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1.4.H: Homework

College Technical Math · LibreTexts

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    From LibreTexts, under CC BY 4.0, as the source states it; its equations are written in TeX, which the PDF shows typeset. This page at LibreTexts.

    Practice Makes Perfect

    Convert from Decimal Notation to Scientific Notation

    In the following exercises, write each number in scientific notation.

    Exercise 1

    340,000

    Answer

    \(3.4 \times 10^{5}\)

    Exercise 2

    1,290,000

    Answer

    \(1.29 \times 10^{6}\)

    Exercise 3

    0.041

    Answer

    \(4.1 \times 10^{-2}\)

    Exercise 4

    0.00000103

    Answer

    \(1.03 \times 10^{-6}\)

    Convert Scientific Notation to Decimal Form

    In the following exercises, convert each number to decimal form.

    Exercise 5

    \(8.3 \times 10^{2}\)

    Answer

    830

    Exercise 6

    \(1.6 \times 10^{10}\)

    Answer

    16,000,000,000

    Exercise 7

    \(3.8 \times 10^{-2}\)

    Answer

    0.038

    Exercise 8

    \(1.93 \times 10^{-5}\)

    Answer

    0.0000193

    Multiply and Divide Using Scientific Notation

    In the following exercises, perform the indicated calculations by using scientific notation. Answer in scientific notation.

    Exercise 9

    \(\left(2 \times 10^{2}\right)\left(1 \times 10^{-4}\right)\)

    Answer

    \(2 \times 10^{-2}\)

    Exercise 10

    \(\left(3.5 \times 10^{-4}\right)\left(1.6 \times 10^{-2}\right)\)

    Answer

    \(5.6 \times 10^{-6}\)

    Exercise 11

    \(0.000 035 \times 0.000 000 76\)

    Answer

    \(2.66 \times 10^{-11}\)

    Exercise 12

    \(970,000,000 \times 0.000 45\)

    Answer

    \(4.365 \times 10^{5}\)

    Exercise 13

    \(\dfrac{5 \times 10^{-2}}{1 \times 10^{-10}}\)

    Answer

    \(5 \times 10^{8}\)

    Exercise 14

    \(\dfrac{8 \times 10^{6}}{4 \times 10^{-1}}\)

    Answer

    \(2 \times 10^{7}\)

    Exercise 15

    \(350,000 \div 140,000,000\)

    Answer

    \(2.5 \times 10^{-3}\)

    Exercise 16

    \(0.0036 \div 0.00000018\)

    Answer

    \(2 \times 10^{4}\)

    Exercise 17

    \(\dfrac{\left(6 \times 10^{-5}\right)\left(6 \times 10^{-3}\right)}{\left(4 \times 10^{-10}\right)\left(9 \times 10^{8}\right)}\)

    Answer

    \(1 \times 10^{-6}\)

    Exercise 18

    \(\dfrac{\left(5 \times 10^{-5}\right)\left(6 \times 10^{6}\right)\left(4 \times 10^{4}\right)}{\left(1.5 \times 10^{-10}\right)\left(4 \times 10^{5}\right)}\)

    Answer

    \(2 \times 10^{11}\)

    Exercise 19

    \(\left(1.4 \times 10^{4}\right)^{3}\)

    Answer

    \(2.744 \times 10^{12}\)

    Exercise 20

    \(\left(3 \times 10^{-6}\right)^{4}\)

    Answer

    \(8.1 \times 10^{-23}\)

    Exercise 21

    \(\left(6.2 \times 10^{-4}\right)\left(4.5 \times 10^{-7}\right)\left(2 \times 10^{8}\right)\)

    Answer

    \(5.58 \times 10^{-2}\)

    Applications

    Solve

    Exercise 22

    The probability of winning the 2010 Megamillions lottery was about 0.0000000057. Write the number in scientific notation.

    Answer

    \(5.7 \times 10^{-9}\)

    Exercise 23

    At the start of \(2012,\) the US federal budget had a deficit of more than \(\$ 1.5 \times 10^{13} .\) Convert this number to decimal form.

    Answer

    15,000,000,000,000

    Exercise 24

    The width of a proton is \(1 \times 10^{-5}\) of the width of an atom. Convert this number to decimal form.

    Answer

    0.00001

    Exercise 25

    Coin production In 1942, the U.S. Mint produced 154,500,000 nickels. Write 154,500,000 in scientific notation.

    Answer

    \(1.545 \times 10^{8}\)

    This page titled 1.4.H: Homework was last modified on Mon, 06 Jul 2026 03:20:47 GMT and is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Kiersten Purves.