Unit of Measurement
A unit of measurement is a standardized quantity of a property that is used as a factor to express how much of that property exists. We have to multiply to convert from a larger unit to a smaller unit. We have to divide to convert from a smaller unit to a larger unit.
Metric Units
A decimal measurement unit used in the metric system (based on meters and kilograms).
Customary Units
These measurement units are most commonly used in the United States. Linear measurement (length and distance), weight (how heavy an object is), capacity (how much liquid a container can hold), and temperature (how hot or cold it is) are all included.
Mass
A large quantity or amount, is referred to as mass. For example, measuring the mass of a book in grams and mass of an airplane and mass of a military tanker etc.
- 1 kilogram (kg) = \( 10^3 \) grams
- 1 hectogram (hg) = \( 10^2 \) grams
- 1 dekagram (dag) = 10 grams
- 1 gram (g) = 1
- 1 decigram (dg) = 0.1 grams
- 1 centigram (cg) = 0.01 grams
- 1 milligram (mg) = 0.001 grams
Weight
It is the amount or quantity of heft. For example, measuring the weight of rice or our own body weight. Weight is measured in ounces, pounds, and tonnes in the United States.
The below conversions can be used to convert one common unit of weight to another.
- 1 pound = 16 ounces
- 1 ton = 2000 pounds
Capacity
Capacity measures volume. For example, the measure of the amount of water in a water can or the amount of milk in a milk tanker is capacity.
- 1 kiloliter (kL) = \( 10^3 \) L
- 1 Hectoliter (hL) = \( 10^2 \) L
- 1 Dekaliter (daL) = 10 L
- 1 liter = 1 L
- 1 deciliter (dL) = 0.1 L
- 1 centiliter (cL) = 0.01 L
- 1 milliliter (mL) = 0.001 L
Ounces, cups, pints, quarts, and gallons are the most common capacity or volume measurement units in the United States. The table below can be used to convert one standard unit of capacity to another.
- 1 cup = 8 fluid ounces
- 1 pint = 2 cups
- 1 quart = 2 pints
- 1 gallon = 4 quarts
Line Plot
A line plot is a graph that displays data frequency on a number line. It’s a quick and easy way to organize information. Simply, a line plot is a graph that displays data as points or check marks above a number line to show the frequency of each value.
Steps Followed to Construct a Line Plot
Step 1: Write the given set of values as fractions with a common denominator.
Step 2: Sort your information into numerical order: Organizing your data from smallest to largest can aid in data interpretation and provide a better understanding of the numbers and the scope of numbers you’re dealing with.
Step 3: Make a horizontal line with your pencil: Examine your data to see what the largest and smallest values are. Because your values are in fractions, the smallest number is 0 and your largest number is 1, so you’ll need to draw a horizontal line from 0 to 1. Mark the further divisions on the number line according to your data.
Step 4: Every time the data appears, place a ‘X’ above that value on the horizontal line. That is, put 1 X above 0 if 0 appears only once.
Step 5: Analyze the data. You can examine a few key components of the data now that you’ve organized it in a line plot.
Solved Examples
Example 1: Convert 9 kilograms to grams?
Solution:
1 kilogram contains 1000 grams.
We had to multiply due to the conversion from a larger unit to a smaller unit.
9 \( \times \) 1000 = 9000 grams.
So, 9 kilograms is 9000 grams.
Example 2: Convert 3900 milligrams to grams?
Solution:
1 gram contains 1000 milligrams.
We had to divide due to the conversion from a smaller unit to a larger unit.
3900 \( \div \) 1000 = 3.9 grams.
So, 3900 milligrams is 3.9 grams.
Example 3: John brought 5600 grams of grapes and ate half of it. How many kilograms of the grapes are left?
Solution:
1 kilogram contains 1000 grams.
We had to divide due to the conversion from a smaller unit to a larger unit.
5600 \( \div \) 1000 = 5.6 kilograms.
So, 5600 grams is 5.6 kilograms of grapes.
He is left with only half of the grapes. So, the grapes left = \( \frac{5.6}{2} \) = 2.8 kilograms of grapes.
Example 4: Convert 21,000 milliliters to liters?
Solution:
1 liter contains 1000 milliliters.
We had to divide due to the conversion from a smaller unit to a larger unit.
21,000 \( \div \) 1000 = 21 liters.
So, 21,000 milliliters is 21 liters.
Example 5: A milkman sold 5 liters of milk. How many milliliters of milk did the milkman sell?
Solution:
Convert 5 liters of milk into milliliters.
