AI Tutor
Back to Contemporary Mathematics

3.9 Scientific Notation

Very large and very small numbers as a coefficient times a power of ten, converting back to standard form, and computing with them.

Contemporary Mathematics, 3.9 Scientific Notation

Status
FlagsLoading your progress…

15 exercises

3.9 Exercise 1

Which of the following numbers are in scientific notation? If the number is not in scientific notation, explain why it is not.

  1. −9.67×1020- 9.67 \times 10^{20}
  2. 145×10−8145 \times 10^{- 8}
  3. 1.451.45
2.5

3.9 Exercise 3

Write the following numbers in scientific notation form:

  1. 428.9
  2. −0.00000981
  3. 8
2.5

3.9 Exercise 5

Change 456.142×105456.142 \times 10^{5} by moving the decimal two places to the left.

2.5

3.9 Exercise 7

Change 12.3×10212.3 \times 10^{2} by moving the decimal five places to the right.

2.5

3.9 Exercise 9

Convert the following into standard form:

  1. 2.78×1092.78 \times 10^{9}
  2. 9.04×10−89.04 \times 10^{- 8}
2.5

3.9 Exercise 11

Calculate the following:

  1. 3.8×10−3+1.006×10−33.8 \times 10^{- 3} + 1.006 \times 10^{- 3}
  2. 9.61×108−3.85×1089.61 \times 10^{8} - 3.85 \times 10^{8}
2.5

3.9 Exercise 13

Calculate the following:

  1. 7.03×1013+8.5×10137.03 \times 10^{13} + 8.5 \times 10^{13}
  2. 4.3×1021−4.613×10214.3 \times 10^{21} - 4.613 \times 10^{21}
2.5

3.9 Exercise 15

Calculate the following:

2.5

3.9 Exercise 17

Calculate the following:
7.9×10−15−6.8×10−137.9 \times 10^{- 15} - 6.8 \times 10^{- 13}

2.5

3.9 Exercise 19

Calculate the following:

  1. (4.3×103)×(1.8×107)\left(4.3 \times 10^{3}\right) \times \left(1.8 \times 10^{7}\right)

  2. (5×10−13)×(7.3×106)\left(5 \times 10^{- 1} ^{3}\right) \times \left(7.3 \times 10^{6}\right)

2.5

3.9 Exercise 21

Calculate the following:

  1. (8.4×1031)/(2.1×107)\left(8.4 \times 10^{31}\right) / \left(2.1 \times 10^{7}\right)
  2. (4.14×10−13)/(8.28×109)\left(4.14 \times 10^{- 13}\right) / \left(8.28 \times 10^{9}\right)
2.5

3.9 Exercise 23

How much farther from the sun is Earth compared to Venus if Venus is 6.7667×1076.7667 \times 10^{7} miles from the sun and Earth is 9.1692×1079.1692 \times 10^{7} miles from the sun?

2.5

3.9 Exercise 25

The probability of winning the Mega Millions lottery is published as 3.304693×10−93.304693 \times 10^{- 9}. The probability of being hit by lightning is approximated to be 2×10−62 \times 10^{- 6}. How many times more likely are you to be hit by lightning than win the Mega Millions?

2.5

3.9 Exercise 27

Sometimes it is entertaining to determine the time it takes for something to happen. Fingernails grow about 8.032×10−118.032 \times 10^{- 11} km per minute. How many kilometers long would fingernails be after 6×1046 \times 10^{4} minutes?

2.5

3.9 Exercise 29

As mentioned in the opening to this section, it is estimated that we’re producing 2.5 quintillion bytes of data per day. A good estimate is that there are 7.674 billion people on the planet. Convert both of those numbers to scientific notation, and then determine how much data is being generated per person each day.

2.5

Adapted from Contemporary Mathematics © 2023 Rice University. Licensed under CC BY 4.0. Source: Contemporary Mathematics. Imported at revision fa7c1a1.