Convert Each of the Following Values to Scientific Notation: a) 29,500 b) 0.000082 c) 650,000,000 d) 0.0100

To convert numbers into scientific notation, we follow a specific format: a number between 1 and 10 multiplied by a power of ten. Let’s break down each of the given values:

1. a) 29,500
   We express 29,500 as 2.95 × 10⁴. We move the decimal point four places to the left to get a number between 1 and 10 and count how many places we moved it, which indicates the exponent of ten.
2. b) 0.000082
   For this value, we write it as 8.2 × 10⁻⁵. We moved the decimal point five places to the right, resulting in a negative exponent.
3. c) 650,000,000
   This number is converted to 6.5 × 10⁸. We shift the decimal point eight places to the left to obtain the number between 1 and 10.
4. d) 0.0100
   Finally, 0.0100 is expressed as 1.00 × 10⁻². We move the decimal point two places to the right to get a valid scientific notation.

In summary, the scientific notations are:

• a) 29,500 = 2.95 × 10⁴
• b) 0.000082 = 8.2 × 10⁻⁵
• c) 650,000,000 = 6.5 × 10⁸
• d) 0.0100 = 1.00 × 10⁻²