. Divide. Write in scientific notation:
    9×1083×105\dfrac{9 \times 10^8}{3 \times 10^5}
  3. 3. Divide. Write in scientific notation:
    6.4×1052×10−2\dfrac{6.4 \times 10^5}{2 \times 10^{-2}}
  4. 4. Divide. Write in scientific notation:
    7.5×10−32.5×102\dfrac{7.5 \times 10^{-3}}{2.5 \times 10^{2}}
  5. 5. Divide. Write in scientific notation:
    4.8×10−41.2×10−7\dfrac{4.8 \times 10^{-4}}{1.2 \times 10^{-7}}
  6. 6. Divide. Write in scientific notation:
    9.9×10103.3×104\dfrac{9.9 \times 10^{10}}{3.3 \times 10^{4}}
  7. 7. Divide. Write in scientific notation:
    8.4×1034×105\dfrac{8.4 \times 10^{3}}{4 \times 10^{5}}
  8. 8. Divide. Write in scientific notation:
    6×10−21.5×10−6\dfrac{6 \times 10^{-2}}{1.5 \times 10^{-6}}

Answer Key

Level 2

  1. 1. 4×1044 \times 10^4
  2. 2. 3×1033 \times 10^3
  3. 3. 3.2×1073.2 \times 10^7
  4. 4. 3×10−53 \times 10^{-5}
  5. 5. 4×1034 \times 10^3
  6. 6. 3×1063 \times 10^6
  7. 7. 2.1×10−22.1 \times 10^{-2}
  8. 8. 4×1044 \times 10^4

Grade 8 Algebra: Multiplying and Dividing in Scientific Notation

Name: ______________________Date: ____________Score: ____ / 8

Level 3

Adjusting the answer to scientific notation

  1. 1. Multiply. Write in scientific notation:
    (5×103)(4×102)(5 \times 10^3)(4 \times 10^2)
  2. 2. Multiply. Write in scientific notation:
    (6×10−4)(7×109)(6 \times 10^{-4})(7 \times 10^{9})
  3. 3. Multiply. Write in scientific notation:
    (2.5×10−3)(8×10−2)(2.5 \times 10^{-3})(8 \times 10^{-2})
  4. 4. Divide. Write in scientific notation:
    2×1058×102\dfrac{2 \times 10^5}{8 \times 10^2}
  5. 5. Divide. Write in scientific notation:
    1.2×10−34×10−6\dfrac{1.2 \times 10^{-3}}{4 \times 10^{-6}}
  6. 6. Simplify. Write in scientific notation:
    (3×104)(6×105)9×103\dfrac{(3 \times 10^4)(6 \times 10^5)}{9 \times 10^{3}}
  7. 7. Multiply. Write in scientific notation:
    (9×105)(9×10−2)(9 \times 10^{5})(9 \times 10^{-2})
  8. 8. Divide. Write in scientific notation:
    3×1046×10−3\dfrac{3 \times 10^{4}}{6 \times 10^{-3}}

Answer Key

Level 3

  1. 1. 2×1062 \times 10^6
  2. 2. 4.2×1064.2 \times 10^6
  3. 3. 2×10−42 \times 10^{-4}
  4. 4. 2.5×1022.5 \times 10^2
  5. 5. 3×1023 \times 10^2
  6. 6. 2×1062 \times 10^6
  7. 7. 8.1×1048.1 \times 10^4
  8. 8. 5×1065 \times 10^6

Grade 8 Algebra: Adding and Subtracting in Scientific Notation

Name: ______________________Date: ____________Score: ____ / 8

Level 1

Same power of 10

  1. 1. Add or subtract. Write in scientific notation:
    (3×104)+(5×104)(3 \times 10^4) + (5 \times 10^4)
  2. 2. Add or subtract. Write in scientific notation:
    (7.2×105)−(2.1×105)(7.2 \times 10^5) - (2.1 \times 10^5)
  3. 3. Add or subtract. Write in scientific notation:
    (1.4×103)+(4.3×103)(1.4 \times 10^3) + (4.3 \times 10^3)
  4. 4. Add or subtract. Write in scientific notation:
    (9.6×107)−(3.6×107)(9.6 \times 10^7) - (3.6 \times 10^7)
  5. 5. Add or subtract. Write in scientific notation:
    (2.05×102)+(3.4×102)(2.05 \times 10^2) + (3.4 \times 10^2)
  6. 6. Add or subtract. Write in scientific notation:
    (8×106)−(2.5×106)(8 \times 10^6) - (2.5 \times 10^6)
  7. 7. Add or subtract. Write in scientific notation:
    (6.3×109)+(2.6×109)(6.3 \times 10^{9}) + (2.6 \times 10^{9})
  8. 8. Add or subtract. Write in scientific notation:
    (4.75×103)−(1.5×103)(4.75 \times 10^{3}) - (1.5 \times 10^{3})

