http://www.ck12.org Chapter 3. Logs and Exponents
- First convert each number to scientific notation individually, then process the exponent and multiplication.
2 , 000 , 0003 · 3 , 0004 = ( 2 · 106 )^3 ·( 3 · 103 )^4
= 8 · 1018 · 81 · 1012
= 648 · 1030
= 6. 48 · 1032
- Resolve in order of standard order of operations
( 4. 713 · 107 )+( 8. 985 · 105 )−( 4. 987 · 102 )·( 7. 3 · 10 −^6 )÷( 6. 74 · 10 −^9 )
= ( 4. 713 · 107 )+( 8. 985 · 105 )−( 5. 40135 · 105 )
= ( 471. 3 · 105 )+( 8. 985 · 105 )−( 5. 40135 · 105 )
= 474. 8836499 · 105
= 4. 748836499 · 107
Practice
Write the following numbers in scientific notation.
- 152,780
- 0.00003256
- 56, 320
- 0.0821
- 1, 000, 000, 000, 000, 000, 000, 000
- 7.32
- If the federal budget is $1.5 trillion, how much does it cost each individual, on average, if there are 300,000,000
people? - The Library of Congress has about 60,000,000 items. How could you express this number in scientific notation?
- The sun develops 5× 1023 horsepower per second. How much horsepower is developed in a day? In a year with
365 days? - A light-year is about 5,869,713,600 miles. A spacecraft travels 8. 23 × 104 miles per hour. How long will it
take the spacecraft to travel a light–year? - Compute the following number and use scientific notation: 324, 000 · 30 , 0003.
- Compute the following number and use scientific notation: 14, 300 · 20 , 2002.
Simplify the following expressions.
13.( 3. 29 · 104 )−( 3. 295 · 105 )+( 1. 25 · 102 )·( 3. 97 · 1015 )·( 5. 8 · 10 −^6 )
14.( 1. 95 · 102 )+( 6. 798 · 106 )+( 2. 896 · 103 )·( 5. 6 · 10 −^3 )÷( 2. 89 · 104 )
15.( 2. 158 · 107 )·( 1. 679 · 106 )−( 9. 98 · 104 )·( 3. 4 · 10 −^2 )