• If you are converting from a 'bigger' unit to a 'smaller' unit, move the decimal point to the right.

• If you are converting from a 'smaller' unit to a 'bigger' unit, move the decimal point to the left.

• 'dec-' means 10 -- as in decimal, decade;  so a decimeter is one-tenth of a meter.  Move one decimal place.

• 'cent-' means 100 -- as in percent, century;  so a centimeter is one-onehundredth of a meter.  Move two decimal places.

• 'milli-' means 1,000 -- as in millipede. Oh, well.  A millimeter is one-onethousandth of a meter.  Move three decimal places.

EXAMPLES:

1. 1 meter is how many millimeters?  [1 m = ? mm]  Meter is bigger than millimeter, so you move the decimal point to the right.  Millimeter differs from meters by three decimal places.  Move the decimal three places to the right.

1 m = 1000 mm.
 
2. 3.2 m is how many centimeters?  [3.2 m = ? cm]  Meter is bigger than centimeter, so you move the decimal point to the right.  Centimeter differs from meter by two decimal places.  Move the decimal two places to the right.

3.2 m = 320 cm.
 
3. 0.5 m is how many mm?  Meters to millimeters is three places to the right.

0.5 m = 500 mm.
 
4. 0.045 m is how many cm?  M to cm is two places to the right.

0.045 m = 4.5 cm.
 
5. 4.5 cm is how many mm?  Cm is bigger than mm.  Cm and mm differ by one decimal point. Move the decimal point one place to the right.

4.5 cm = 45 mm.
 
6. 45 mm are how many m?  Mm is smaller than m, so the decimal point moves to the left.  Mm differ from m by three decimal places.  Move the decimal point to the left three places.

45 mm = 0.045 m.
 
7. 3.2 cm are how many m?  Cm is smaller than m, so the decimal moves to the left.  Cm differs from m by two decimal places.  Move the decimal point to the left two places.

3.2 cm = 0.032 m.
 
8. 354 mm are how many cm?  mm is smaller than cm, so the decimal moves to the left.  Mm differs from cm by one decimal place.  Move the decimal point to the left one decimal place./

354 mm = 35.4 cm.

Exercises:

1. 5.6 cm = _______  mm
2. 2.67 cm = _______ mm
3. 0.356 m = _______ mm
4. 4 m = _______ cm
5. 3.4 mm = _______ cm
6. 5.6 cm = _______ m
7. 2.67 cm = _______ m
8. 0.356 m = _______ cm
9. 3.4 cm = ______ mm
10. 5 mm = ______ m
11. 5 cm = ______ m
12. 4.33 mm = ______ m

1 in = 2.54 cm
1 cm = 0.3937 in

Now, you remember from basic algebra that you can always multiply something times 1.  So, as long as what you have is in either inches or cm, you can convert to the other system.  You do that by multiplying what you are given times one in the form of one of these fractions.

EXAMPLES:

1. What is 40 cm in inches?  Well, to cancel cm and give us inches we need a fraction that equals 1 and has cm in the denominator and inches in the numerator.  We can use (0.3937 in)/(1 cm) or we can use (1 in)/(2.54 cm).  Lets use the first one.  We are given 40 cm.  (40)(1) = 40, so

cancels the cm leaving us with inches, and (40)(0.3937) = 15.902... in, which we can round to 16 inches if we want to.  You might as well memorize that one right now, while you are at it:   40 cm = 16 inches.

2. What is one meter in inches?  Well, we have fractions that convert cm to inches, so lets convert the 1 meter to cm.  1 m = 100 cm, right?  So, we want 100 cm in inches.

The cm cancel, and we have 39.37 inches, which we can round to 40 inches if we want to.  You might as well memorize that one as well:  1 meter = 40 inches.
 
3. What is 6.5 inches in mm?  Convert inches to cm first, then convert to cm to mm.  Use a fraction with cm in the numerator and inches in the denominator.  It does not matter which fraction you use.

The inches cancel, and (6.5)(2.54) = 16.51 cm.  Now, to convert cm to mm you move the decimal point one place to the right:  16.51 cm = 165.1 mm, rounds to 165 mm.  Sound like a temple length to you?

4. How many feet are there in one meter?  We are going to convert cm to inches, so convert 1 m to 100 cm  Now, convert 100 cm to inches.

(100)/(2.54) = 39.37 inches.  How do you convert inches to feet?  There are 12 inches in a foot, so divide 39.37 in/12 = 3.28... feet.  There are just over 3 feet in a meter.  If I have a meter stick and you have a yard stick, my meter stick will reach just a little further under the storage shed than your yard stick.

Exercises:

1. Convert 45 cm to feet.
2. If a temple is marked 6.75 inches, what mm length temple would be the equivalent length?
3. A woman's laptop screen is 30 in away.  How far is that in meters?
4. A lens brings light to a focus at 2 feet.  How long is that length in meters?
5. Convert 3.26 meters to feet.
6. The glasses wearer's frame has 155 mm temples.  What temple length in inches would be the equivalent in the safety frame temple?

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