Answer Key

Level 1

  1. 1. 8×1048 \times 10^4
  2. 2. 5.1×1055.1 \times 10^5
  3. 3. 5.7×1035.7 \times 10^3
  4. 4. 6×1076 \times 10^7
  5. 5. 5.45×1025.45 \times 10^2
  6. 6. 5.5×1065.5 \times 10^6
  7. 7. 8.9×1098.9 \times 10^9
  8. 8. 3.25×1033.25 \times 10^3

Grade 8 Algebra: Adding and Subtracting in Scientific Notation

Name: ______________________Date: ____________Score: ____ / 8

Level 2

Different powers of 10

  1. 1. Add or subtract. Write in scientific notation:
    (3×105)+(2×104)(3 \times 10^5) + (2 \times 10^4)
  2. 2. Add or subtract. Write in scientific notation:
    (6.5×106)−(5×105)(6.5 \times 10^6) - (5 \times 10^5)
  3. 3. Add or subtract. Write in scientific notation:
    (4.1×103)+(9×102)(4.1 \times 10^3) + (9 \times 10^2)
  4. 4. Add or subtract. Write in scientific notation:
    (1.2×108)−(3×106)(1.2 \times 10^8) - (3 \times 10^6)
  5. 5. Add or subtract. Write in scientific notation:
    (7×104)+(6×102)(7 \times 10^4) + (6 \times 10^2)
  6. 6. Add or subtract. Write in scientific notation:
    (5.5×105)−(5×104)(5.5 \times 10^5) - (5 \times 10^4)
  7. 7. Add or subtract. Write in scientific notation:
    (2.4×106)+(3×105)(2.4 \times 10^{6}) + (3 \times 10^{5})
  8. 8. Add or subtract. Write in scientific notation:
    (9×103)−(4×102)(9 \times 10^{3}) - (4 \times 10^{2})

Answer Key

Level 2

  1. 1. 3.2×1053.2 \times 10^5
  2. 2. 6×1066 \times 10^6
  3. 3. 5×1035 \times 10^3
  4. 4. 1.17×1081.17 \times 10^8
  5. 5. 7.06×1047.06 \times 10^4
  6. 6. 5×1055 \times 10^5
  7. 7. 2.7×1062.7 \times 10^6
  8. 8. 8.6×1038.6 \times 10^3

Grade 8 Algebra: Adding and Subtracting in Scientific Notation

Name: ______________________Date: ____________Score: ____ / 8

Level 3

Negative exponents and regrouping

  1. 1. Add or subtract. Write in scientific notation:
    (4×10−3)+(3×10−3)(4 \times 10^{-3}) + (3 \times 10^{-3})
  2. 2. Add or subtract. Write in scientific notation:
    (6×10−2)−(4×10−3)(6 \times 10^{-2}) - (4 \times 10^{-3})
  3. 3. Add or subtract. Write in scientific notation:
    (8×104)+(5×104)(8 \times 10^4) + (5 \times 10^4)
  4. 4. Add or subtract. Write in scientific notation:
    (2×10−5)+(9×10−6)(2 \times 10^{-5}) + (9 \times 10^{-6})
  5. 5. Add or subtract. Write in scientific notation:
    (1.5×103)−(9×102)(1.5 \times 10^3) - (9 \times 10^2)
  6. 6. Add or subtract. Write in scientific notation:
    (9.5×106)+(8×105)(9.5 \times 10^6) + (8 \times 10^5)
  7. 7. Add or subtract. Write in scientific notation:
    (7×10−4)−(5×10−5)(7 \times 10^{-4}) - (5 \times 10^{-5})
  8. 8. Add or subtract. Write in scientific notation:
    (6.5×102)+(4.5×102)(6.5 \times 10^{2}) + (4.5 \times 10^{2})

Answer Key

Level 3

  1. 1. 7×10−37 \times 10^{-3}
  2. 2. 5.6×10−25.6 \times 10^{-2}
  3. 3. 1.3×1051.3 \times 10^5
  4. 4. 2.9×10−52.9 \times 10^{-5}
  5. 5. 6×1026 \times 10^2
  6. 6. 1.03×1071.03 \times 10^7
  7. 7. 6.5×10−46.5 \times 10^{-4}
  8. 8. 1.1×1031.1 \times 10^3

