3.1. Units of Measurement http://www.ck12.org
FIGURE 3.2
The Sun is very large and very distant, so solar data is better expressed in
scientific notation. The mass of the Sun is 2.0× 1030 kg and its diameter
is 1.4× 109 m.Very small numbers can also be expressed using scientific notation. The mass of an electron in decimal notation
is 0.000000000000000000000000000911 grams. In scientific notation, the mass is expressed as 9.11× 10 −^28 g.
Notice that the value of the exponent is chosen so that the coefficient is between 1 and 10.
Example 3.4
A common mosquito weights approximately 0.0000025 kg. Write the mosquito’s weight in scientific notation.
In scientific notation we will write this quantity as a coefficient multiplied by 10 raised to some power.
Step 1: Our coefficient must be a number between 1 and 10. From 0.0000025 kg, we determine the coefficient to be
2.5.
Step 2: The quantity 0.0000025 kg is less than 1, so 10 must be raised to a negative exponent. The decimal place
must be moved to the right by 6 places to write the coefficient 2.5, so we will write 10−^6 as our power of 10
Step 3: Coefficient + Power of 10. This gives us 2.5× 10 −^6 kg. Remember, our units in this case have not changed,
we are just changing the way we are writing the numerical value.
Adding and Subtracting
There are times when we will want to add or subtract numbers that are expressed in scientific notation. We will
approach such calculations in one of two ways.
Same Base Units
Example 3.5
- 235 × 103 meters+ 3. 45 × 102 meters
Step 1: Convert numbers to regular notation.
1235 meters+345 meters
Step 2: Add.
1235 meters
+345 meters
1580 metersStep 3: Convert back to scientific notation (depending on the result, this is not always necessary).
- 580 × 103 m
We would follow the same steps for subtraction, as well as for numbers with negative exponents.