var index1=Math.round(Math.random()*(4-1))+1; var question1=new Array(5); var truevalue1=new Array(5); var closevalue1=new Array(5); var exp1=new Array(5); question1[0]='

12.2 cm to m = mm

'; truevalue1[0]='0.122'; closevalue1[0]='.122'; question1[1]='

12.2 cm to m = mm

'; truevalue1[1]='0.122'; closevalue1[1]='.122'; question1[2]='

17.0 m to mm = x 10

mm

'; truevalue1[2]='1.70'; closevalue1[2]='1.7'; exp1[2]='4'; question1[3]='

18.0 dm to nm = x 10

nm

'; truevalue1[3]='1.8'; closevalue1[3]='1.80'; exp1[3]='9'; question1[4]='

3.10 x 10⁶ µm to cm = x 10

cm

'; truevalue1[4]='3.10'; closevalue1[4]='3.1'; exp1[4]='2'; question1[5]='

34.8 nm to µm = x 10

µm

'; truevalue1[5]='3.48'; closevalue1[5]='3.48'; exp1[5]='-2'; window.document.write('

Metric-Metric Conversions

A. General Conversion Method:
When you first determine a math problem involves the conversion of one unit to another, you may find it useful to use the following general approach.

Decide on the sequence of conversions and write down the path.
Write the starting term, along with units, and all the conversion factors that follow.
Make sure that the units cancel properly.
Calculate the answer.
Determine if the answer is reasonable by estimating the answer (if possible).

Let´s try carrying out some conversions of length, volume, and mass.

'); window.document.write('

B. Length Conversions:
Let´s start with a one step conversion. Convert 71 km to m.

This conversion can be accomplished in one step. The initial requirement is that we know that:

1 km = 10³ m

Now we write down the starting term, and then the conversion factor. Don´t forget to include all the units.

	10³ m
71 km x
	1 km

Notice that the units of km cancel out, leaving the desired unit of meters.

	10³ m
71 km x
	1 km

Now multiply the two numbers, and then convert the answer to scientific notation.

71 x 10³ m = 7.1 x 10⁴ m

Is the answer reasonable? Since a kilometer is large compared to a meter, if kilometers are converted to meters, we would expect a larger number to result.

If neither of the units in the problem are the basic unit (meter), then several steps are required. In general the starting unit should be converted to the basic unit, and then the basic unit may be converted to the desired unit. Here´s an example. Convert 477 nm to mm.

The sequence of conversions would be:

	1 m		10³ mm
477 nm x		x
	10⁹ nm		1 m

The units now cancel out to give only the desired unit of millimeters.

	1 m		10³ mm
477 nm x		x
	10⁹ nm		1 m

Multiply the numbers, and then convert the answer to scientific notation.

477 x 10^-6 mm = 4.77 x 10^-4 mm

Try the following conversions among different length units.

' + question1[index1]); var index2=Math.round(Math.random()*(4-1))+1; var question2=new Array(5); var truevalue2=new Array(5); var exp2=new Array(5); question2[0]='

1,470,000 mL to L = x 10

L

'; truevalue2[0]='1.47'; exp2[0]='3'; question2[1]='

1,470,000 mL to L = x 10

L

'; truevalue2[1]='1.47'; exp2[1]='3'; question2[2]='

8.71 µL to L = x 10

L

'; truevalue2[2]='8.71'; exp2[2]='-6'; question2[3]='

34.8 mL to µL = x 10

µL

'; truevalue2[3]='3.48'; exp2[3]='4'; question2[4]='

1.29 x 10⁸ nL to mL = x 10

mL

'; truevalue2[4]='1.29'; exp2[4]='2'; question2[5]='

893 mL to µL = x 10

µL

'; truevalue2[5]='8.93'; exp2[5]='5'; window.document.write('

C. Volume Conversions:
As with the conversions of the units of length, if the basic unit is not present in the problem, you will have to use several conversion factors. Convert the starting unit to the basic unit, and then convert the basic unit to the desired unit. Let´s try the following example. Convert 50 µL to mL.

The sequence of conversions would be:

	1 L		10³ mL
50 µL x		x
	10⁶ µL		1 L

The units now cancel out to give only the desired unit of milliliters.

	1 L		10³ mL
50 µL x		x
	10⁶ µL		1 L

Multiply the numbers, and then convert the answer to scientific notation.

50 x 10^-3 µL = 5 x 10^-2 mL

The answer could also be expressed in decimal form as 0.05 mL.

Try another conversion using different volume units.

' + question2[index2]); var index3=Math.round(Math.random()*(4-1))+1; var question3=new Array(5); var truevalue3=new Array(5); var exp3=new Array(5); question3[0]='

57.8 kg to g = x 10

g

'; truevalue3[0]='5.78'; exp3[0]='4'; question3[1]='

57.8 kg to g = x 10

g

'; truevalue3[1]='5.78'; exp3[1]='4'; question3[2]='

8,750 ng to g = x 10

g

'; truevalue3[2]='8.75'; exp3[2]='-6'; question3[3]='

1.67 x 10⁵ kg to mg = x 10

mg

'; truevalue3[3]='1.67'; exp3[3]='11'; question3[4]='

8.89 x 10⁹ µg to mg = x 10

mg

'; truevalue3[4]='8.89'; exp3[4]='6'; question3[5]='

936 cg to mg = x 10

mg

'; truevalue3[5]='9.36'; exp3[5]='3'; window.document.write('

D. Mass Conversions:
The conversion of one mass unit to another follows the same procedure that we looked at in the discussion of length and volume conversions. Let´s try the following example. Convert 15,900 mg to kg.

The sequence of conversions would be:
1 g 1 kg
15,900 mg x
x
10³ mg 10³ g

The units now cancel out to give only the desired unit of kilograms.

	1 g		1 kg
15,900 mg x		x
	10³ mg		10³ g

Multiply the numbers, and then convert the answer to scientific notation.

15,900 x 10^-6 kg = 1.59 x 10^-2 kg

Try another conversion using different mass units.

' + question3[index3]); 3]);