Conversion of Units Part 1: Centimeters, Meters, Kilometers

Converting from one unit to another is one of the skills that you should learn before taking the Civil Service Examinations. It sometimes makes calculations easier and therefore saves time.

In this series, I will discuss the different methods that can be used in converting from one unit to another. I will illustrate several examples such as conversion among centimeters (cm), meters (m) and kilometers (km). Take note that the methods used here can also be used in conversion of other units of measure.

It is important that you memorize some standard conversions such as the following:

1 m = 100 cm

1 km = 1000 m

1 kg = 1000 g

1 ft = 30 cm

1 ft = 12 inches

1 mile = 1.6 km 

Now, let’s have some examples.

Example 1: Convert 3.4 m to cm.

Method 1: Ratio and Proportion

We can use ratio and proportion to solve conversion problems. Recall that in the proportion a: b = c : d, the product of the outside terms (a and d) called extremes is equal to the product of the inside terms (b and c) called means. That is, a × d = b × c. Therefore, if we let x be the unknown in Example 1, we have

1 m: 100 cm = 3.4 m: x cm

In setting up the proportion, be sure that the order of the units is the same; in this case, meters before centimeters. We used meter is to centimeters in the ratio 1m : 100cm on the left hand side of the equation, so we should also use the same order on the right hand side (3.4m : x cm). If we use centimeters before meters, then the other ratio should also be in that order.

To calculate, we remove the units (to simplify), solve for x by multiplying the extremes (1 and x) and then equating the product to the means (100 and 3). That is,

1: 100 = 3.4: x

(1)(x) = (100)(3.4)

x = 340

Method 2: Cross Multiplication

This method is very similar to Method 1. This is because the ratio a : b can be written as a fraction a/b.

So,

1 : 100 = 3.4 : x can be written as 1/100 = 3.4/x.

Cross multiplying, we have

(1)(x) = (3.4)(100)

x = 340.

Method 3: Multiplication

There are 100 cm per meter, so we can write 100cm / 1m. We placed 1m at the denominator in order to cancel out m as unit.

3.4 m × (100cm / 1 m) = 340 cm.

Take note of the difference in Methods 3 in the next example.

Example 2: Convert 25 cm to m.

Method 1: Ratio and Proportion

Again, the order of the units must be the same on the left hand side and the right hand side of the equation.

1 m: 100cm = x m: 25 cm

Let’s remove the units and solve for x:

1: 100 = x:25

Multiplying the extremes and equating it to the means, we have

100(x) = 25

x = 25/100

x = 0.25

Answer: 0.25m

Method 2: Cross Multiplication

1/100 = x/25

100x = 25

x = 25/100

x = 0.25

Answer: 0.25m

Method 3: Multiplication

25 cm × (1m /100 cm) = 25/100 m = 0.25m

Notice the difference between Method 3 in Example 1. This time, we placed cm at the denominator of the fraction, so we can cancel out the cm in 25cm.

In the next post, we are going to have more examples.

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