Donna Kirk

Figure 9.12 Weight scale at the local Antigua market (credit: “Weight scale at the local Antigua market” by Lucía García González/Flickr, CC0 1.0 Public Domain Dedication)

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.

Video

Metric System: Units of Weight

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

1.

Which represents a reasonable value for the weight of a penny:
2.5 g or 2.5 kg

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

1.

Which represents a reasonable value for the weight of a car:
1,300 g, 130 kg, or 1,300 kg?

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.

Video

Using Drones to Weigh Whales?

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

1.

The Etruscan shrew is one of the world’s smallest mammals. It has a huge appetite, eating almost twice its weight in food each day. Its heart beats at a rate of 25 beats per second! Which of the following is a reasonable value for the weight of an Etruscan shrew: 2 g, 2 kg, or 2 mt? Explain your answer.

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.

An illustration shows three units: milligram, gram, and kilogram.

Figure 9.13 Common Conversion Factors for Metric Weight Units

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.

\begin{matrix} \frac{24,300,000 mg}{1,000} & = & 24,300 g \\ \frac{24,300 g}{1,000} & = & 24.3 kg \end{matrix}

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

Your Turn 9.34

1.

How many kilograms are in 175,000 milligrams?

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.

127 kg \times 1,000 = 127,000 g

The average ostrich weighs 127,000 grams.

Your Turn 9.35

1.

The world’s heaviest tomato weighed 4.869 kg when measured on July 15, 2020. How much did the tomato weigh in grams?

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.

\begin{matrix} 0.025 kg \times 1,000 = 25 g \\ 25 g \times 1,000 = 25,000 mg \end{matrix}

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

Your Turn 9.36

1.

How many milligrams are there in 1.23 kilograms?

Video

Metric Units of Mass: Convert mg, g, and kg

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.

23,700 g \div 1,000 = 23.7 kg

Step 2: Compare the two weights.

23.7 kg < 29 kg

Yes, the child can safely use the car seat.

Your Turn 9.37

1.

The dosage recommendations for a popular brand of acetaminophen are listed in table below. What is the recommended dosage for a child who weighs 17,683 grams?

Weight	Dosage
11 kg to 15 kg	5 mL
16 kg to 21 kg	7.5 mL
22 kg to 27 kg	10 mL

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.

350 g \times 4 = 1,400 g

Step 2: Convert from grams to kilograms.

\frac{1,400 g}{1,000} = 1.4 kg

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

Your Turn 9.38

1.

A croissant recipe calls for 500 g of flour. How many kilograms of flour are required to make 10 batches of croissants?

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.

140 g \times 125,000 = 17,500,000 g

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

17,500,000 g \div 1,000 = 17,500 kg

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

17,500 kg \div 12 kg \approx 1,458

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

Your Turn 9.39

1.

The average potato weighs 225 grams. A grocery chain orders 5,000 bags of potatoes. Each bag weighs 5 kg. Approximately how many potatoes did they order?

Check Your Understanding

For the following exercises, determine the most reasonable value for each weight.

25.

Candy bar:
50 kg, 50 g, or 50 mg

26.

Lion:
180 kg, 180 g, or 180 mg

27.

Basketball:
624 kg, 624 g, or 624 mg

For the following exercises, convert the given weight to the units shown.

28.

8,900 g = __________ kg

29.

17 g = __________ mg

30.

0.07 kg = __________ g

For the following exercises, determine the total weight in the units shown.

31.

three 48 g granola bars ________ kg

32.

seven 28 g cheese slices ________ mg

33.

six 15 mg tea bags ________ g

Section 9.4 Exercises

For the following exercises, determine the most reasonable value for each weight.

1 .

Aspirin tablet:
300 kg, 300 g, or 300 mg

2 .

Elephant:
5,000 kg, 5,000 g, or 5,000 mg

3 .

Baseball:
145 kg, 145 g, or 145 mg

4 .

Orange:
115 kg, 115 g, or 115 mg

5 .

Pencil:
6 kg, 6 g, or 6 mg

6 .

Automobile:
1,300 kg, 1,300 g, or 1,300 mg

For the following exercises, convert the given weight to the units shown.

7 .

3,500 g = __________ kg

8 .

53 g = __________ mg

9 .

0.02 kg = __________ g

10 .

200 mg = __________ g

11 .

2.3 g = _________ mg

12 .

20 kg = _______ mg

13 .

2,300 kg = __________ g

14 .

8,700 mg = _________ g

15 .

9,730 mg = _______ kg

16 .

0.0078 kg = __________ g

17 .

2.34 g = _________ mg

18 .

234.5 mg = _______ g

For the following exercises, determine the total weight in the units shown.

19 .

Three 350 mg tablets ________ g

20 .

Seven 115 g soap bars ________ kg

21 .

Six 24 g batteries ________ mg

22 .

Fifty 3.56 g pennies ________ mg

23 .

Eight 2.25 kg bags of potatoes ________ g

24 .

Four 23 kg sacks of flour ________ g

25 .

Ten 2.5 kg laptops ________ g

26 .

Seven 1,150 g chickens ________ kg

27 .

Ninety 4,500 mg marbles ________ kg

28 .

There are 26 bags of flour. Each bag weighs 5 kg. What is the total weight of the flour?

29 .

The average female hippopotamus weighs 1,496 kg. The average male hippopotamus weighs 1,814 kg. How much heavier, in grams, is the male hippopotamus than the female hippopotamus?

30 .

Twelve pieces of cardboard weigh 72 grams. What is the weight of one piece of cardboard?

31 .

Miguel’s backpack weighs 2.4 kg and Shanayl’s backpack weighs 2,535 grams. Whose backpack is heavier and by how much?

32 .

A souvenir chocolate bar weighs 1.815 kg. If you share the candy bar equally with two friends, how many grams of chocolate does each person get?

33 .

You purchase 10 bananas that weigh 50 grams each. If bananas cost $5.50 per kilogram, how much did you pay?

34 .

A family-size package of ground meat costs $15.75. The package weighs 4.5 kg. What is the cost per gram of the meat?

35 .

A box containing 6 identical books weighs 7.2 kg. The box weighs 600 g. What is the weight of each book in grams?

36 .

A 2.316 kg bag of candy is equally divided into 12 party bags. What is the weight of the candy, in grams, in each party bag?

37 .

A store has 450 kg of flour at the beginning of the day. At the end of the day the store has 341 kg of flour. If flour costs $0.35 per kilogram, how much flour, in dollars, did the store sell that day?

38 .

A local restaurant offers lobster for $110 per kilogram. What is the price for a lobster that weighs 450 grams?

39 .

A student’s backpack weighs 575 grams. Their books weigh 3.5 kg. If the student’s weight while wearing their backpack is 58.25 kg, how much does the student weigh in kilograms?

40 .

The weight of a lamb is 41 kg 340 g. What is the total weight, in kilograms, of four lambs of the same weight?

9.4 Measuring Weight

Learning Objectives

Reasonable Values for Weight

Identifying Reasonable Units for Weight

Solution

Determining Reasonable Values for Weight

Solution

How Do You Measure the Weight of a Whale?

Explaining Reasonable Values for Weight

Solution

Converting Like Units of Measures for Weight

Converting Metric Units of Weight Using Multistep Division

Solution

Converting Metric Units of Weight Using Multiplication

Solution

Converting Metric Units of Weight Using Multistep Multiplication

Solution

Solving Application Problems Involving Weight

Comparing Weights to Solve Problems

Solution

Solving Multistep Weight Problems

Solution

Solving Complex Weight Problems

Solution

Check Your Understanding

Section 9.4 Exercises