Solve unit transformation exercises with multiples and sub-multiples of the meter and problems with measures of length. Train with the entrance exams and competitions questions solved step by step.
Exercise 1
Transform the measurement from 4.81 meters (m) to millimeters (mm).
Using the table of length measurements, we will transform the measurement in meters to its equivalent in millimeters.
Step 1: write the measurement in meters.
The whole part of the number (before the comma) must end in the column of the unit that the measurement is, in this case, the meter.
Each digit after the comma must fill a column in the table in sequence.
| multiples | base measure | submultiples | ||||
|---|---|---|---|---|---|---|
| kilometer (km) | hectometer (hm) | dekameter (dam) | meter (m) | decimeter (dm) | centimeter (cm) | millimeter (mm) |
| 4, | 8 | 1 |
Step 2: Fill with zeros up to the column of the multiple or sub-multiple for which we want to transform the measure, in this case, the millimeter.
| multiples | base measure | submultiples | ||||
|---|---|---|---|---|---|---|
| kilometer (km) | hectometer (hm) | dekameter (dam) | meter (m) | decimeter (dm) | centimeter (cm) | millimeter (mm) |
| 4, | 8 | 1 |
Step 3: Move the comma to the column for which we are transforming the measure, in this case the millimeter.
| multiples | base measure | submultiples | ||||
|---|---|---|---|---|---|---|
| kilometer (km) | hectometer (hm) | dekameter (dam) | meter (m) | decimeter (dm) | centimeter (cm) | millimeter (mm) |
| 4 | 8 | 1 |
|
As the comma is at the end of the number, there are no decimal places after it, we can suppress its writing.
Therefore, 4.81 m is equal to 4,810 mm.
Exercise 2
0.9 kilometer (km) equals how many centimeters (cm)?
Using the table of length measurements, we will transform the measurement in kilometers to its equivalent in centimeters.
Step 1: write the measurement in kilometers.
The whole part of the number (before the comma) must end in the column of the unit that the measurement is, in this case, the kilometer.
Each digit after the comma must fill a column in the table in sequence.
| multiples | base measure | submultiples | ||||
|---|---|---|---|---|---|---|
| kilometer (km) | hectometer (hm) | dekameter (dam) | meter (m) | decimeter (dm) | centimeter (cm) | millimeter (mm) |
| 0, | 9 |
Step 2: Fill with zeros up to the column of the multiple or sub-multiple for which we want to transform the measure, in this case, the centimeter.
| multiples | base measure | submultiples | ||||
|---|---|---|---|---|---|---|
| kilometer (km) | hectometer (hm) | dekameter (dam) | meter (m) | decimeter (dm) | centimeter (cm) | millimeter (mm) |
| 0, | 9 |
Step 3: Move the comma to the column for which we are transforming the measure, in this case the centimeter.
| multiples | base measure | submultiples | ||||
|---|---|---|---|---|---|---|
| kilometer (km) | hectometer (hm) | dekameter (dam) | meter (m) | decimeter (dm) | centimeter (cm) | millimeter (mm) |
| 0 | 9 |
|
As the comma is at the end of the number, there are no decimal places after it, we can suppress its writing.
Therefore, 0.9 km is equal to 90 000 cm.
Exercise 3
43.4 centimeters equals how many decameters?
Using the table of length measurements, we will transform the measurement in centimeters to its equivalent in decameters.
Step 1: write the measurement in centimeters.
