Download Scientific Notation

Scientific Notation
When you are given a number in scientific notation it will always be the number
times 10 raised to an exponent
This is to help write big numbers in an easier to read way!
A. When converting from scientific notation to standard form (the whole entire
number) you will:
-move the decimal point to the right if the exponent is positive:
Ex. 3.25 x 102 = 325 (moved the decimal to the right 2 places since the
exponent was a positive 2)
Ex. 3.6 x 105 = 360000 (moved the decimal to the right 5 places since the
exponent was a positive 5) ***notice since there weren’t any other whole
numbers after the 6 I added zeroes for each additional place the decimal
was moved
-move the decimal point to the left if the exponent is negative:
Ex. 4.36-2 = .0436 (moved the decimal to the left 2 places since the
exponent was a negative 2) ***notice since there was only one whole
number to the left of the decimal, I added a zero for the additional place
the decimal was moved.
Ex. 5.346-4 = .0005346
B. When converting from standard form to scientific notation you will:
- move the decimal point to the left if it is a whole number until the decimal is
behind the first digit.
Ex. 436 = 4.36 x 102 (moved the decimal point to the left behind the 4
then said that it would be times 10 to the 2nd because I moved the decimal
2 places to the left)
***It is a positive power because you started with a whole number
Ex. 5079 = 5.079 x 103
- move the decimal point to the right if it is a decimal (# less than 1) to start
with until it is behind the first number other than zero.
Ex. .00217 = 2.17 x 10-3 (moved the decimal point to the right behind the 2
then said it would be times 10 to the -3 because I moved the decimal 3
places)
*****It is negative because you started with a decimal (# less than 1)
Ex. .0000893 = 8.93 x 10-5
NAME ________________________________________ DATE ______________ PERIOD
Practice: Skills
Scientific Notation
Write each number in standard form.
1. 6.7 x 101
2. 1.6 x 103
3. 2.91 x 105
4. 3.35 x 10-1
5. 1.49 x 10-7
6. 5.2277 x 10-3
7. 3.46 x 102
8. 8.651 x 107
9. 7.3 x 10-6
11. 4.0027 x 10-4
12. 8.50284 x 10-2
Write each number in scientific notation.
13. 34
14. 79,700
15. 4,733,800
16. 0.00916
17. 0.00000571
18. 0.0121
19. 273
20. 6,590
21. 2,204,000,000
22. 0.29
23. 0.0008331
24. 0.00000018
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Practice: Word Problems
Scientific Notation
1. MEASUREMENT There are about 25.4 millimeters in one
inch. Write this number in scientific notation.
2. POPULATION In the year 2000, the population of Rahway,
New Jersey, was 26,500. Write this number in scientific notation.
3. MEASUREMENT There are 5,280 feet in one mile. Write this
number in scientific notation.
4. PHYSICS The speed of light is about 1.86 x 105 miles per
second. Write this number in standard notation.
5. COMPUTERS A CD can store about 650,000,000 bytes of
data. Write this number in scientific notation.
6. SPACE The diameter of the Sun is about 1.39 x 109 meters.
Write this number in standard notation.
7. ECONOMICS The U.S. Gross Domestic Product in the year
2000 was 9.87 x 1012 dollars. Write this number in standard
notation.
8. MASS The mass of planet Earth is about 5.98 x 1024 kilograms.
Write this number in standard notation.