Question

Measurement Convert each measurement to meters. Write your answers as both fractions and decimals. \(50 \mathrm{cm}\)

Short answer

The conversion of 50 cm to meters is \( \frac{1}{2} \) meters or 0.5 meters.

Step-by-step solution

Understand the Conversion Factor

In order to convert centimeters to meters, use the conversion factor: 1 meter = 100 centimeters.

Set Up the Conversion

Write the given measurement in terms of centimeters: 50 cm.

Perform the Conversion

Convert the measurement to meters using the conversion factor. 50 cm = 50 / 100 meters.

Simplify the Fraction

Simplify the fraction: \( \frac{50}{100} \) meters = \( \frac{1}{2} \) meters.

Convert to Decimal

Convert the simplified fraction to a decimal: \( \frac{1}{2} \) meters = 0.5 meters.

Key concepts

Converting Centimeters to Meters

To convert a measurement from centimeters to meters, you need to understand the conversion factor. The basic idea here is that 1 meter equals 100 centimeters.

This relationship can be very useful:

• When you're given a measurement in centimeters, to find the equivalent value in meters, you typically divide by 100.
  
  For example, when we are given 50 centimeters, we can write this as: \(50 \text{ cm} = \frac{50 \text{ cm}}{100} \text{ m}\).
  
• Similarly, if you have a measurement of more than 100 cm, say 250 cm, you can convert it to meters by dividing by 100: \(250 \text{ cm} = \frac{250}{100} \text{ m} = 2.5 \text{ m} \).
  

This approach of dividing by 100 is derived straight out of the unit conversion rule, making it simple and powerful.

Fraction to Decimal Conversion

When you have a fraction like \( \frac{50}{100} \), it often helps to convert this into a decimal as it makes further calculations easier.

Here's a simple way to think of it:

• The fraction \( \frac{50}{100} \) can be simplified by dividing both the numerator (top number) and the denominator (bottom number) by their greatest common divisor (GCD).
  
  In this case, both 50 and 100 can be divided by 50, resulting in: \( \frac{50}{50} = 1 \) and \( \frac{100}{50} = 2 \), thus, \( \frac{50}{100} = \frac{1}{2} \)
  
  
• Next, remember that \( \frac{1}{2} \) is another way of saying 1 divided by 2.
  
  Performing this division gives you a decimal: 0.5.
  
  So, \( \frac{1}{2} \) meters = 0.5 meters.
  
  

This technique of fraction to decimal conversion is crucial for making sense of many scientific and mathematical calculations.

Simplifying Fractions

Understanding how to simplify fractions is fundamental in math. It allows you to work with numbers more easily and to better understand the proportions between quantities.

Here's how you do it:

• Take the fraction \( \frac{50}{100} \) from our earlier example.
  
  To simplify, we need to find the greatest common divisor (GCD) of the numerator and the denominator.
  
  The GCD of 50 and 100 is 50.
  
• Divide both the numerator and the denominator by the GCD:
  
  \( \frac{50}{100} = \frac{50 \text{ ÷ } 50}{100 \text{ ÷ } 50} = \frac{1}{2} \).
  
  This gives us the simplified fraction of \( \frac{1}{2} \).
  
• Sometimes, finding the GCD isn't straightforward.
  
  A handy trick is to break down each number into its prime factors.
  
  For example, 50 is \( 2 \times 5 \times 5 \) and 100 is \( 2 \times 5 \times 10 \).
  
  Remove the common terms (here it's one 2 and one 5), then divide both numerator and denominator by the remaining product to get the simplified fraction.
  
  

Mastering fraction simplification helps to make other math operations, such as addition, subtraction, and multiplication of fractions, far more manageable.