Chapter 3.1

3.1 Using and Expressing Measurements

3.2 Units of Measurement

3.3 Solving Conversion Problems

To multiply numbers written in scientific notation, multiply the coefficients and add the exponents.

Example:

To divide numbers written in scientific notation, divide the coefficients and subtract the exponent in the denominator from the exponent in the numerator.

Example:

If you want to add or subtract numbers expressed in scientific notation and you are not using a calculator, then the exponents must be the same.

In other words, the decimal points must be aligned before you add or subtract the numbers.

 $(5.4×10^3)+(8.0×10^2)$  

 $=(5.4×10^3)+(0.80×10^3)$  
 $=(5.4+0.80)×10^3$  
 $=6.2×10^3$  

1. Every nonzero digit in a reported measurement is assumed to be significant.

2. Zeros appearing between nonzero digits are significant.

3. Leftmost zeros appearing in front of nonzero digits are not significant. They act as placeholders. By writing the measurements in scientific notation, you can eliminate such placeholding zeros.

4. Zeros at the end of a number and to the right of a decimal point are always significant.

5.  Zeros at the rightmost end of a measurement that lie to the left of an understood decimal point are not significant if they serve as placeholders to show the magnitude of the number.

6. There are two situations in which numbers have an unlimited number of significant figures. The first involves counting. A number that is counted is exact. (Ex. 23 people in the classroom, 1 hr = 30 min)