Grade 8 Algebra: Word Problems: Scientific Notation

Name: ______________________Date: ____________Score: ____ / 8

Level 1

Writing real-world numbers

  1. 1. Write in scientific notation:
    The\text{The}Sun\text{Sun}is\text{is}about\text{about}150000000\text{150000000}km\text{km}from\text{from}Earth.\text{Earth.}
  2. 2. Write in scientific notation:
    A\text{A}human\text{human}hair\text{hair}is\text{is}about\text{about}0.00008\text{0.00008}mm\text{}wide.\text{wide.}
  3. 3. Write in scientific notation:
    About\text{About}8000000000\text{8000000000}people\text{people}live\text{live}on\text{on}Earth.\text{Earth.}
  4. 4. Write in scientific notation:
    A\text{A}grain\text{grain}of\text{of}sand\text{sand}has\text{has}a\text{a}mass\text{mass}of\text{of}about\text{about}0.0000044\text{0.0000044}kg.\text{kg.}
  5. 5. Write in standard form:
    The\text{The}Moon\text{Moon}is\text{is}about\text{about}3.84×1053.84\times 10^{5}\text{}km\text{km}from\text{from}Earth.\text{Earth.}
  6. 6. Write in standard form:
    A\text{A}dust\text{dust}particle\text{particle}is\text{is}about\text{about}2.5×10−62.5\times 10^{-6}\text{}mm\text{}wide.\text{wide.}
  7. 7. Write in scientific notation:
    A\text{A}red\text{red}blood\text{blood}cell\text{cell}is\text{is}about\text{about}0.000007\text{0.000007}mm\text{}wide.\text{wide.}
  8. 8. Write in standard form:
    Earth\text{Earth}is\text{is}about\text{about}4.5×1094.5\times 10^{9}\text{}years\text{years}old.\text{old.}

Answer Key

Level 1

  1. 1. 1.5×108 km1.5 \times 10^8\text{ km}
  2. 2. 8×10−5 m8 \times 10^{-5}\text{ m}
  3. 3. 8×1098 \times 10^9
  4. 4. 4.4×10−6 kg4.4 \times 10^{-6}\text{ kg}
  5. 5. 384 000 km384\,000\text{ km}
  6. 6. 0.0000025 m0.0000025\text{ m}
  7. 7. 7×10−6 m7 \times 10^{-6}\text{ m}
  8. 8. 4 500 000 000 years4\,500\,000\,000\text{ years}

Grade 8 Algebra: Word Problems: Scientific Notation

Name: ______________________Date: ____________Score: ____ / 8

Level 2

Multiplying and dividing

  1. 1. Solve:
    A\text{A}factory\text{factory}makes\text{makes}4×1054\times 10^{5}\text{}bottles\text{bottles}each\text{each}day.\text{day.}How\text{How}many\text{many}bottles\text{bottles}does\text{does}it\text{it}make\text{make}in\text{in}3×1023\times 10^{2}\text{}days?\text{days?}
  2. 2. Solve:
    Light\text{Light}travels\text{travels}3×1083\times 10^{8}\text{}mm\text{}per\text{per}second.\text{second.}How\text{How}far\text{far}does\text{does}it\text{it}travel\text{travel}in\text{in}6×1016\times 10^{1}\text{}seconds?\text{seconds?}
  3. 3. Solve:
    A\text{A}city\text{city}spends\text{spends}6×1086\times 10^{8}\text{}dollars\text{dollars}on\text{on}2×1052\times 10^{5}\text{}people.\text{people.}How\text{How}much\text{much}is\text{is}that\text{that}per\text{per}person?\text{person?}
  4. 4. Solve:
    One\text{One}sheet\text{sheet}of\text{of}paper\text{paper}is\text{is}1×10−41\times 10^{-4}\text{}mm\text{}thick.\text{thick.}How\text{How}tall\text{tall}is\text{is}a\text{a}stack\text{stack}of\text{of}5×1035\times 10^{3}\text{}sheets?\text{sheets?}
  5. 5. Solve:
    A\text{A}hard\text{hard}drive\text{drive}holds\text{holds}2×10122\times 10^{12}\text{}bytes.\text{bytes.}Each\text{Each}photo\text{photo}uses\text{uses}4×1064\times 10^{6}\text{}bytes.\text{bytes.}How\text{How}many\text{many}photos\text{photos}fit?\text{fit?}
  6. 6. Solve:
    A\text{A}heart\text{heart}beats\text{beats}about\text{about}1×1051\times 10^{5}\text{}times\text{times}per\text{per}day.\text{day.}About\text{About}how\text{how}many\text{many}beats\text{beats}is\text{is}that\text{that}in\text{in}3.65×1023.65\times 10^{2}\text{}days?\text{days?}
  7. 7. Solve:
    A\text{A}truck\text{truck}carries\text{carries}2×1042\times 10^{4}\text{}kg.\text{kg.}How\text{How}much\text{much}do\text{do}3×1033\times 10^{3}\text{}trucks\text{trucks}carry?\text{carry?}
  8. 8. Solve:
    A\text{A}school\text{school}uses\text{uses}9×1059\times 10^{5}\text{}sheets\text{sheets}of\text{of}paper\text{paper}in\text{in}3×1023\times 10^{2}\text{}days.\text{days.}How\text{How}many\text{many}sheets\text{sheets}is\text{is}that\text{that}per\text{per}day?\text{day?}