The whole part of the number (before the comma) must end in the column of the unit that the measurement is, in this case, the centimeter
Each digit must fill a column in the table in sequence.
| multiples | base measure | submultiples | ||||
|---|---|---|---|---|---|---|
| kilometer (km) | hectometer (hm) | dekameter (dam) | meter (m) | decimeter (dm) | centimeter (cm) | millimeter (mm) |
| 4 | 3, | 4 |
Step 2: Fill with zeros up to the column of the multiple or sub-multiple for which we want to transform the measure, in this case, the dekameter.
| multiples | base measure | submultiples | ||||
|---|---|---|---|---|---|---|
| kilometer (km) | hectometer (hm) | dekameter (dam) | meter (m) | decimeter (dm) | centimeter (cm) | millimeter (mm) |
4 |
3, | 4 |
Step 3: Move the comma to the column for which we are transforming the measure, in this case the dekameter.
| multiples | base measure | submultiples | ||||
|---|---|---|---|---|---|---|
| kilometer (km) | hectometer (hm) | dekameter (dam) | meter (m) | decimeter (dm) | centimeter (cm) | millimeter (mm) |
| 4 | 3 | 4 |
Therefore, 43.4 cm is equal to 0.0434 dam.
Exercise 4
Convert 457 meters to kilometers.
In this case, the comma is suppressed after the units digit, as it is an integer. The digit 7 must be in the meter column.
| multiples | base measure | submultiples | ||||
|---|---|---|---|---|---|---|
| kilometer (km) | hectometer (hm) | dekameter (dam) | meter (m) | decimeter (dm) | centimeter (cm) | millimeter (mm) |
| 4 | 5 | 7 |
So, we fill with zero up to the measure to which we want to transform, in this case, the kilometer.
| multiples | base measure | submultiples | ||||
|---|---|---|---|---|---|---|
| kilometer (km) | hectometer (hm) | dekameter (dam) | meter (m) | decimeter (dm) | centimeter (cm) | millimeter (mm) |
| 0 | 4 | 5 | 7 |
We put the comma in the kilometer column.
| multiples | base measure | submultiples | ||||
|---|---|---|---|---|---|---|
| kilometer (km) | hectometer (hm) | dekameter (dam) | meter (m) | decimeter (dm) | centimeter (cm) | millimeter (mm) |
0, |
4 | 5 | 7 |
Therefore, 457 meters equals 0.457 km.
Exercise 5
To leave point A and go to point B, a cyclist consults a map and notices that the scale is 1/600 000 cm. By checking the distance in a straight line between points A and B, he finds the measurement of 2 cm. Thus, the distance in kilometers between the two points is
a) 6000 dm.
b) 60 dm.
c) 6 hm.
d) 6 km.
e) 6 dam.
Answer: letter d) 6 km.
Each centimeter on the map is equivalent to 600 000 real cm.
Using the table of multiples and submultiples of m, this transformation can be done.
Step 1: write the measurement in centimeters.
| multiples | base measure | submultiples | ||||
|---|---|---|---|---|---|---|
| kilometer (km) | hectometer (hm) | dekameter (dam) | meter (m) | decimeter (dm) | centimeter (cm) | millimeter (mm) |
| 6 | 0 | 0 | 0 | 0 | 0 |
Step 2: having filled all the cells in the table up to the kilometer column, move the comma in its column.
| multiples | base measure | submultiples | ||||
|---|---|---|---|---|---|---|
| kilometer (km) | hectometer (hm) | dekameter (dam) | meter (m) | decimeter (dm) | centimeter (cm) | millimeter (mm) |
| 6, | 0 | 0 | 0 | 0 | 0 |
Since all digits after 6 are zeros, it is not necessary to type them, as it is an integer.
Therefore, the distance in a straight line between the two cities is 6 km.
Exercise 6
(Moreilândia City Hall, Community Health Agent 2020) Jessica went to the Armarinho in her city to buy material to make a dress, her mother asked her to bring 2.8 meters of fabric. When asked how many centimeters she would want, Jessica replied that she wants to buy:
a) 28 centimeters
b) 100 centimeters
c) 520 centimeters
d) 140 centimeters
e) 280 centimeters
Correct answer: e) 280 centimeters
A meter is 100 cm, so just multiply 2.8 times 100.
2.8 x 100 = 280 centimeters.
To multiply by 100, just move the decimal point two places to the right.
