MATHS AND ENERGY

WRITE   THESE  NUMBERS IN SCIENTIFIC  NOTATION:

 

 

1. Length of a year. 31,560,000.0 seconds

 

 

2. Speed of light: 299,792.4 kilometers/sec

 

 

3. Mass of the sun: 1,989,000,000,000,000,000,000,000,000,000,000 grams

 

 

4. Mass of Earth: 5,974,000,000,000,000,000,000,000 kilograms

 

 

5. One light-year : 9,460,500,000,000 kilometers

 

 

6. Power output of sun : 382,700,000,000,000,000,000,000,000 watts

 

 

7. Mass of an electron: 0.00000000000000000000000000000091096 kilograms

 

 

8. Energy equivalent of one electron-Volt : 0.00000000000000000016022 joules

 

 

9. Ratio of proton to electron mass: 1,836.2

 

 

10. Planck's Constant: 0.000000000000000000000000006626068 ergs seconds

 

 

11. Radius of hydrogen atom : 0.00000000529177 centimeters

 

 

12. Radius of Earth's orbit: 14,959,789,200,000 centimeters

 

 

13. Smallest unit of physical distance: 0.0000000000000000000000000000000016 centimeters

 

 

14. Diameter of Visible Universe: 26,000,000,000,000,000,000,000,000,000 centimeters

The following problems involve the multiplication and division of numbers expressed in Scientific Notation. Report all answers to two significant figures. For example:

1.34 x 10⁸ x 4.5 x 10⁶ = (1.34 x 4.5) x 10⁽⁸⁺⁶⁾

= 6.03 x 10¹⁴

To 2 significant figures this becomes… 6.0 x 10¹⁴

3.45 x 10^-5 / 2.1 x 10⁶ = ( 3.45/2.1) x 10 ^{(-5 - (6))}

= 1.643 x 10^-11

To 2 significant figures this becomes… 1.6 x 10¹⁴

 

• Number of nuclear particles in the sun: 2.0 x 10³³ grams / 1.7 x 10^-24 grams/particle

 

 

 

• Number of stars in the visible universe: 2.0 x 10¹¹ stars/galaxy x 8.0 x 10¹⁰ galaxies

 

 

 

• Age of universe in seconds: 1.4 x 10¹⁰ years x 3.156 x 10⁷ seconds/year

 

 

 

• Number of electron orbits in one year: (3.1 x 10⁷ seconds/year) / (2.4 x 10^-24 seconds/orbit)

 

 

 

• Energy carried by visible light: (6.6 x 10^-27 ergs/cycle) x 5 x 10¹⁴ cycles

 

 

 

• Lengthening of Earth day in 1 billion years: (1.0 x 10⁹ years) x 1.5 x 10^-5 sec/year

 

 

 

• Tons of TNT needed to make crater 100 km across: 4.0 x 10¹³ x (1.0 x 10¹⁵)/(4.2 x 10¹⁶)

 

 

 

• Average density of the Sun: 1.9 x 10³³ grams / 1.4 x 10³³ cm³

 

 

 

• Number of sun-like stars within 300 light years: (2.0 x 10^-3 stars ) x 4.0 x 10⁶ cubic light-yrs

 

 

10) Density of the Orion Nebula: (3.0 x 10² x 2.0 x 10³³ grams) / (5.4 x 10⁵⁶ cm³ ) Weekly Math Problems http://spacemath.gsfc.nasa.gov

 

 

 

Answer Key:

1) Number of nuclear particles in the sun: 2.0 x 10³³ grams / 1.7 x 10^-24 grams/particle

1.2 x 10⁵⁷ particles (protons and neutrons)

2) Number of stars in the visible universe: 2.0 x 10¹¹ stars/galaxy x 8.0 x 10¹⁰ galaxies

1.6 x 10²² stars

3) Age of universe in seconds: 1.4 x 10¹⁰ years x 3.156 x 10⁷ seconds/year

4.4 x 10¹⁷ seconds

4) Number of electron orbits in one year: (3.1 x 10⁷ seconds/year) / (2.4 x 10^-24 seconds/orbit)

1.3 x 10³¹ orbits of the electron around the nucleus

5) Energy carried by visible light: (6.6 x 10^-27 ergs/cycle) x 5 x 10¹⁴ cycles

3.3 x 10^-12 ergs

6) Lengthening of Earth day in 1 billion years: (1.0 x 10⁹ years) x 1.5 x 10^-5 sec/year

1.5 x 10⁴ seconds or 4.2 hours longer

7) Tons of TNT needed to make crater 100 km across: 4.0 x 10¹³ x (1.0 x 10¹⁵)/(4.2 x 10¹⁶)

9.5 x 10¹¹ tons of TNT (equals 950,000 hydrogen bombs!)

8) Average density of the Sun: 1.9 x 10³³ grams / 1.4 x 10³³ cm³

1.4 grams/cm³

9) Number of sun-like stars within 300 light years: (2.0 x 10^-3 stars ) x 4.0 x 10⁶ cubic light-yrs

8.0 x 10³ stars like the sun.

10) Density of the Orion Nebula: (3.0 x 10² x 2.0 x 10³³ grams) / (5.4 x 10⁵⁶ cm³ )

1.1 x 10^-21 grams/cm³