Answer Key

Level 2

  1. 1. 1.2×1081.2 \times 10^8
  2. 2. 1.8×1010 m1.8 \times 10^{10}\text{ m}
  3. 3. 3×103=3000 dollars3 \times 10^3 = 3000\text{ dollars}
  4. 4. 5×10−1=0.5 m5 \times 10^{-1} = 0.5\text{ m}
  5. 5. 5×1055 \times 10^5
  6. 6. 3.65×1073.65 \times 10^7
  7. 7. 6×107 kg6 \times 10^7\text{ kg}
  8. 8. 3×1033 \times 10^3

Grade 8 Algebra: Word Problems: Scientific Notation

Name: ______________________Date: ____________Score: ____ / 8

Level 3

Comparing and combining

  1. 1. Solve:
    Earth\text{Earth}has\text{has}a\text{a}mass\text{mass}of\text{of}about\text{about}6×10246\times 10^{24}\text{}kg.\text{kg.}The\text{The}Moon\text{Moon}has\text{has}a\text{a}mass\text{mass}of\text{of}about\text{about}7.5×10227.5\times 10^{22}\text{}kg.\text{kg.}How\text{How}many\text{many}times\text{times}heavier\text{heavier}is\text{is}Earth?\text{Earth?}
  2. 2. Solve:
    A\text{A}virus\text{virus}is\text{is}1×10−71\times 10^{-7}\text{}mm\text{}long.\text{long.}A\text{A}cell\text{cell}is\text{is}2×10−52\times 10^{-5}\text{}mm\text{}long.\text{long.}How\text{How}many\text{many}times\text{times}longer\text{longer}is\text{is}the\text{the}cell?\text{cell?}
  3. 3. Solve:
    Country\text{Country}XX\text{}has\text{has}3.2×1073.2\times 10^{7}\text{}people\text{people}and\text{and}Country\text{Country}YY\text{}has\text{has}8×1068\times 10^{6}\text{}people.\text{people.}What\text{What}is\text{is}their\text{their}total\text{total}population?\text{population?}
  4. 4. Solve:
    A\text{A}tank\text{tank}holds\text{holds}5×1045\times 10^{4}\text{}liters.\text{liters.}1.5×1041.5\times 10^{4}\text{}liters\text{liters}are\text{are}used.\text{used.}How\text{How}much\text{much}is\text{is}left?\text{left?}
  5. 5. Solve:
    Which\text{Which}is\text{is}longer,\text{longer,}4.2×10−34.2\times 10^{-3}\text{}mm\text{}or\text{or}9×10−49\times 10^{-4}\text{}m?m\text{?}By\text{By}how\text{how}much?\text{much?}
  6. 6. Solve:
    A\text{A}star\text{star}is\text{is}9×10159\times 10^{15}\text{}mm\text{}away.\text{away.}Light\text{Light}travels\text{travels}3×1083\times 10^{8}\text{}mm\text{}per\text{per}second.\text{second.}How\text{How}many\text{many}seconds\text{seconds}does\text{does}its\text{its}light\text{light}take\text{take}to\text{to}reach\text{reach}us?\text{us?}
  7. 7. Solve:
    A\text{A}phone\text{phone}costs\text{costs}8×1028\times 10^{2}\text{}dollars.\text{dollars.}A\text{A}company\text{company}sells\text{sells}5×1065\times 10^{6}\text{}phones.\text{phones.}How\text{How}much\text{much}money\text{money}is\text{is}that?\text{that?}
  8. 8. Solve:
    A\text{A}bacterium\text{bacterium}is\text{is}2×10−62\times 10^{-6}\text{}mm\text{}long.\text{long.}How\text{How}many\text{many}fit\text{fit}end\text{end}to\text{to}end\text{end}in\text{in}1×10−21\times 10^{-2}\text{}m?m\text{?}

Answer Key

Level 3

  1. 1. 8×101=808 \times 10^1 = 80
  2. 2. 2×102=2002 \times 10^2 = 200
  3. 3. 4×1074 \times 10^7
  4. 4. 3.5×104 L3.5 \times 10^4\text{ L}
  5. 5. 4.2×10−3 m, by 3.3×10−3 m4.2 \times 10^{-3}\text{ m, by } 3.3 \times 10^{-3}\text{ m}
  6. 6. 3×107 s3 \times 10^7\text{ s}
  7. 7. 4×109 dollars4 \times 10^9\text{ dollars}
  8. 8. 5×1035 \times 10^3