3.2. SCIENTIFIC NOTATION OF NUMBERS
SOLVE
1. Write the following numbers in scientific notation.
(a) 4200 = 4.2 × 10³
(b) 5200 = 5.2 × 10³
(c) 64000 = 6.4 × 10⁴
(d) 82000 = 8.2 × 10⁴
(e) 930000 = 9.3 × 10⁵
(f) 410000 = 4.1 × 10⁵
(g) 7200000 = 7.2 × 10⁶
(h) 9900000 = 9.9 × 10⁵
2. Write the following numbers in scientific notation:(a) 5,03,000 = 5.03 × 105
(b) 2,345,000 = 2.345 × 106
(c) 62,500,000,000 = 6.25 × 1010
(d) 8,900,000,000,000 = 8.9 × 1012
3. Write the following numbers in scientific notation.
(a) 0.00345 = 3.45 × 10⁻³
(b) 0.0000532 = 5.32 × 10⁻⁵
(c) 0.0000628 = 6.28 × 10⁻⁵
(d) 0.00000893 = 8.93 × 10⁻⁶
(e) 0.0000000000487 = 4.87 × 10⁻¹¹
(f) 0.0000000000679 = 6.79 × 10⁻¹¹
(g) 0.00000000001234 = 1.234 × 10⁻¹¹
(h) 0.00000000005678 = 5.678 × 10⁻¹¹
4. Change the following numbers in scientific notation into standard form:
(a) 2.34 × 10⁵ = 234, 000
(b) 4.56 × 10⁸ = 456, 000, 000
(c) 3.14 × 10⁹ = 3, 140, 000, 000
(d) 2.71 × 10¹² = 2, 710, 000, 000, 000
(e) 6.02 × 10²³ = 602, 000, 000, 000, 000, 000, 000, 000
(f) 7.9 × 10⁻³ = 0.0079
(g) 9.87 × 10⁻⁴ = 0.000987
(h) 5.67 × 10⁻⁵ = 0.0000567
(i) 1.23 × 10⁻⁶ = 0.00000123
(j) 8.62 × 10⁻⁷ = 0.000000862
(k) 3.45 × 10⁻⁸ = 0.0000000345
(l) 2.054 × 10⁻⁹ = 0.000000002054
5. Rewrite the following information of big numbers in scientific notation.
(a) Physics: The speed of light is approximately 299,792,458 meters per second, a very large number = 2.998 × 10⁸ meters per second
(b) Biology: The number of cells in the human body is estimated to be around 37 trillion = 3.7 × 10¹³ cells
(c) Genetics: The human genome consists of around 3 billion base pairs = 3.0 × 10⁹ base pairs
(d) Astronomy: The estimated number of stars in the observable universe is over 100 billion = 1.0 × 10¹¹ stars (minimum estimate)
(e) Geography: The tallest mountain in the world, Mount Everest, is over 8848860 mm = 8.849 × 10⁶ mm
(f) Technology: The total number of Google searches per day is estimated to be over 3.5 billion in last year = 3.5 × 10⁹ searches per day
6. Rewrite the following information of small numbers in scientific notation.
(a) The smallest known mammal species is the bumblebee bat, which weighs only around kg. 0.002 kg.
= 2 × 10⁻³ kg
(b) A nanometer is one billionth of a meter and is used to measure extremely small objects, such as atoms and molecules, 0.000000001 meters.
= 1 × 10⁻⁹ meters
(c) The smallest recognized fish species in the world is the Paedocypris fish, which measures only about 7.9 millimeters in length or 0.0079 meters.
= 7.9 × 10⁻³ meters
(d) A single human blood cell has a diameter of approximately 7 microns or 0.000007 meters.
= 7 × 10⁻⁶ meters
(e) The smallest recognized particle in physics is the neutrino, which has a mass of only about 0.0000000000000000000016 milligrams.
= 1.6 × 10⁻²⁴ milligrams
(f) The charge of a single electron is approximately 0.0000000000000000000000001602 Coulombs.
= 1.602 × 10⁻¹⁹ Coulombs
7. Rewrite the following information of numbers in usual/standard notation.
(a) The speed of nerve impulses in the human body is typically around 1 × 10² m/s.
= 100 m/s
(b) The speed of light in a vacuum is approximately 3 × 10⁸ m/s.
= 300,000,000 m/s
(c) The number of base pairs in the human genome is approximately 3.2 × 10⁹ base pairs.
= 3,200,000,000 base pairs
(d) The estimated number of cells in the human body is approximately 3 to 4 × 10¹³ cells.
= 30,000,000,000,000 to 40,000,000,000,000 cells
(e) The estimated number of stars in the observable universe is around 10²².
= 10,000,000,000,000,000,000,000
(f) The mass of the Sun is approximately 1.989 × 10³⁰ kg.
= 1,989,000,000,000,000,000,000,000,000,000 kg
(g) The radius of a hydrogen atom is approximately 5.29 × 10⁻¹¹ meters.
= 0.0000000000529 meters
(h) The charge of an electron is approximately 1.602 × 10⁻¹⁹ Coulombs.
= 0.0000000000000000001602 Coulombs
(i) The mass of an electron is approximately 9.109 × 10⁻³¹ kg.
= 0.0000000000000000000000000009109 kg
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