Signifigant Figures and Scientific Notation

Scientific Notation

• scientists use a short hand method to express very large or very small numbers

• made up of a coeffecient (greater than 1, less than 10) and a base (10 to the power of x)

Steps of scientific notation, using 300 000 000:

Step 1. Put the decimal directly after the first number and drop all of the zeros that remain after our 3 significant figures

3.00

Step 2. Count how many places we moved the decimal to get to the number

Our base is 10 to the power of 8

Step 3. Put the coefficient and base together

3.00 × 10 (8) m/s

Now, with a very small number:

0.000 000 000 000 753g

7.53 × 10 ( -13) g

Significant figure rules:

1. All non zero numbers are significant

   • 143.257 has 6 sigfigs

2. All zeros between non zeros are significant

   • 3408 and 1.205 both have 4 sigfigs

3. All leading zeros are not significant, they just set the decimal place

   • 0.00004 has 1 sigfig

4. All trailing zeros after the decimal are significant

   • 4.20 has three sigfigs

5. All trailing zeros before a decimal are significant. Trailing zeros in a number may be signficiant if the number does not contain a decimal

   • 100. has 3 sigfigs. 100 has 1, 2, or 3 sigfigs.

Addition and subtraction: round the number to the least number of decimal places

Multipacation and division: round the number to the least number of significant figures