### MATH in SCIENCE SKILL: USING SCIENTIFIC NOTATION

Comparing Sizes

Measuring the sizes of very small things like atoms or very large things like planets requires numbers with many places. For example, the diameter of the nucleus of a cell is around 1/100,000 of a meter, while the diameter of Earth is 12,756,000 meters. How can you compare these sizes?

**Example**

**(1)**Express a large number as a number between 1 and 10 multiplied by a power of 10.12,756,000 = 1.2756× 10

^{7}**The exponent is the number of places following the first place.****(2)**Express any number smaller than 1 as a negative power of 10.**The exponent is the number of places following the decimal point.****(3)**Compare −5 and 7 to see that 7 is 12 more than −5.

**ANSWER** Earth's diameter is roughly 10^{12} times bigger than the
diameter of a cell's nucleus.

**Answer the following questions.**

**1.**An oxygen atom measures 60/100,000,000,000 of a meter across. Write the width of the oxygen atom as a decimal number.**2.**Write the width of the oxygen atom in scientific notation.**3.**A chloroplast measures 5 millionths of a meter across. Write its width in standard form and in scientific notation.**4.**A redwood tree stands 100 meters tall. There are 1000 millimeters in a meter. Express the height of the redwood tree in millimeters. Write the number in scientific notation.**5.**A typical plant cell measures 1 millionth of a meter in width. Express the width in standard form and in scientific notation.

**CHALLENGE** The yolk of an ostrich egg is about
8 centimeters in diameter. A full-grown male ostrich itself is
about 2.4 meters tall. Write each of these lengths in the same
unit, and express them in scientific notation. Then tell how
many times taller the ostrich is than the yolk.