Exercise 36 Page 342

We want to use the given table to calculate how many micrometers are in a meter.

Unit of Length	Length (meter)
Decimeter	10^(- 1)
Centimeter	10^(- 2)
Millimeter	10^(- 3)
Micrometer	10^(- 6)
Nanometer	10^(- 9)

All the given units of length are expressed in terms of meters. Next, we will calculate the ratio of meters to micrometers. It divides a meter into parts with the length of one micrometer. The result is the number of micrometers in a meter.

1meter/1micrometer = 1 meter/10^(- 6) meters In the denominator we have a power with a negative exponent. We will use the Negative Exponent Property to simplify it,.

Negative Exponents

For any integer n and any nonzero number a, a^(- n) is the reciprocal of a^n.

Let's apply this property to our quotient! Notice that we can forget about units for a moment for simplicity.

1/10^(- 6)

NegExponentToFrac

a^(- m)=1/a^m

1/1/10^6

DivByFracD

a/b/c= a * c/b

1 * 10^6/1

Finally, we can simplify the expression and calculate the power.

1 * 10^6/1

IdPropMult

Identity Property of Multiplication

10^6/1

DivByOne

a/1=a

10^6

CalcPow

Calculate power

1 000 000

We found that there are 1 000 000 micrometers in a meter.