Question

Convert the following metric measures by moving the decimal. \(6.28 \mathrm{~kg}=\) ______\(\mathrm{g}\)

Short answer

6.28 kg is 6280 g.

Step-by-step solution

Identify the Units of Conversion

The problem requires converting kilograms (kg) to grams (g).

Understand the Conversion Factor

Know that 1 kilogram equals 1000 grams. Therefore, to convert kilograms to grams, multiply the number of kilograms by 1000.

Perform the Conversion

Take 6.28 kilograms and multiply by 1000 to convert to grams: \[ 6.28\, \text{kg} \times 1000 = 6280\, \text{g} \]

Verify Your Work

Check the multiplication to ensure the conversion is correct. The multiplication \(6.28 \times 1000\) indeed gives 6280 grams.

Key concepts

Kilograms to Grams Conversion

When converting between kilograms and grams, it's important to remember that these are both units in the metric system used to measure mass. Kilograms (kg) are a larger unit, typically used for heavier items, while grams (g) are smaller and useful for measuring lighter objects.

A fundamental understanding here is that 1 kilogram is equal to 1000 grams. This conversion relationship forms the basis for converting any value from kilograms to grams or vice versa. You can think of the kilogram as the parent unit, and grams as the smaller sub-units that make it up.

The process is straightforward: when you want to convert kilograms to grams, you simply multiply the number of kilograms by 1000 because each kilogram consists of 1000 grams. In our exercise, you would take 6.28 kilograms and perform the multiplication to get:

• 6.28 kg × 1000 = 6280 g

This multiplication shows not only how many grams 6.28 kilograms are, but also reinforces the solid understanding of how these units relate to each other in the metric system.

Decimal Movement in Metric System

The metric system is renowned for its simplicity, largely because it is based on the decimal system. This makes converting between units straightforward through simple decimal movement.

When converting units in the metric system, a power of 10 conversion requires just moving the decimal point. This eliminates complex calculations, making it easier for anyone to toggle between different units.

In the kilograms to grams conversion, multiplying by 1000 shifts the decimal point three places to the right. So, if you have 6.28 kilograms, you simply move the decimal three places to the right to convert it to grams:

• 6.28 kg becomes 6280 g by moving the decimal point.

It's all about the shift in positions which corresponds to multiplying by powers of 10, and this is mirrored in all metric conversions, not only between kilograms and grams. This system allows for quick mental calculations and an innate sense of accuracy.

Conversion Factors

Conversion factors are crucial tools in converting one unit of measurement to another, particularly within the metric system. A conversion factor is a number used to change one set of units to another, by multiplying or dividing the original quantity.

In the metric system, conversion factors are typically powers of ten, because the system itself is built on these powers. For converting kilograms to grams, the conversion factor is 1000. This is because there are 1000 grams in one kilogram.

• To convert kilograms into grams: multiply by 1000.
• To convert from grams back to kilograms: you would divide by 1000.

Conversion factors make it easy to switch between units of measurement without losing accuracy. They ensure that even complex conversions can be accomplished with straightforward multiplication or division, maintaining the integrity of the metric system's design for simplicity.