Exercise 7
(Enem 2015) You want to buy eyeglass lenses. The lenses should have thicknesses as close as possible to the 3 mm measurement. In a store's stock, there are lenses of thickness: 3.10 mm; 3.021 mm; 2.96 mm; 2.099 mm and 3.07 mm.
If the lenses are purchased at this store, the chosen thickness will be, in millimeters, of
a) 2,099.
b) 2.96.
c) 3.021.
d) 3.07.
e) 3.10.
Correct answer: c) 3.021.
As the measurement should be as close as possible to 3 mm we want the smallest difference, or, the number closest to 3 mm.
Of numbers larger than 3 mm, we first compare the tenths looking for the smallest. With that the option and is eliminated. We started to compare the hundredths and, with that, the option d is eliminated.
It is necessary to check the numbers smaller than 3 mm and we look for the largest possible. Comparing the option tenths The is eliminated.
Making the differences between option values B and ç with 3 mm, we have:
3mm - 2.96mm = 0.04mm
3 mm - 3.021 mm = 0.021 mm
Thus, the closest measurement to 3 mm is 3.021 mm.
Exercise 8
(Enem 2021) The current distance between the centers of the Earth and its natural satellite (Moon) is 384 405 km. This distance increases by 4 cm per year. The system's center of gravity (or barycentre), formed by the two celestial bodies, is 1 737 km from the Earth's surface, and this distance gradually decreases. This center of gravity will be located outside the Earth in 3 billion years and, with that, the Moon will no longer be our satellite, becoming a planet.
How many centimeters per year, on average, will the system's center of gravity approach the Earth's surface, until the Moon becomes a planet?
a) 0.0579
b) 0.5790
c) 5.7900
d) 12.8135
e) 17.2711
Correct answer: letter a) 0.0579
The statement says that it took 3 billion years for the Moon to become a planet, and for that the center of gravity will shift 1 737 km. We want to determine how far it will travel per year, in centimeters.
Step 1: transform the measure from km to cm.
Using the table of multiples and sub-multiples of the meter, the last integer of the measurement, in this case 7, must be in the column in km. So, we fill in the missing squares with zeros.
| multiples | base measure | submultiples | ||||
|---|---|---|---|---|---|---|
| kilometer (km) | hectometer (hm) | dekameter (dam) | meter (m) | decimeter (dm) | centimeter (cm) | millimeter (mm) |
| 1 737 | 0 | 0 | 0 | 0 | 0 |
Thus, 1 737 km are equivalent to 173 700 000 cm
Step 2: divide 173 700 000 cm by 3 billion years.
To facilitate the division, we write the numbers in scientific notation, with powers of base 10.
Dividing only the numbers without the powers:
Dividing the powers, we repeat the bases and subtract the exponents.
In this way, we have , or:
Exercise 9
(PM - PI 2021) If 1000 meters is equal to 1 kilometer, and 100 centimeters is equal to 1 meter, how many centimeters is 1.25 kilometers?
Right answer:
1 kilometer is 1000 meters, of which each meter is 100 centimeters. Thus,
1 km = 1000 x 100 cm = 100 000 cm
Therefore, 1.25 kilometers, in centimeters is equal to:
1.25 x 100 000 = 125 000 cm
In the form of a power of 10, we have:
Exercise 10
(São Roque do Canaã City Hall - ES - Oral Health Assistant 2020) Every day Carlos walks 10 laps running around a rectangular-shaped square that measures 80 m wide and 100 meters in length. length. How many kilometers does Carlos run in this activity?
a) Carlos runs 8000 km.
b) Carlos runs 3.6 km.
c) Carlos runs 0.036 km.
d) Carlos runs 3600 km.
e) Carlos runs 8 km.
Correct answer: b) Carlos runs 3.6 km.
For each lap Carlos runs:
80 m + 80 m + 100 m + 100 m = 360 m
For every 10 laps, we have:
360 m x 10 = 3600 m
As each kilometer is 1 000 m, Carlos runs 3.6 km per day because:
learn more from length measurements.
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