Problems #11 - 25

Special note on a particular conversion not mentioned above.

Metric conversions where two units (numerator and denominator) are converted

**Problem #11:** Convert 2.1 Å to nanometers

**Solution:**

1) Often, a two-step method is used. In the first step, the unit given in the problem is converted to the base unit. In this problem, the base unit is meters. Convert Å to meter:

1 Å = 10¯^{8}cm (by definition)

1 cm 1 Å x ––––––– = 10¯ ^{8}cm10 ^{8}Å

1 m 10¯ ^{8}cmx ––––––– = 10¯ ^{10}m100 cm 1 Å = 10¯

^{10}m

2) In the second step, you convert from the base unit to the target unit. Convert from 2.1 x 10¯^{10} m to nanometers:

(2.1 x 10¯^{10}m) (10^{9}nm / 1 m) = 0.21 nm

3) Make sure to remember that the base unit is the unit __without__ a prefix. Examples of base units include m, s, L, and g.

**Problem #12:** Convert 0.0030 mm to nm

**Solution:**

There are 10^{6}nanometers in one millimeter.

10 ^{6}nm3.0 x 10¯ ^{3}mmx ––––––– = 3.0 x 10 ^{3}nm1 mm If we were to convert to the base unit first, it would look like this:

1 m 10 ^{9}nm3.0 x 10¯ ^{3}mmx ––––––– x ––––––– = 3.0 x 10 ^{3}nm10 ^{3}mm1 m The first conversion is millimeters to meters and the second is meters to nanometers.

**Problem #13:** Convert 6.25 x 10¯^{4} s to ms

**Solution:**

10 ^{3}ms6.25 x 10¯ ^{4}sx ––––––– = 0.625 ms 1 s Notice that this is a conversion starting from a base unit.

**Problem #14:** Convert 38.0 centiliters to kiloliters.

**Solution:**

1 kL 38.0 cL x ––––––– = 3.80 x 10¯ ^{4}kL10 ^{5}cLkilo- is 10

^{3}and centi- is 10¯^{2}. The absolute exponential distance between them is 10^{5}.You could also convert the cL to the base unit of L first, then convert L to kL.

**Problem #15:** How many Mg are there in 100,000,000 mg?

**Solution:**

I will do this conversion in two steps: (a) convert mg to g, then (b) convert g to Mg.

1 g 1 x 10 ^{8}mgx ––––––– = 1 x 10 ^{5}g10 ^{3}mg

1 Mg 1 x 10 ^{5}gx ––––––– = 0.1 Mg 10 ^{6}g

**Problem #16:** Convert 0.050 kg to mg.

**Solution:**

First conversion is kg to g and the second is g to mg.

10 ^{3}g10 ^{3}mg0.050 kg x ––––––– x ––––––– = 5.0 x 10 ^{4}mg1 kg 1 g

**Problem #17:** Convert 722 μg to mg.

**Solution:**

1) A direct micro- to milli- conversion:

722 μg times (1 mg / 1000 μg) = 0.722 mg

2) Here's the two-step conversion. The first conversion is micrograms to grams, followed by grams being converted to milligrams.

1 g 10 ^{3}mg722 μg x ––––––– x ––––––– = 0.722 mg 10 ^{6}μg1 g

**Problem #18:** How many pg in a ng?

**Solution:**

1 ng times (1000 pg / 1 ng) = 1000 pgRemember, nano- means 10¯

^{9}and pico- means 10¯^{12}. There are 1000 of the smaller thing (pico-) in one of the larger thing (nano-).

