Scientific notation:
Is a format: a number is expressed as a number between 1 and
10 multiplied by a power of 10: 5.3
* 107
· Convert to ordinary notation:
1.5 * 109
7.06 * 10-2
· Convert to scientific notation:
52,000
0.00038
· Calculate (no calculator) and round to 2 decimal places:
9 * 102 + 1.5 * 103
· By how much do they differ? (as a power of 10)
1 billion, 1 thousandth
· Rewrite in scientific notation:
Corporate profits in the US in 1996 were 632 billion dollars.
· Approximate with scientific notation, estimate without calculator and then check with calculator:
-12.5 * 11,890
An order of magnitude estimate specifies only a broad range of values (in the thousands, in the millions)
· The numbers of breaths you take each week.
· Amount you spend on food in a year.
· Using Adefovir the number of Hepatitis B viruses decreases by an order of magnitude of 3 in the blood of the patient. If the patient has a count of 1.8*106 per milliliter. How many viruses does he have after the Adefovir per milliliter?
Understanding big numbers:
· There are approximately 132 million births worldwide in a year. Express this quantity in births per minute.
· How many average candy bars would you have to eat to supply the energy needed for 4 hours of running?
1 candy bar releases 1*106 joule
1 hr running requires 4*106 joule
· How many kg of uranium would be required to supply the energy needs of the US for 1 year?
US annual energy consumption 1* 1020 joule
1 kg uranium 235 releases (fission) 5.6* 1013 joule
Scale ratio:
1 cm on the map represents 1 km on the ground.
1 km = 1000 m = 100,000 cm.
So the scale ratio is: 1 : 100,000
· You are constructing a model of the solar system. Scale down by 1 billion : 1.
Planet radius distance from the sun
Mercury 4880 km 57.9 million km
Pluto 2260 km 5900 million km
· A few billion years from now, after exhausting its nuclear engines, the sun will become a type of remnant star called a white dwarf. It will still have nearly the same mass (2 * 1030 kg) as the sun today, but its radius will be only about that of the earth(6366km).
a) Calculate the density in kg/cm3. (Sphere volume = 4/3 * pi * radius3 )
b) A neutron star is a stellar remnant compressed to even greater density. Suppose that a neutron star has a mass 1.4 times the mass of the sun but a radius of only 10 km.
What is the density?
Compare the mass of 1 cm3 of neutron star material to the total mass of Mt Everest (5 * 1010 kg)