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SCIENTIFIC NOTATION

its an abreviation to write down numbers that are really big or really small

steps of the process

1. where the decimal place would be?

2. move it and count number of spots until one digit to the left of the decimal place

3. write the short version of the big or small number and then add "x10^13"

rules

1. All non-zero numbers ARE significant.

2. Zeros between two non-zero digits ARE significant.

3. Leading zeros are NOT significant.

4. Trailing zeros to the right of the decimal ARE significant.

5. Trailing zeros in a whole number with the decimal shown ARE significant.

6. Trailing zeros in a whole number with no decimal shown are NOT significant.

7. Exact numbers have an INFINITE number of significant figures.

8. For a number in scientific notation: N x 10x, all digits comprising N ARE significant by the first 6 rules; "10" and "x" are NOT significant.

examples

25,300,000,000,000 miles

<--- 13 spots

2.53 x 10^13 miles

0.000,000,02.03 seconds

--->8 spots

2.03 x 10^-8 seconds

where would the decimal point be? at the end of the last 0

move the decimal point until you have only one digit left

2.

7.921x10^8 =792,100,000

4.13x10^3 = 4,130

8.2x 10^-5 = 0.000 082

5.2216x10^-9= 0.000 000 005 221

3.

0.004 4x10^-3

0.000000000000000123 =1.23x10^-16

452,000,000,000,000 =4.52x10^-14

698.25400000000000000 = 6.9824x10^2

-3.28 x 10 to the 8= 328000000

4.

0.866=8.66x10^-1

-5.41x10^0=-5.41

-47.9=4.79x10^1

5.17x10^8= 517000000

-667000000= -6.67x10^8

5.

6.91x10^-1= 0.691

1.91x10^3= 1910

978= 9.78x10^2

4.18x10^0=4.18

175000000=1.75x10^8

93000= 9.3x10^4

-98700= 9.87x10^4

4.12x10^-4= -0.000412

3.92x10^8= 392000000