Converting units of measure - prefixes

When we put prefixes in a line from large to small we get something like this

Mega     kilo      hecto      deca     BASIC    deci    centi    milli    micro    nano

(M)      (k)          (h)         (da)      UNIT       (d)       (c)      (m)      (µ)         (n)

1,000,000    1,000             100                  10                  1                   .1             .01           .001        .000001     .000000001

106       103       102           101         100         10-1     10-2     10-3      10-6       10-9

To do a conversion all you need is an equality.  Here’s a few examples of how to:

1.   5250 m (meters) = how many km (kilometers)?

a.  The equality needed is:

1 km  =  1000 m

b.  Now use the equality as a fraction in a grid:

 5250 m 1 km Ans 5.25 km 1 1,000 m

2.  346 hL (hectoliters) = how many µL (microliter)

a.                        1 hL =  100 L     and   1 µL  =  10-6 L

(Notice in the equalities we substituted 100 for h, and 10-6 for µ .)

b.      Now we use these equalities in our grid:

 346 hL 100 L 1 µL =  34,600 µL = 3.46 x 1010 µL 1 1 hL 10-6 L =    10-6

3.  489 mg = how many kg ?

a.       1 mg =  10-3 g   and   1 kg  =  1 x 103 g

b.      now we use both equalities in our grid:

 489 mg 1 x  10-3 g 1 kg =  489 x 10-3 kg =  489 x 10-6 kg 1 1 mg 1 x 103 g =  1 x 103

In scientific notation this would be   =     4.89 x 10-6 kg