1 liter contains 1000 milliliters.
We had to multiply due to the conversion from a larger unit to a smaller unit.
5 \( \times \) 1000 = 5000 milliliters.
So, 5 liters is 5000 milliliters.
The milkman sold 5000 milliliters of milk.
Example 6: Convert 88 ounces to pounds using a tape diagram?
Solution:
There are 16 ounces in 1 pound.
Each part in the tape diagram represents 16 oz. But we know that 1 lb = 16 oz. So we have 5 whole parts so 5 lb and 8 oz is remaining. But 8 oz is half a pound.
So 88 oz = 5 + 0.5 lb
= 5.5 lb
So, 88 ounces is \( 5\frac{1}{2} \) pounds.
Example 7: Convert 90 ounces to pounds?
Solution:
There are 16 ounces in 1 pound.
We had to divide due to the conversion from a smaller unit to a larger unit.
90 \( \div \) 16 = 5.625 pounds.
So, 90 ounces is 5.625 pounds.
Example 8: Convert \( 7\frac{1}{2} \) tons to pounds?
Solution:
There are 2000 pounds in 1 ton.
We had to multiply due to the conversion from a larger unit to a smaller unit.
\( 7\frac{1}{2} \times 2000 = (7\times 2000) + (\frac{1}{2} \times 2000) = 15000 \) pounds.
So, \( 7\frac{1}{2} \) tons is 15000 pounds.
Example 9: A baby elephant weighs 6000 pounds. What is the baby elephant’s weight in tons?
Solution:
Convert 6000 pounds into tons.
There are 2000 pounds in 1 ton.
We had to divide due to the conversion from a smaller unit to a larger unit.
6000 \( \div \) 2000 = 3 tons.
So, The weight of the 6000 pound elephant in tons is 3 tons.
Example 10: Convert the capacity 7 gallons to quarts?
Solution:
1 gallon contains 4 quarts.
We had to multiply due to the conversion from a larger unit to a smaller unit.
7 \( \times \) 4 = 28 quarts.
So, 7 gallons is 28 quarts.
Example 11: Every week Kevin is drinking 60 pints of milk. How many gallons of milk did he drink in a week?
Solution:
Convert 60 pints of milk to quarts then to gallons.
There are 2 pints in 1 quart and there are 4 quarts in 1 gallon.
We had to divide due to the conversion from a smaller unit to a larger unit.
Therefore, 60 pints = 60 \( \div \) 2 = 30 quarts.
We had to divide due to the conversion from a smaller unit to a larger unit.
30 quarts = 30 \( \div \) 4 = 7.5 gallons.
So, there are 7.5 gallons of milk Kevin will drink every week.
Example 12: Peter recorded the amount of pizza eaten by his 12 family members at a party. How many members ate more than \( \frac{3}{4} \) th part of the pizza?
Pizza in parts:
Solution:
Step 1: Writing the data values as fractions with a common denominator. The data values in the denominators are 2, 4 and 8. 8 is the common denominator Because 2 and 4 are factors of 8.
So, \( \frac{1}{2}=\frac{1\times 4}{2\times 4}=\frac{4}{8} \),
\( \frac{3}{4}=\frac{3\times 2}{4\times 2}=\frac{6}{8} \)
Step 2: Arrange the values from the smallest to the largest
\( \frac{3}{8},\frac{3}{8},\frac{4}{8},\frac{4}{8},\frac{4}{8},\frac{5}{8},\frac{5}{8},\frac{6}{8},\frac{6}{8},\frac{6}{8},\frac{6}{8},\frac{7}{8}\)
Step 3: Draw a number line and mark from 0 to \( 1(\frac{8}{8})\). Also mark the further divisions according to the data set.
Step 4: Mark an X on the number line for each data value.
To find the number of people who ate more than \( \frac{3}{4} \) th of the pizza. We count the number of Xs after \( \frac{6}{8} \). Hence only 1 member ate more than \( \frac{3}{4} \) th of the pizza.
Multiply the weight by the conversion ratio to convert a ton measurement to a pound measurement. Because one ton equals 2,000 pounds, you can convert using this simple formula:
Pounds = 2,000 \( \times \) Ton (The ton multiplied by 2,000 equals the weight in pounds)
We first learn the conversion factors between the two units. Then, depending on the situation or the question provided we multiply or divide the given quantity to obtain the result in the desired unit.
No, the value of the quantity does not change. Expressing a quantity in different units is simply different ways to represent that quantity, the innate amount or value of that quantity does not change.