Chapter 2: Problem 13
Measurement Convert each measurement to meters. Write your answers as both fractions and decimals. \(50 \mathrm{mm}\)
Short Answer
Expert verified
50 mm = \(\frac{1}{20}\) meters = 0.05 meters.
Step by step solution
01
Understand the Problem
The goal is to convert 50 millimeters (mm) to meters (m) and write the answer as both a fraction and a decimal.
02
Conversion Factor
Remember that 1 meter (m) equals 1000 millimeters (mm). This means the conversion factor from millimeters to meters is \(\frac{1}{1000}\).
03
Apply the Conversion Factor
To convert 50 millimeters to meters, use the conversion factor \(\frac{1}{1000}\). Multiply 50 mm by this factor: \(50 \times \frac{1}{1000} = \frac{50}{1000}\).
04
Simplify the Fraction
Simplify the fraction \(\frac{50}{1000}\). Divide both the numerator and the denominator by their greatest common divisor (GCD), which is 50. This gives \(\frac{50 \div 50}{1000 \div 50} = \frac{1}{20}\).
05
Convert to Decimal
To convert the simplified fraction to a decimal, divide the numerator by the denominator: \(\frac{1}{20} = 0.05\).
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
unit conversion
Unit conversion is the process of changing a measurement from one unit to another. This is essential in science, engineering, and everyday activities to understand measurements correctly.
Let's see how to convert millimeters to meters:
- We know that 1 meter equals 1000 millimeters.
- This means, to convert millimeters to meters, we divide the number of millimeters by 1000.
For example, to convert 50 millimeters to meters, we multiply by the conversion factor \(\frac{1}{1000}\):
**Step-by-step:**
Understanding how to use conversion factors will help you easily switch between different units of measurement.
Let's see how to convert millimeters to meters:
- We know that 1 meter equals 1000 millimeters.
- This means, to convert millimeters to meters, we divide the number of millimeters by 1000.
For example, to convert 50 millimeters to meters, we multiply by the conversion factor \(\frac{1}{1000}\):
**Step-by-step:**
- 50 mm \(\times \frac{1}{1000}\)
Understanding how to use conversion factors will help you easily switch between different units of measurement.
fractions
Fractions represent parts of a whole. They are useful for precise calculations in various fields like cooking, science, and construction.
A fraction consists of a numerator and a denominator.
Taking the example above, after converting 50 mm to meters, we got the fraction \(\frac{50}{1000}\).
Simplifying fractions involves reducing the numerator and denominator to their smallest possible values. Here's how we simplify \(\frac{50}{1000}\):
Simplifying fractions makes them easier to work with and understand.
A fraction consists of a numerator and a denominator.
Taking the example above, after converting 50 mm to meters, we got the fraction \(\frac{50}{1000}\).
Simplifying fractions involves reducing the numerator and denominator to their smallest possible values. Here's how we simplify \(\frac{50}{1000}\):
- Identify the Greatest Common Divisor (GCD) of 50 and 1000, which is 50.
- Divide both the numerator and the denominator by 50.
Simplifying fractions makes them easier to work with and understand.
decimals
Decimals are another way to represent fractions, especially useful for calculations and comparisons.
Decimals show a part of a whole number, where the decimal point separates the whole number part from the fractional part.
For instance, converting the fraction \(\frac{1}{20}\) from the previous example into a decimal involves basic division:
Decimals are more accessible for many people to understand at a glance compared to fractions.
Knowing how to convert between fractions and decimals is a useful skill in everyday life.
Decimals show a part of a whole number, where the decimal point separates the whole number part from the fractional part.
For instance, converting the fraction \(\frac{1}{20}\) from the previous example into a decimal involves basic division:
- Perform division: 1 divided by 20
Decimals are more accessible for many people to understand at a glance compared to fractions.
Knowing how to convert between fractions and decimals is a useful skill in everyday life.
simplifying fractions
Simplifying fractions means reducing them to their simplest form so they're easier to understand and use.
The goal is to make the numerator and the denominator as small as possible by dividing them by their greatest common divisor (GCD).
Consider the fraction from our example: \(\frac{50}{1000}\).
By simplifying fractions, we make them less cumbersome and easier to work with in further calculations.
The goal is to make the numerator and the denominator as small as possible by dividing them by their greatest common divisor (GCD).
Consider the fraction from our example: \(\frac{50}{1000}\).
- First, find the GCD of 50 and 1000, which is 50.
- Then, divide both the numerator (50) and the denominator (1000) by the GCD (50).
By simplifying fractions, we make them less cumbersome and easier to work with in further calculations.