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Measuring Weight

Identify reasonable values for weight applications.

Learning Objectives

After completing this section, you should be able to:

  1. Identify reasonable values for weight applications.
  2. Convert units of measures of weight.
  3. Solve application problems involving weight.

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.

Identifying Reasonable Units for Weight

Try it.

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.

Determining Reasonable Values for Weight

Try it.

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.

Explaining Reasonable Values for Weight

Try it.

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.

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 .

Converting Metric Units of Weight Using Multistep Division

Try it.

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.

\[\begin{array}{lll}\frac{24,300,000\text{mg}}{1,000} & = & 24,300g \\ \frac{24,300g}{1,000} & = & 24.3\text{kg}\end{array}\]

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

Converting Metric Units of Weight Using Multiplication

Try it.

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.

\[127\text{kg}\times 1,000=127,000g\]

The average ostrich weighs 127,000 grams.

Converting Metric Units of Weight Using Multistep Multiplication

Try it.

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.

\[\begin{array}{l}0.025\text{kg}\times 1,000=25g \\ 25g\times 1,000=25,000\text{mg}\end{array}\]

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

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.

Comparing Weights to Solve Problems

Try it.

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.

\[23,700g\div 1,000=23.7\text{kg}\]

Step 2: Compare the two weights.

\[23.7\text{kg}<29\text{kg}\]

Yes, the child can safely use the car seat.

Solving Multistep Weight Problems

Try it.

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.

\[350g\times 4=1,400g\]

Step 2: Convert from grams to kilograms.

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

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

Solving Complex Weight Problems

Try it.

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.

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

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

\[17,500,000g\div 1,000=17,500\text{kg}\]

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

\[17,500\text{kg}\div 12\text{kg}\approx 1,458\]

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

Key Concepts

  • Mass is the amount of matter in an object whereas weight is the force exerted on an object by gravity. The mass of an object never changes; the weight of an object changes depending on the force of gravity. An object with the same mass would weigh less on the moon than on Earth because the moon’s gravity is less than that of Earth.
  • In the metric system, weight and mass are often used interchangeably and are expressed in terms in grams or kilograms.

Practice (9)

Try each one on paper first. Reveal the answer to check; verified ones can be opened in the solver for every step.

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

    • 3.5 kg or
    • 3.5 g?
    Paljasta vastaus

    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.

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

    • 250 g,
    • 2,500 g, or
    • 250 kg?
    Paljasta vastaus

    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.

  3. 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.

    Paljasta vastaus

    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.

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

    Paljasta vastaus

    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.

    \[\begin{array}{lll}\frac{24,300,000\text{mg}}{1,000} & = & 24,300g \\ \frac{24,300g}{1,000} & = & 24.3\text{kg}\end{array}\]

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

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

    Paljasta vastaus

    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.

    \[127\text{kg}\times 1,000=127,000g\]

    The average ostrich weighs 127,000 grams.

  6. How many milligrams are there in 0.025 kilograms?

    Paljasta vastaus

    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.

    \[\begin{array}{l}0.025\text{kg}\times 1,000=25g \\ 25g\times 1,000=25,000\text{mg}\end{array}\]

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

  7. 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?

    Paljasta vastaus

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

    \[23,700g\div 1,000=23.7\text{kg}\]

    Step 2: Compare the two weights.

    \[23.7\text{kg}<29\text{kg}\]

    Yes, the child can safely use the car seat.

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

    Paljasta vastaus

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

    \[350g\times 4=1,400g\]

    Step 2: Convert from grams to kilograms.

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

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

  9. 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?

    Paljasta vastaus

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

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

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

    \[17,500,000g\div 1,000=17,500\text{kg}\]

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

    \[17,500\text{kg}\div 12\text{kg}\approx 1,458\]

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

Symbols used here

\approx
approximately equal
Equal to the precision shown, not exactly.
\pm
plus or minus
Both signs at once: x = 3 ± 2 means 5 and 1.
\neq
not equal
The two sides are different.
\leq,\ \geq
less/greater than or equal
Inequalities that allow equality; < and > exclude it.
\sqrt{x},\ \sqrt[n]{x}
square root, n-th root
The non-negative number whose square (n-th power) is x.
a \bmod n
remainder
What is left after dividing a by n.
\%
per cent
Per hundred: 15% = 15/100.
a : b,\ \frac{a}{b}
ratio, fraction
a for every b; a divided by b.

How to: Measuring Weight

  1. Identify reasonable values for weight applications.
  2. Convert units of measures of weight.
  3. Solve application problems involving weight.
  4. 3.5 kg or
  5. 3.5 g?
  6. 250 g,
  7. 2,500 g, or
  8. 250 kg?

Questions people ask

Why does the order of operations matter?

Because 2 + 3 × 4 would otherwise be two different numbers. The convention (brackets, exponents, multiplication and division, addition and subtraction) exists so every reader gets the same value from the same expression.

How do I check an arithmetic answer?

Estimate first (round every number and compute roughly), then compare. If the estimate and the exact answer disagree by more than a little, one of them is wrong. The solver shows every operation, so you can find which line went astray.

Why are fractions harder than decimals?

They are not harder, they are more exact: 1/3 is a precise number, 0.333 is an approximation. Fractions need a common denominator to add, which is the one extra step people trip on.

Kokeile omaasi

Parts of this page are adapted from OpenStax Contemporary Mathematics (CC BY-NC-SA 4.0). Condensed and re-explained here; errors are ours.

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