the step method generally only covers the prefixes kilo- to milli-. what happens if you have mega...

Converting Metric UnitsUsing exponents

Why use exponents?

The step method generally only covers the prefixes kilo- to milli-.

What happens if you have Mega (106)???????

Exponent Rules

xmxn = xm+n

› x2x3 = x2+3 = x5

xm/xn = xm-n

› x6/x2 = x6-2 = x4

(xm)n = xmn

› (x2)3 = x2×3 = x6

(xy)n = xnyn

› (xy)3 = x3y3

Metric Conversions

You must change from the prefix to the base, then to the new prefix.

Example:› 3 mL to DL?

In this problem, you will have to change milliliters to liters to Decaliters.

3 mL to DL?

3 mL 10-3 L 1 DL

1mL 101 L

Clean up the exponents!

We have 3 x 10-3 in the numerator.We have 1 x 101 in the denominator.

xm/xn = xm-n

This exponent rule makes unit conversion very easy!

10(-3-1)

10-4

3 x 10-4 DL

Metric Conversion Power of 10 method

Exponent value must be known for each prefix.

To convert subtract exponents from the measurements prefix.

WHAT??????

Converting these units always has two steps:› 1. Change to the base› 2. Change to the new prefix

When we change to the base, the second exponent will always be in the denominator!

To bring it to the numerator, we move it up. When it is moved up, it changes sign.

Examples

1/n5 = 1 x (n-5)

103/107 = 10(3-7) = 10-4

To solve these problems, get the value of the prefixes, then subtract them!

The bases are multiplied or divided like always!