Question

Convert the following metric measures by moving the decimal. \(0.025 \mathrm{~kg}=\) ______\(\mathrm{g}\)

Short answer

0.025 kg = 25 g.

Step-by-step solution

Identify Units and Conversion Factor

Recognize that we're converting from kilograms (kg) to grams (g). The conversion factor is that 1 kg = 1000 g.

Apply the Conversion Factor

To convert from kg to g, multiply the given value by 1000. This is because there are 1000 grams in a kilogram.

Move the Decimal Point

Since multiplying by 1000 is equivalent to moving the decimal point 3 places to the right, we move the decimal of 0.025 three places to the right.

Perform the Calculation

Move the decimal three places to the right: 0.025 becomes 25. Thus, 0.025 kg = 25 g.

Key concepts

Unit Conversion

Unit conversion is all about changing a measurement from one unit to another. This might seem tricky at first, but with the right steps, it's quite straightforward! To convert units, you first need to understand the relationship between the units. In our exercise, we're converting kilograms to grams. The metric system is organized in powers of ten, which makes these conversions easier.

Here's a simple strategy to follow:

• Identify the units you are converting (e.g., kg to g).
• Use the conversion factor that relates these units (1 kg = 1000 g).

The conversion process itself involves using this factor to switch from one unit to another. If you're converting from a larger unit to a smaller one, you'll multiply by the conversion factor. Conversely, if converting from a smaller unit to a larger one, you'll divide.

In this case, since we're converting from kg to g, we multiply by 1000 because a kilogram is larger than a gram. This multiplication moves us from one unit to the other effectively.

Decimal Movement

Decimal movement comes into play when multiplying or dividing by powers of ten. When you're asked to convert between metric units, such as kg to g, you can simplify your calculations by thinking of it in terms of decimal movement rather than long multiplication.

Here's how it works:

• To multiply by 1000 (or move to a smaller unit), move the decimal point three places to the right.
• To divide by 1000 (or move to a larger unit), move the decimal point three places to the left.

In our example where we convert 0.025 kg to g, moving the decimal three places to the right transforms it into 25. This means you don’t have to manually calculate the multiplication; instead, a simple slide of the decimal does the trick. Remember, each step to the right makes your number multiply by ten: 0.025 becomes 0.25, then 2.5, and finally 25.

Once you grasp this concept, converting within the metric system can become a quick and easy task.

Multiplication in Metric System

Multiplication in the metric system benefits from its neat organization into powers of ten. This makes it simple to scale values up or down with ease. For instance, converting kilograms to grams, liters to milliliters, or meters to centimeters all involve multiplying by powers of ten.

Shared rules in the metric system help with consistent multiplication:

• When multiplying, count the number of zeros in the conversion factor to know how many decimal places you'll move.
• The direction of the movement (left or right) corresponds to whether you're going to a larger or smaller unit.

In our scenario, 1 kg equals 1000 g, hence the conversion factor has three zeros. This translates to moving the decimal three places to the right when converting from kg to g, scaling up 0.025 kg to 25 g.

This orderly structure of multiplication allows you to tackle conversions without complex calculations. The critical step is understanding and identifying the conversion factor accurately, which then dictates how the multiplication process unfolds.