Exercise 19 Page 417

Practice makes perfect

a To write one hundredth and one micron in standard form, let's begin by writing one hundredth as a fraction.

\frac{1}{1 0 0}

FracToDiv

$\frac{a}{b} = a \div b$

0.01

Let's do the same for one micron.

\frac{1}{1 0 0 0 0 0 0}

FracToDiv

$\frac{a}{b} = a \div b$

0.000001

In standard form one hundredth is

0.01,

and one micron is

0.000001 .

b Let's review the steps of going from standard form to scientific notation.

Move the decimal to the right of the first nonzero digit. This results in a real number $a .$
Note the number of places $n$ and the direction that you moved the decimal point.
If the decimal point is moved left, write the number as $a \times 1 0^{n} .$ If the decimal point is moved right, write the number as $a \times 1 0^{- n} .$
Remove any unnecessary zeros.

To write one hundredth and one micron in scientific notation, let's reference the standard form written in Part A.

0.01 & 0.000001

Now we can follow the steps. Let's begin with one hundredth.

Step	Work	Result
$1$		$a = 001$
$2$	The decimal point moved $2$ places to the right.	$n = 2$
$3$	Since the decimal moved to the right, we will write it as $a \times 1 0^{- n} .$	$001 \times 1 0^{- 2}$
$4$	Remove the unnecessary zeros.	$1 \times 1 0^{- 2}$

Let's continue with one micron. $0.000001$

Step	Work	Result
$1$		$a = 000001$
$2$	The decimal point moved $6$ places to the right.	$n = 6$
$3$	Since the decimal moved to the right, we will write it as $a \times 1 0^{- n} .$	$00000001 \times 1 0^{- 6}$
$4$	Remove the unnecessary zeros.	$1 \times 1 0^{- 6}$

So one hundredth written in scientific notation is $1 \times 1 0^{- 2}$ and one micron is $1 \times 1 0^{- 6} .$

c The smallest size particle that the filter will stop is one hundredth of a micron. We can get the standard form by multiplying their standard form equivalent. Then we will do the same for the scientific version.