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Chapter 1: Problem 870

Convert the units. Dimitri's daughter weighed 3.8 kilograms at birth. Convert this to grams.

Short Answer

Expert verified
3,800 grams

Step by step solution

01

- Understand the Conversion Factor

Determine how many grams are in a kilogram. There are 1,000 grams in a kilogram.
02

- Set Up the Conversion

To convert from kilograms to grams, multiply the number of kilograms by the conversion factor. In this case: \(3.8 \text{ kg} \times 1,000 \frac{\text{g}}{\text{kg}}\)
03

- Perform the Calculation

Carry out the multiplication: \(3.8 \times 1,000 = 3,800\) grams.
04

- State the Final Result

Dimitri's daughter weighed 3,800 grams at birth.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

kilograms to grams
When we talk about converting units in the metric system, one common conversion is from kilograms to grams. The kilogram is a larger unit of mass compared to the gram.
For instance, if you're given Dimitri's daughter鈥檚 weight, which is 3.8 kilograms, and you need to find out how much that is in grams, you need to convert the kilograms to grams.
This conversion helps you understand the weight in a smaller and more manageable unit, which is often easier to work with for many everyday applications.
multiplication
Multiplication plays a crucial role in converting units, especially in our kilogram to gram conversion. To convert a given weight from kilograms to grams, you multiply by a specific number known as the conversion factor.
For example, Dimitri's daughter's weight is 3.8 kilograms. By multiplying 3.8 by the conversion factor 1,000 (which is the number of grams in one kilogram), we perform the needed calculation.
So, 3.8 kilograms times 1,000 gives us 3,800 grams. This multiplication process helps efficiently transfer the value from kilograms to grams.
conversion factor
A conversion factor is a number used to change one set of units to another by multiplying or dividing.
For the exercise of converting 3.8 kilograms to grams, the conversion factor is 1,000.
Here's why:
  • The metric system is based on powers of ten, making it straightforward to convert between units.
  • There are 1,000 grams in a kilogram. So every kilogram equals 1,000 grams.
By knowing the conversion factor, you can quickly and accurately change the units, ensuring you maintain the true value of the measurement.
metric system
The metric system is an internationally recognized system of measurement based on powers of ten. It simplifies conversions due to its consistent structure.
In the given problem, converting Dimitri's daughter's weight from kilograms to grams is a straightforward process due to the metric system's design.
Key points about the metric system include:
  • Units are logically related by factors of 10.
  • Common units of mass include kilograms, grams, and milligrams.
  • Each unit can be easily converted to another by multiplying or dividing by powers of 10.
This system is used worldwide, simplifying international communication and ensuring uniformity in measurement.

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