Question

Convert the following metric measures by moving the decimal. \(0.65 \mathrm{~kg}=\) ______ \(\mathrm{g}\)

Short answer

0.65 kg equals 650 grams.

Step-by-step solution

Understand the Conversion

In this step, we recognize the conversion factor from kilograms to grams. We know that 1 kilogram is equal to 1000 grams.

Apply the Conversion Factor

Now, we apply the conversion factor. Since we need to convert kilograms to grams, we multiply the number of kilograms, which is 0.65, by 1000 grams per kilogram. This is expressed as: \[ 0.65 \times 1000 \text{ grams/kilogram} = 650 \text{ grams} \]

Place the Decimal

Since multiplying by 1000 involves moving the decimal point three places to the right, 0.65 becomes 650. This completes the conversion process.

Key concepts

Decimal Movement

Decimal movement is a simple and effective way to convert between metric units. When we talk about moving the decimal, we're essentially referring to shifting the decimal point in a number to convert it into a different unit of measure. Understanding decimal movement can be very handy, especially with metrics like kilograms to grams, where conversion involves multiplying or dividing by powers of ten.
When multiplying by 1000, which is the conversion factor in this example, you move the decimal three places to the right. Each position shift to the right represents a power of ten increase. So, starting with 0.65 and moving the decimal three places to the right gives us 650. Let's break it down:

• First move: 6.5
• Second move: 65
• Third move: 650

This movement signifies the relationship between different metric units and helps in easy conversion.

Kilograms to Grams

Converting kilograms to grams is a foundational metric conversion in the decimal system. The metric system is structured in such a way that these conversions are simple and involve multiplying or dividing by powers of ten. Most students start with this conversion, as it is a stepping stone to understanding more complex unit conversions.
One kilogram is equal to 1000 grams. This means that to convert any amount in kilograms to grams, you multiply by 1000. If you have 0.65 kg, simply multiply:\[0.65 imes 1000 = 650 \text{ grams}\]
This multiplication tells you that 0.65 kg is equivalent to 650 grams. This understanding not only helps in this specific conversion but also assists in other metric conversions by recognizing the pattern of using powers of ten.

Conversion Factor

The term "conversion factor" refers to a number used to change one set of units to another by multiplying or dividing. Understanding and using conversion factors is key to mastering metric conversions. In metric conversions, these factors are very straightforward, often powers of ten, which simplify calculations significantly.
For the conversion from kilograms to grams, the conversion factor is 1000. This implies:

• 1 kilogram equals 1000 grams
• Thus, to find the number of grams, multiply the number of kilograms by 1000

Knowing the conversion factor allows for quick and accurate transitions between units. It requires no memorization of complex multipliers, making metric conversions efficient and accessible to students of all levels. The simplicity of the conversion factor ensures that you can easily verify your results. If you multiply correctly and apply the factor, your decimal placement will always be accurate.