exponents and scientific notation
find N so that the number sentence below is true.
23x43= 23x2N =29
what is...
N=6
Let M=993,456,789,098,765. Find the smallest power of 10 that will exceed M.
what is...
993,456,789,098,765<999,999,999,999,999<1,000,000,000,000,000 =1015
ANSWER: 1015
The mass of Earth is 5.9×1024 kg. The mass of Pluto is 13,000,000,000,000,000,000,000 kg. Compared to Pluto, how much greater is Earth’s mass than Pluto’s mass?
HINT: PUT IN EVERYTHING IN SCIENTIFIC FORM AND THEN MINUS THEM.
WHAT IS...
5.887X1024
Write the RATIO that compares the mass of a proton to the mass of an electron.
if the mass of a proton is:0.000000000000000000000000001672622 kg
if the mass of an electron is: 0.000000000000000000000000000000910938291 kg
hint: put them into scientific notation (d x10n) and ratio is (dx10n) : (dx10n)
what is...
ratio:
1.672622 x10-27:9.10938291 x10-31
Compare 9.3×1028 and 9.2879×1028.
HINT: USE STANDARD FORM AND EXPONENTIAL NOTATION
FIND OUT IF THEY ARE GREATER THAN OR LESS THAN
WHAT IS...
93,000>92,879
9.3X1028>9.2879X1028
solve this scientific notation.
(9.3x1010) -(9x1010)
what is...
3x109
Scott said that 0.09 was a bigger number than 0.1. Use powers of 10 to show that he is wrong.
WHAT IS...
0.09 =9/102 =9X10-2
0.1 = 1/101 =1X10-1
THERFORE.0.09 is SMALLER THAN 0.1. becaues 0.09 is closer than 0
The speed of light is 300,000,000 meters per second. The sun is approximately 1.5×1011 meters from Earth. How many seconds does it take for sunlight to reach Earth?
HINT: PUT EVERYTHING IN SCIENTIFIC FORM.
FIGURE OUT IF THE EQUATION IS DIVIDING OR MULTIPLYING
WHAT IS...
5 X 102
The U.S. national debt as of March 23, 2013, rounded to the nearest dollar, is $16,755,133,009,522. According to the 2012 U.S. census, there are about 313,914,040 U.S. citizens. What is each citizen’s approximate share of the debt?
HINT: 1.6755X1013/3.14 X108
PUT THE ANSWER IN STANDARD FORM
WHAT IS...
53360
The Fornax Dwarf galaxy is 4.6×105 light-years away from Earth, while Andromeda I is 2.430×106 light-years away from Earth. Which is closer to Earth?
HINT: HAVE BOTH BE WITH THE SAME 10TH POWER.
USE GREATER THAN OR LESS THAN
WHAT IS...
4.6X105<2.430X106
solve this properties of exponents
621 x 107/ 307
what is...
314 x 221
There are about 100 million smartphones in the U.S. Your teacher has one smartphone. What share of U.S. smartphones does your teacher have? Express your answer using a negative power of 10.
HINT: ONLY NEED TO FIND THE NEGATIVE POWER OF 10, USING THE EXPONENT NOTATION WAY
WHAT IS...
1/ 100,000,000 =1/108 =10-8
The mass of the moon is about 7.3×1022 kg. It would take approximately 26,000,000 moons to equal the mass of the sun. Determine the mass of the sun.
HINT: PUT EVERYTHING IN SCIENTIFIC FORM.
FIGURE OUT IF THE EQUATION IS DIVIDING OR MULTIPLYING
WHAT IS...
1.898X1030
The geographic area of California is 163,696 sq. mi., and the geographic area of the U.S. is 3,794,101 sq. mi. Let’s round off these figures to 1.637×105 and 3.794×106. In terms of area, roughly estimate how many Californias would make up one U.S. Then compute the answer to the nearest ones.
HINT: ANSWER SHOULD BE IN STANDARD FORM.
FIGURE OUT IF THE EQUATION IS DIVIDING, MULTIPLYING, ADDING, OR SUBTRACTING
what is...
23.18
The wavelength of the color red is about 6.5×10-9 m. The wavelength of the color blue is about 4.75×10-9 m. Show that the wavelength of red is longer than the wavelength of blue.
WHAT IS...
