← Back to Topic 5

Word Problems: Scientific Notation: Classroom Packet

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