Question

Convert the following metric measures by moving the decimal. \(40 \mathrm{mg}=\) ______ \(\mathrm{g}\)

Short answer

40 mg equals 0.040 g.

Step-by-step solution

Understand the metric units

The problem requires converting milligrams (mg) to grams (g). In the metric system, 1 gram (g) is equal to 1000 milligrams (mg). Thus, we need to convert 40 mg to g.

Apply the conversion factor

Since 1 g = 1000 mg, to convert from milligrams to grams, divide the number of milligrams by 1000. Therefore, you need to calculate \(\frac{40}{1000}\).

Simplify the division

Perform the division \(\frac{40}{1000}\) by moving the decimal point three places to the left, because dividing by 1000 in a decimal moves the decimal three places to the left. Hence, \(\frac{40}{1000} = 0.040\).

Conclusion and write the result

After the conversion, \(40 \mathrm{mg} = 0.040 \mathrm{g}\). Ensure units are also written correctly in the result.

Key concepts

Metric System

The metric system is a decimal-based system of measurement used worldwide, mainly in scientific and technical fields. It relies on units like meters for length, liters for volume, and grams for mass, each scaling with prefixes to signify magnitude. Common prefixes include kilo (k), centi (c), and milli (m), indicating factors of 1000 and 0.001, respectively.

It is the standard system in many countries because it makes calculations straightforward, thanks to its base-10 structure. For instance, since 1 kilogram equals 1000 grams, to convert kilograms to grams, you simply multiply by 1000. This ease of conversion saves time and prevents miscalculations.

Furthermore, using a single system for scientific and international communication simplifies data exchange, reducing confusion and potential errors when working across different systems. This uniformity helps standardize experiments, trade, and communication worldwide.

Decimal Movement

Decimal movement in metric conversions refers to shifting the decimal point in a number to easily change between units. This technique simplifies arithmetic when dealing with metric units that differ by powers of ten.

For example, when converting milligrams to grams, you convert from a smaller unit to a larger unit, and hence move the decimal point to the left.

• In our original exercise, we moved the decimal three places left to convert from milligrams (mg) to grams (g) because 1000 milligrams equals 1 gram.
• If converting from a larger unit to a smaller unit, such as grams to milligrams, the decimal point moves to the right.

This simplified movement allows for quick and efficient conversions without manual division or multiplication, especially when dealing with multiples of ten.

Unit Conversion

Unit conversion involves changing a measure from one unit to another, which is crucial when comparing or analysing data in different units. Understanding conversion factors and how to apply them is key.

A conversion factor is a ratio derived from the relationship between two units. In this particular case, the conversion factor from milligrams to grams is \(\frac{1 \,\text{g}}{1000 \,\text{mg}}\), so to convert 40 mg to grams, the milligrams are divided by 1000, resulting in 0.040 grams.

Here are some general tips for unit conversions:

• Always ensure your units cancel out appropriately in the conversion setup.
• Double-check your calculations, especially the direction of decimal movement.
• Write down each step to avoid confusion, maintaining clarity in calculations.

Mastering unit conversion is not only important for science students but also useful in daily life when dealing with various measurement systems.