**Problem #19:** How many mm in a km?

**Solution:**

1) Two-step (going through the base unit):

10 ^{3}m10 ^{3}mm1 km x ––––––– x ––––––– = 1 x 10 ^{6}mm1 km 1 m

2) One-step, using the total exponential distance from kilo- to mlli-:

10 ^{6}mm1 km x ––––––– = 1 x 10 ^{6}mm1 km

3) One step, done in the sty;e oft-seen on the Internet:

1 km times (10^{6}mm / 1 km) = 1 x 10^{6}mm

**Problem #20:** How many km in a mm?

**Solution:**

1) Two-step (going through the base unit of m):

1 m 1 km 1 mm x ––––––– x ––––––– = 1 x 10¯ ^{6}km10 ^{3}mm10 ^{3}m

2) One-step, using the total exponential distance from kilo- to mlli-:

1 km 1 mm x ––––––– = 1 x 10¯ ^{6}km10 ^{6}mm

**Problem #21:** Convert 3000 mL to daL.

**Solution:**

1) milli- means 10¯^{3} and deca- means 10^{1}. That gives an absolute exponential distance of 4, therefore:

3000 mL times (1 daL / 10^{4}mL) = 0.3 daL

2) Done as a two-step through the base unit of L:

1 L 1 daL 3000 mL x ––––––– x ––––––– = 0.3 daL 10 ^{3}mL10 L In the first conversion, L is the larger of the units (so the 1 goes with it), but in the second conversion, L is the smaller of the two units (so the 1 goes with daL).

**Problem #22:** Consider this problem:

____ cm = ____ m

Fill in the blanks by placing numerical values in front of the m and the cm.

**Solution #1:**

1) Let us decide to put a 1 in front of the meter. The problem then becomes this:

____ cm = 1 m

2) In words, the problem becomes:

How many cm are in 1 meter?

3) To answer the question, think back to this definition:

centi- means hundredththerefore:

centimeter means a hundredth of a meter

4) How many centimeters in one meter?

Since one centimeter is 1/100th of a meter, you need 100 centimeters to make 1 meter.

5) The answer to the fill-in question is:

100 cm = 1 m

**Solution #2:**

1) Let us decide to put a 1 in front of the centimeter. The problem then becomes this:

1 cm = ____ m

2) In words, the problem becomes:

How many meters are in 1 cm?

3) To answer the question, think back to this definition:

centi- means hundredththerefore:

centimeter means a hundredth of a meter

4) How many meters in one centimeter?

Since one centimeter is 1/100th of a meter, you need 1/100th of a meter to make 1 centimeter.

5) The answer to the fill-in question is:

1 cm = 0.01 m

**Problem #23:** Convert 0.005 kg to dag

**Solution:**

kilo- means 10^{3}and da- means 10^{1}, so there is a 10^{2}absolute difference between the two.0.005 kg x (___ dg / ___ kg) <--- this is done so as to allow the kg to cancel and put the dag in the numerator, which is where we want it

0.005 kg x (___ dg / 1 kg) <--- I teach a method that ALWAYS puts a 1 in front of the larger unit, so you have to know that kilo is bigger than deca

0.005 kg x (10

^{2}dg / 1 kg) <--- the two factors are now in place and it reads this way: there are 10^{2}dag in one kg0.5 dag is the answer.

**Problem #24:** Convert 35 mL to dL

**Solution:**

1) Set up the conversion with units in place:

35 mL x (___ dL / ___ mL)milli = 10¯

^{3}and deci- = 10¯^{1}, so there is 10^{2}in absolute exponential distance between the two units.

2) deci- is bigger than milli-. Therefore, the 1 is placed with the dL:

35 mL x (1 dL / ___ mL)

3) There is 10^{2} in absolute exponential distance:

35 mL x (1 dL / 10^{2}mL) = 0.35 dL

**Problem #25:** Convert 6.31 Ms to hs

**Solution:**

Done as a two-step conversion through the base unit of s:

10 ^{6}s1 hs 6.31 Ms x ––––––– x ––––––– = 6.31 x 10 ^{4}hs1 Ms 10 ^{2}s

Special note on a particular conversion not mentioned above.

Metric conversions where two units (numerator and denominator) are converted