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Chapter 1: Problem 39

How does the prefix kilo affect the gram unit in kilogram?

Short Answer

Expert verified
1 kilogram (kg) equals 1,000 grams (g).

Step by step solution

01

Understanding the Metric System Prefix: Kilo

The prefix 'kilo' in the metric system represents a factor of 1,000. This means that whenever 'kilo' is used as a prefix, the unit it is attached to is multiplied by 1,000.
02

Apply the Prefix to Gram

The base unit here is a gram (g). When 'kilo' is added to gram, it becomes kilogram (kg). This implies that one kilogram is equal to 1,000 grams.
03

Mathematical Expression

Using the information from the previous steps, one can state this relationship mathematically as follows: 1 kg = 1,000 g.

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Key Concepts

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

kilo
The prefix 'kilo-' in the metric system is one of the most commonly used prefixes. It indicates a factor of 1,000. So, when you see 'kilo' attached to a unit, it means that unit is multiplied by 1,000. This is extremely useful for measuring larger quantities efficiently.

For example:
  • 1 kilometer (km) equals 1,000 meters (m).
  • 1 kiloliter (kL) equals 1,000 liters (L).
  • 1 kilogram (kg) equals 1,000 grams (g).
Understanding the role of 'kilo' can make conversions and understanding large quantities much easier.
gram
A gram (g) is a basic unit of mass in the metric system. It is a small unit, often used to measure lighter objects.

Some common examples include:
  • A paperclip weighs about 1 gram.
  • A standard playing card weighs approximately 2 grams.
  • One teaspoon of sugar is about 4 grams.
Grams are suitable for situations where precision is needed, such as in cooking or scientific experiments. They are the building blocks for larger units of mass like kilograms.
kilogram
A kilogram (kg) is a unit of mass that combines 'kilo-' with the gram (g). Since 'kilo-' indicates 1,000, 1 kilogram equals 1,000 grams.

This means:
  • 1 kg = 1,000 g
  • 2 kg = 2,000 g
  • 0.5 kg = 500 g
Kilograms are commonly used to measure heavier objects compared to grams. For example, when you weigh yourself on a scale or buy fruits and vegetables at a market, the weight is usually in kilograms. Understanding the relationship between kilograms and grams makes it easier to switch between smaller and larger units of mass.
metric units conversion
Converting between metric units, like grams and kilograms, is straightforward once you understand the prefixes. Because 'kilo' means 1,000, converting grams to kilograms involves dividing by 1,000, while converting kilograms to grams involves multiplying by 1,000.

For example:
  • To convert 4,500 grams to kilograms: \[ 4500 \text{ g} \times \left( \frac{1 \text{ kg}}{1000 \text{ g}} \right) = 4.5 \text{ kg} \]
  • To convert 7 kilograms to grams: \[ 7 \text{ kg} \times 1000 = 7000 \text{ g} \]
Using these simple multiplication and division techniques makes metric conversions quick and hassle-free. This consistency and ease are key reasons why the metric system is used worldwide.

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Most popular questions from this chapter

For each of the following pairs, which is the larger unit? a. milligram or kilogram b. milliliter or microliter c. \(\mathrm{m}\) or \(\mathrm{km}\) d. \(\mathrm{kL}\) or \(\mathrm{dL}\) e. nanometer or picometer

When three students use the same meterstick to measure the length of a paper clip, they obtain results of \(5.8 \mathrm{~cm}, 5.75 \mathrm{~cm}\), and \(5.76 \mathrm{~cm}\). If the meterstick has millimeter markings, what are some reasons for the different values?

The density of lead is \(11.3 \mathrm{~g} / \mathrm{mL}\). The water level in a graduated cylinder initially at \(215 \mathrm{~mL}\) rises to \(285 \mathrm{~mL}\) after a piece of lead is submerged. What is the mass, in grams, of the lead?

Round off or add zeros to each of the following to give an answer with two significant figures: a. \(5100000 \mathrm{~L}\) b. \(26711 \mathrm{~s}\) c. \(0.003378 \mathrm{~m}\) d. \(56.982 \mathrm{~g}\)

For each of the following problems, give an answer with the correct number of significant figures: a. \(45.7 \times 0.034\) b. \(0.00278 \times 5\) c. \(\frac{34.56}{1.25}\) d. \(\frac{(0.2465)(25)}{1.78}\)
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