Problem 46 - Calculate With Confidence

Question

Convert the following metric measures by moving the decimal. 400 g = ___________________________ kg

Step-by-Step Solution

Answer

400 g = 0.4 kg

Step 1: Understand the Conversion Factor

Understand that to convert grams (g) to kilograms (kg), you need to know the conversion factor. There are 1000 grams in a kilogram, so to convert grams to kilograms, you divide the number of grams by 1000.

Step 2: Set up the Conversion

Set up the conversion using the understanding from Step 1. We have 400 grams that need to be converted to kilograms, so we use the formula: \( \text{kilograms} = \frac{\text{grams}}{1000} \).

Step 3: Perform the Division

Perform the division by moving the decimal point three places to the left (because dividing by 1000 is equivalent to this operation). For 400 grams, move the decimal point from 400.0 to the left three places, giving you 0.400 kg.

Step 4: Write the Final Answer

Write down the final converted value. After moving the decimal place accordingly, 400 grams is equal to 0.400 kilograms. Therefore, the converted value is \( 0.4 \) kg.

Key Concepts

Decimal Movement

When converting metric measurements, understanding how to move the decimal is crucial. Decimal movement is a straightforward way to adjust numbers without manually performing division or multiplication.

In the metric system, different units are based on powers of ten. This means you can simplify conversions by shifting the decimal point in the number, rather than doing any complex calculations. For example, converting grams to kilograms requires moving the decimal three places to the left because 1 kilogram is equal to 1000 grams.

This works because shifting the decimal point left essentially divides the number by powers of ten. Let's break it down further:

• Each move to the left divides the number by 10.
• Three moves to the left divide the number by 1000 (which is 10³).

This method is convenient, quick, and error-reducing, which is why it's widely used for simple conversions in the metric system.

Grams to Kilograms

The process of converting grams to kilograms is a common task due to the relationship between these units in the metric system. It's based on the fact that there are 1000 grams in one kilogram. This knowledge provides a basic conversion pathway.

To perform the conversion, consider a simple two-step rule:

• First, identify the number of grams you wish to convert. Let's say you have 400 grams.
• Next, apply the conversion by moving the decimal point three places to the left to switch the units from grams to kilograms.

With this method, we can convert the 400 grams to kilograms by adjusting the decimal: From 400.0 to 0.400 kg (or simply 0.4 kg when rounded appropriately). This process highlights the simplicity of metric conversions when you understand how the units relate as multiples of ten.

Conversion Factor

A conversion factor is a number used to change one set of units to another, by multiplying or dividing. When converting between grams and kilograms, the conversion factor is key: 1000 grams equals 1 kilogram.

Here's how it works:

• Identify the conversion factor necessary for the change. Here, the factor is 1000.
• To convert grams to kilograms, divide the grams by 1000, as the conversion factor suggests that there is 1 part kilogram for every 1000 parts grams.

Understanding and using conversion factors simplifies unit changes and applies to various dimensions beyond just mass. Knowing your conversion factors thoroughly validates any conversions you perform and ensures you're getting accurate results when translating measurements between different scales.