## Learning Objectives

After completing this section, you should be able to:

- Identify reasonable values for weight applications.
- Convert units of measures of weight.
- Solve application problems involving weight.

In the metric system, weight is expressed in terms of grams or kilograms, with a kilogram being equal to 1,000 grams. A paper clip weighs about 1 gram. A liter of water weighs about 1 kilogram. In fact, in the same way that 1 liter is equal in volume to 1 cubic decimeter, the kilogram was originally defined as the mass of 1 liter of water. In some cases, particularly in scientific or medical settings where small amounts of materials are used, the milligram is used to express weight. At the other end of the scale is the metric ton (mt), which is equivalent to 1,000 kilograms. The average car weighs about 2 metric tons.

Any discussion about metric weight must also include a conversation about mass. Scientifically, mass is the amount of matter in an object whereas weight is the force exerted on an object by gravity. The amount of mass of an object remains constant no matter where the object is. Identical objects located on Earth and on the moon will have the same mass, but the weight of the objects will differ because the moon has a weaker gravitational force than Earth. So, objects with the same mass will weigh less on the moon than on Earth.

Since there is no easy way to measure mass, and since gravity is just about the same no matter where on Earth you go, people in countries that use the metric system often use the words mass and weight interchangeably. While scientifically the kilogram is only a unit of mass, in everyday life it is often used as a unit of weight as well.

## Reasonable Values for Weight

To have an essential understanding of metric weight, you must be able to identify reasonable values for weight. When testing for reasonableness, you should assess both the unit and the unit value. Only by examining both can you determine whether the given weight is reasonable for the situation.

## Example 9.31

### Identifying Reasonable Units for Weight

Which is the more reasonable value for the weight of a newborn baby:

- 3.5 kg or
- 3.5 g?

### Solution

Using our reference weights, a baby weighs more than 3.5 paperclips, so 3.5 kilograms is a more reasonable value for the weight of a newborn baby.

## Your Turn 9.31

## Example 9.32

### Determining Reasonable Values for Weight

Which of the following represents a reasonable value for the weight of three lemons?

- 250 g,
- 2,500 g, or
- 250 kg?

### Solution

Because a kilogram is about 2.2 pounds, we can eliminate 250 kg as it is way too heavy. 2,500 grams is equivalent to 2.5 kilograms, or about five pounds, which is again, too heavy. So, a reasonable value for the weight of three lemons would be 250 grams.

## Your Turn 9.32

## Who Knew?

### How Do You Measure the Weight of a Whale?

It is impossible to weigh a living whale. Fredrik Christiansen from the Aarhus Institute of Advanced Studies in Denmark developed an innovative way to measure the weight of whales. Using images taken from a drone and computer modeling, the weight of a whale can be estimated with great accuracy.

## Example 9.33

### Explaining Reasonable Values for Weight

The blue whale is the largest living mammal on Earth. Which of the following is a reasonable value for the weight of a blue whale: 149 g, 149 kg, or 149 mt? Explain your answer.

### Solution

A reasonable value for the weight of a blue whale is 149 metric tons. Both 149 g and 149 kg are much too small a value for the largest living mammal on Earth.

## Your Turn 9.33

## Converting Like Units of Measures for Weight

Just like converting units of measure for distance, you can convert units of measure for weight. The most frequently used conversion factors for metric weight are illustrated in Figure 9.13.

## Example 9.34

### Converting Metric Units of Weight Using Multistep Division

How many kilograms are in 24,300,000 milligrams?

### Solution

Use division to convert from a smaller metric weight unit to a larger metric weight unit. To convert from milligrams to kilograms,

**Step 1:** Divide the value of the weight in milligrams by 1,000 to first convert from milligrams to grams.

**Step 2:** Divide by 1,000 again to convert from grams to kilograms.

So, 24,300,000 milligrams are equivalent to 24.3 kilograms.

## Your Turn 9.34

## Example 9.35

### Converting Metric Units of Weight Using Multiplication

The average ostrich weighs approximately 127 kilograms. How many grams does an ostrich weigh?

### Solution

Use multiplication to convert from a larger metric weight unit to a smaller metric weight unit. To convert from kilograms to grams, multiply the value of the weight by 1,000.

The average ostrich weighs 127,000 grams.

## Your Turn 9.35

## Example 9.36

### Converting Metric Units of Weight Using Multistep Multiplication

How many milligrams are there in 0.025 kilograms?

### Solution

Use multiplication to convert from a larger metric weight unit to a smaller metric weight unit. To convert from kilograms to grams,

**Step 1:** Multiply the value of the weight by 1,000.

**Step 2:** Multiply the result by 1,000 to convert from grams to milligrams.

So, 0.025 kilograms is equivalent to 25,000 milligrams.

## Your Turn 9.36

## Solving Application Problems Involving Weight

From children’s safety to properly cooking a pie, knowing how to solve problems involving weight is vital to everyday life. Let’s review some ways that knowing how to work with metric weight can facilitate important decisions and delicious eating.

## Example 9.37

### Comparing Weights to Solve Problems

The maximum weight for a child to safely use a car seat is 29 kilograms. If a child weighs 23,700 grams, can the child safely use the car seat?

### Solution

**Step 1:** Convert the child’s weight in grams to kilograms.

**Step 2:** Compare the two weights.

Yes, the child can safely use the car seat.

## Your Turn 9.37

## Example 9.38

### Solving Multistep Weight Problems

A recipe for scones calls for 350 grams of flour. How many kilograms of flour are required to make 4 batches of scones?

### Solution

**Step 1:** Multiply the grams of flour need by 4 to determine the total amount of flour needed.

**Step 2:** Convert from grams to kilograms.

So, 1.4 kilograms of flour are needed to make four batches of scones.

## Your Turn 9.38

## Example 9.39

### Solving Complex Weight Problems

The average tomato weighs 140 grams. A farmer needs to order boxes to pack and ship their tomatoes to local grocery stores. They estimate that this year’s harvest will yield 125,000 tomatoes. A box can hold 12 kilograms of tomatoes. How many boxes does the farmer need?

### Solution

**Step 1:** Determine the total estimated weight of the harvested tomatoes.

**Step 2:** Convert the total weight from grams to kilograms.

**Step 3:** Divide the weight of the tomatoes by the weight each box can hold.

So, the farmer will need to order 1,458 boxes.