SCIENTIFIC NOTATION WORKSHEET

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 SCIENTIFIC NOTATION WORKSHEET #1 CHANGE EACH OF THE FOLLOWING COMMON NUMBERS INTO PROPER SCIENTIFIC NOTATION 93,000,000 mi. – 9.3×10 m distance to the sun 2. 130,000,000 km – 13 x 10 K _distance to the sun 58,666,000,000,000 mi – 58.Chexib distance to the nearest star 300,000,000 m/sec = 3 x US speed of light 600,000,000,000,000,000,000,000 – 609 molecules in 2g hydrogen 0.000000027 m-_2.11n diameter of an atom 0.0000010 km – length of one mm 350,000,000 – _ 3.5 VD number of people in USA 9. 0.000000010001 = a single dollars part of national debt 10. 365 days in a year CHANGE EACH OF THE FOLLOWING SCIENTIFIC NUMBERS INTO COMMON NUMBERS 11. 3.6 X 10- 0.000026 12. 7.7 X 102 0.000000000077 13. 9.3 X 10 – 43poopoo 14. 6.0 X 10 – 15. 3.2 X 10% = 0.00032 16. 6.8 X 10'-69 MULTIPLY EACH OF THE FOLLOWING MEASUREMENTS USING PROPER SCIENTIFIC NOTATION: 17. (1.8 x 10g)(3.6 x 10g) – 18. (4.7 x 109 m)(5.5 x 10 sec) – 19. (3.0 x 10' mm)4.0 x 10 mm)(1.2 x 10mm) DIVIDE EACH OF THE FOLLOWING PRORLES GIVING YOUR ANSWERS IN PROPER SCIENTIFIC NOTATION: 20. 4×102- 2 x 10 21. – 4x 10 2 x 1012 2x 10- 4x 1012 23. 6x 10 2 x 10* = ADD OR SUBTRACT EACH OF THE FOLLOWING PROBLEMS AND GIVE YOUR ANSWERS IN PROPER SCIENTIFIC NOTATION 24. 6.3 x 10 + 4.2 x 10 25. 3.32 x 10 -5.00 x 10

The Correct Answer and Explanation is :

Here are the correct answers to your Scientific Notation Worksheet #1, along with a 300-word explanation of how scientific notation works:

Conversion of Common Numbers to Scientific Notation

  1. 93,000,000 mi → 9.3 × 10⁷ mi
  2. 130,000,000 km → 1.3 × 10⁸ km
  3. 58,666,000,000,000 mi → 5.8666 × 10¹³ mi
  4. 300,000,000 m/sec → 3.0 × 10⁸ m/sec
  5. 600,000,000,000,000,000,000,000 molecules → 6.0 × 10²³ molecules
  6. 0.000000027 m → 2.7 × 10⁻⁸ m
  7. 0.0000010 km → 1.0 × 10⁻⁶ km
  8. 350,000,000 → 3.5 × 10⁸
  9. 0.000000010001 → 1.0001 × 10⁻⁸
  10. 365 days (already in standard notation)

Conversion of Scientific Notation to Common Numbers

  1. 3.6 × 10⁻⁶ → 0.0000036
  2. 7.7 × 10² → 770
  3. 9.3 × 10⁴ → 93,000
  4. 6.0 × 10⁻¹ → 0.6
  5. 3.2 × 10⁻³ → 0.0032
  6. 6.8 × 10⁻⁹ → 0.0000000068

Multiplication Using Scientific Notation

  1. (1.8 × 10⁹) × (3.6 × 10⁹)
    = 6.48 × 10¹⁸
  2. (4.7 × 10⁹ m) × (5.5 × 10⁶ sec)
    = 2.585 × 10¹⁶ m·s
  3. (3.0 × 10³ mm) × (4.0 × 10² mm) × (1.2 × 10¹ mm)
    = 1.44 × 10⁷ mm³

Division Using Scientific Notation

  1. (4 × 10²) ÷ (2 × 10¹)
    = 2 × 10¹
  2. (4 × 10⁻⁶) ÷ (2 × 10¹²)
    = 2 × 10⁻¹⁸
  3. (2 × 10⁻⁴) ÷ (4 × 10¹²)
    = 5 × 10⁻¹⁷
  4. (6 × 10⁶) ÷ (2 × 10⁴)
    = 3 × 10²

Addition & Subtraction Using Scientific Notation

  1. (6.3 × 10⁵) + (4.2 × 10⁵)
    = 1.05 × 10⁶
  2. (3.32 × 10³) – (5.00 × 10²)
    = 2.82 × 10³

Explanation of Scientific Notation (300 Words)

Scientific notation is a way of expressing very large or very small numbers in a compact form, making calculations easier, especially in science and engineering. It consists of a number (called the coefficient) between 1 and 10, multiplied by 10 raised to an exponent (power of ten).

For example, 93,000,000 is written as 9.3 × 10⁷, because we move the decimal 7 places to the left. Similarly, 0.0000010 is written as 1.0 × 10⁻⁶, because we move the decimal 6 places to the right.

In multiplication, the coefficients are multiplied, and exponents are added:
[
(3 × 10⁴) × (2 × 10³) = 6 × 10⁷
]
In division, the coefficients are divided, and exponents are subtracted:
[
(8 × 10⁶) ÷ (2 × 10³) = 4 × 10³
]
For addition or subtraction, numbers must have the same exponent before performing the operation. For example,
[
(6.3 × 10⁵) + (4.2 × 10⁵) = 1.05 × 10⁶
]
because the exponents match.

Scientific notation is widely used in physics, chemistry, and astronomy to simplify working with extremely large or small values, such as the speed of light (3.0 × 10⁸ m/s) or the charge of an electron (1.6 × 10⁻¹⁹ C).

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