6.5X10-9>4.75X10-9
OR
4.75X10-9< 6.5 X10-9
solve this scientific notation
(1.2x104)+(2x104)+(2.8x104)/3
what is...
2x104
2PART ANSWERS
HINT: ITS EASIER TO PUT IN SCIENTIFIC FORM
(1/2)The average person takes about 30,000 breaths per day. Express this number as a single-digit integer times a power of 10.
(2/2)If the average American lives about 80 years (or about 30,000 days). HOW many total breaths will a person take in her lifetime?
WHAT IS...
PART 1 ANSWER: 30,000=3X104
PART 2 ANSWER: (3X104) X (3X104)=9 X108
On average, Mercury is about 57,000,000 km from the sun, whereas Neptune is about 4.5×109 km from the sun. What is the difference between Mercury’s and Neptune’s distances from the sun?
HINT: PUT EVERYTHING IN SCIENTIFIC FORM.
FIGURE OUT IF THE EQUATION IS DIVIDING, MULTIPLYING, ADDING, OR SUBTRACTING
WHAT IS...
4.443 X 109
Compute how many times heavier a proton is than an electron (i.e., find the value of the ratio). Round your final answer to the nearest WHOLE NUMBER.
WHEN... PROTON IS 0.000000000000000000000000001672622
WHEN... ELECTRON IS 0.000000000000000000000000000000910938291
HINT: ANSWER SHOULD BE IN STANDARD FORM.
FIGURE OUT IF THE EQUATION IS DIVIDING, MULTIPLYING, ADDING, OR SUBTRACTING
WHAT IS...
1836
The average lifetime of the Z boson is approximately 3×10-25 seconds, and the average lifetime of a neutral rho meson is approximately 4.5×10-24 seconds.
PART 1: Without using the theorem from today’s lesson, explain why the neutral rho meson has a longer average lifetime.
HINT: GREATER THAN OR LESS THAN
PART 2: Approximately how much longer is the lifetime of a neutral rho meson than a Z boson?
WHAT IS...
PART 1 ANSWER: 3X10-25< 4.5X10-24
PART 2 ANSWER: 45:3 OR 15 TIME LONGER
prove to see if this equation is correct?
hint: if they are equal or not equal
(63m x 10m)/30m =23m x32m
what is... they are equal.
(INFORMATION): The number of users of social media has increased significantly since the year 2001. In fact, the approximate number of users has tripled each year. It was reported that in 2005 there were 3 million users of social media.
PROBLEM: assuming that the number of users continues to triple each year, for the next three years, determine the number of users in 2006,2007,2008.
HINT: READ THE QUESTION CAREFULLY!!!!!!
WHAT IS...
2006- 9 MILLION
2007- 27 MILLION
2008- 81 MILLION
The mass of Earth is approximately 5.9×1024 kg, and the mass of Venus is approximately 4.9×1024 kg.
PART 1:Find their combined mass.
PART2: Given that the mass of the sun is approximately 1.9×1030 kg. How many Venuses and Earths would it take to equal the mass of the sun?
HINT FOR PART 2:USE THE ANSWER FROM PART 1 TO FIND THE ANSWER.
FIGURE OUT IF THE EQUATION IS DIVIDING OR MULTIPLYING
WHAT IS...
PART 1 ANSWER: 1.08X1025
PART 2 ANSWER:1.8 X 105
The average distance from Earth to the moon is about 3.84×105 km, and the distance from Earth to Mars is approximately 9.24×107 km in year 2014. On this simplistic level, how much farther is traveling from Earth to Mars than from Earth to the moon?
HINT: ANSWER SHOULD BE IN STANDARD FORM
WHAT IS...
92,016,000
3-PART ANSWER!!!!!!
Let’s compare the population of New York City to the population of New York State. Specifically, let’s find out how many times greater the population of New York State is compared to that of New York City.
(1/3) The population of New York City is 8,336,697. Let’s round this number to the nearest million; this gives us 8,000,000. Written as single-digit integer times a power of 10:
(2/3)The population of New York State is 19,570,261. Rounding to the nearest million gives us 20,000,000. Written as a single-digit integer times a power of 10:
(3/3) CAMPARING THE TWO POPULATIONS
WHAT IS...
PART 1:NEW YORK CITY
8,000,000=8X106
PART 2: NEW YORK STATE
20,000,000=2X107
PART 3: COMPARING..
8X106/2X107= 0.25X101 OR 2.5