Practice with the units of measurement exercises. Make unit conversions and calculations in magnitude exercises such as: length, capacity, time, area, volume and mass.
Exercise 1 - length
The straight-line distance between the cities of São Paulo and Rio de Janeiro is approximately 357.37 km (kilometers). This same distance in meters is equal to:
Answer: 357 370 meters
As the unit m (meter) is smaller than km (kilometers), we must perform a multiplication.
1 km = 1000 meters
Thus, each of the 357.37 km contains 1000 m. To convert the measurement to meters, multiply by 1000.
357.37 km x 1 000 = 357 370 m
Another way to determine is by consulting the table of multiples and submultiples of the meter.
multiples
base measure
submultiples
kilometer (km)
hectometer (hm)
decameter (dam)
meter (m)
decimeter (dm)
centimeter (cm)
millimeter (mm)
357,
3
7
As the measurement is in km, the comma must be in this column. Each remaining digit occupies the next columns.
We must convert km to m. For this, we pass the comma to this column and fill in the empty spaces with zeros.
Since the comma is at the end of the number, we can omit it.
We thus have 357 370 m.
Exercise 2 - length
Convert 1 275 mm (millimeters) to dm (decimeters).
Answer: 12.75 dm
Checking the table of multiples and submultiples of the meter, we see that the decimeters are two places to the left of the millimeters.
multiples
base measure
submultiples
kilometer (km)
hectometer (hm)
decameter (dam)
meter (m)
decimeter (dm)
centimeter (cm)
millimeter (mm)
In this way, the comma that is omitted after the last digit of the number 1 275 must be moved two places to the left.
1 275 mm = 12.75 dm
In practice, we divide by 10 each column on the left. Since we passed two columns, we divided by 100.
practice more with length measurement exercises.
Exercise 3 - capacity
A thermos with a capacity of 1.5 l (liters) will be used to serve coffee to meeting participants. The drink will be served in 60 ml (milliliter) cups. Determine the number of cups that can be served.
Answer: 25 cups
As the measures are in different units, liter and milliliters, we must transform one of them so that they are the same.
As each liter corresponds to 1 000 ml, just multiply 1.5 by 1 000.
1.5 liters x 1000 = 1500 milliliters
To determine the amount of milliliters, we divide 1 500 by 60.
Thus, 25 cups can be served.
Exercise 4 - capacity
Convert the measurement of 457 ml (milliliters) into l (liters).
Answer: 0.457 l
Checking the table of multiples and submultiples of the liter, we see that, from milliliters to liters, we move three columns to the left.
The comma in 457, which is omitted after the 7, must move three orders to the left.
multiples
base measure
submultiples
kiloliter (kl)
hectoliter (hl)
dekaliter (dal)
liter
(l)
deciliter
(dl)
centiliter (cl)
milliliter (ml)
457 ml = 0.457 l
In practice, what we do is divide 457 by 1000, as we move three orders to the left.
learn more about capacity measures.
Exercise 5 - time
In schools, it is common to divide study time into 50-minute classes. If a student attends 6 classes a day and studies 5 days in a week, the number of hours he will be in the classroom will be:
Answer: 25h
The total number of classes attended is: 6 x 5 = 30.
As each class has 50 minutes, in total, the student will attend:
50 x 30 = 1500 minutes
As the problem asks us for the number of hours, and each hour has 60 minutes, we divide 1,500 by 60.
The student will attend, in one week, 25 h (hours) of classes.
Exercise 6 - time
The number of minutes in a week is:
Answer: 10 080 min
One hour has 60 minutes.
There are 24 hours in a day, so 60 x 24 = 1440 minutes.
A week has 7 days, so 1 440 x 7 = 10 080 min.
See too time measurements.
Exercise 7 - area
The hectare is a surface measure widely used to measure large properties. One hectare equals the area of a square 100 m (meters) long on each side. In an advertisement, a site with 76 ha (hectares) is for sale. The number of square meters and square kilometers of this site are, respectively:
Answer: 760 000 m² and 0.76 km²
Each hectare corresponds to a square with an area of:
As there are 76 ha, we have:
To convert m² into km², we divide by 1 000 000, as we divide by 100 in each column of multiples of the meter, on the left.
Exercise 8 - area
Convert 95 000 m² (square meters) to km² (square kilometers).
Answer: 0.095 km²
Observing the table of multiples and submultiples of the m² (square meter), we move three columns to the left.
multiples
base measure
submultiples
kilometer
square (km²)
hectometer
square (hm²)
decameter
square (dam²)
subway
square (m²)
decimeter square (dm²)
centimeter
square (cm²)
millimeter
square (mm²)
As the measures are squared, in each column we advance two places with the comma, also to the left. In total, we move six spaces to the left.
95 000 m² = 0.095 km²
In practice, as the measures are squared, we divide by 100 each column on the left. As we advance three columns, we divide by 1 000 000.
Exercise 9 - volume
A swimming pool in the shape of a parallelepiped has a volume of 30 m³ (cubic meters). The measures of length, width and height of the pool are, in meters, 5 m, 3 m and 2 m, in that order. The volume of the pool in cubic decimeters is:
Answer: 30 000 dm³
As we have the measurements of length, width and height in meters, we can pass them to decimeters.
1 dm (decimeter) is one-tenth of a meter. Thus, we multiply each measurement by 10.
5m = 50dm
3m = 30dm
2 m = 20 dm
Now, we can calculate the volume of the pool with the measurements in dm (decimeter).
The volume of a parallelepiped is given by multiplying the measures of the three dimensions.
50 dm x 30 dm x 20 dm = 30 000 dm³
Exercise 10 - volume
Convert 57 dm³ (cubic decimeters) into cm³ (cubic centimeters).
Answer: 57 000 dm³
Observing the table of multiples and submultiples of the m³ (cubic meter), we verify that the cubic centimeter is one column to the right. Thus, we move the decimal point three "places" to the right.
multiples
base measure
submultiples
cubic kilometer (km³)
hectometer
cubic
(hm³)
cubic dekameter (dam³)
cubic meter (m³)
cubic decimeter (dm³)
cubic centimeter (cm³)
cubic millimeter (mm)
In practice, for each column on the right, we multiply by 1000.
57 dm³ x 1 000 = 57 000 cm³
As the measure is cubic (raised to the cube), each cubic decimeter is equal to 1000 cm³. In other words, it takes 1000 cubes of 1 cm³ each to form a cube of 1 dm³.
learn more about volume measurements.
Exercise 11 - mass
A truck is transporting 5.5 T (tons) of wheat. This mass of wheat in kg (kilograms) and g (grams) is:
Answer: 5 500 kg and 5 500 000 g
1 T (ton) corresponds to 1 000 kg (kilograms). Thus, to convert a measurement from tons to kilograms, just multiply by 1000.
5.5 T x 1000 = 5500 kg
As each kilogram corresponds to 1000g, to convert a measurement from kilograms to grams, simply multiply by 1000.
5 500 kg x 1 000 = 5 500 000 g
Exercise 12 - mass
Convert 25 725 g (grams) into kg (kilograms).
Answer: 25.725 kg
As the kg (kilogram) is a unit 1000 times larger than the g (gram), we divide by 1000.
learn more about mass measurements.
See too:
Units of Measure
Unit conversion
International System of Units
Length Measurements
ASTH, Rafael. Exercises on units of measure solved.All Matter, [n.d.]. Available in: https://www.todamateria.com.br/exercicios-sobre-unidades-de-medidas/. Access at:
