Problem 47 - Calculate With Confidence

Question

Convert the following metric measures by moving the decimal. \(0.024 \mathrm{~L}=\) ______ \(\mathrm{mL}\)

Step-by-Step Solution

Answer

0.024 L is 24 mL.

Step 1: Understanding Metric Conversion

We need to convert liters (L) to milliliters (mL). The metric prefix 'milli-' means one-thousandth, so 1 liter is equal to 1000 milliliters.

Step 2: Moving the Decimal

Since 1 liter equals 1000 milliliters, to convert from liters to milliliters, we multiply the number by 1000. This is equivalent to moving the decimal point three places to the right. Starting with 0.024 L, move the decimal three places right.

Step 3: Applying the Conversion

Move the decimal point in 0.024 three places to the right: 1st move: 0.24 2nd move: 2.4 3rd move: 24.0 Thus, 0.024 L becomes 24 mL.

Key Concepts

liters to milliliters

Converting liters to milliliters involves understanding how these two units relate in the metric system. A liter and a milliliter are both units of volume in this system, which is internationally recognized for its simplicity and precision. Here’s a fundamental fact:

• 1 liter (L) is equal to 1000 milliliters (mL).

This relation arises from the prefix "milli-" which denotes a thousandth of a unit in the metric system. So, when converting from liters to milliliters, you're essentially determining how many "thousandths" exist in a given number of whole liters.
For example, if you have 1 liter of water, it can be divided into 1000 equal portions, each being 1 milliliter. Therefore, when converting any quantity in liters to milliliters, you multiply by 1000. In our specific example, if you have 0.024 liters, multiplying by 1000 gives you 24 milliliters.

decimal movement in metric system

The metric system's beauty lies in its straightforward conversion mechanisms, which often involve moving the decimal point. When converting between units that are separated by powers of ten, like liters to milliliters, it's all about decimal movement.
To convert from liters to milliliters, since 1 liter equals 1000 milliliters, you move the decimal point three places to the right. This is because multiplying a number by 1000 (or \(10^3\)) shifts the decimal three positions to the right.

• Start with 0.024 (liters) in this case.
• 1st move: 0.24
• 2nd move: 2.4
• 3rd move: 24.0

Now, you've successfully converted 0.024 liters to 24 milliliters. The decimal movement is a quick, visual way to perform conversions without needing a calculator for powers of ten.

understanding metric prefixes

Metric prefixes help us understand and navigate the metric system's structure, allowing us to grasp different scales and quantities. Each prefix signifies a power of ten, simplifying the conversion process between units. Here's how some common metric prefixes work:

• "milli-" means one-thousandth (or \(10^{-3}\)).
• "centi-" means one-hundredth (or \(10^{-2}\)).
• "kilo-" means a thousand times (or \(10^3\)).

Knowing these relations makes it straightforward to change between units like kilograms to grams, or in our case, liters to milliliters. For instance, when dealing with liters and milliliters, you know that the prefix "milli-" indicates that a milliliter is a thousandth of a liter.
This consistent and logical structure is what makes metric conversions so efficient and easy to use.