Units Conversion Formulas and Solved Examples of Length Mass and Capacity
In mathematics, a unit is a standard quantity of measurement of length, mass and capacity. A unit of measurement is a definite magnitude of some physical property that is used as a standard for measurement. The word measure is used to describe the quantity of something. Measurement is a process of determining the dimensions and properties of an object or space. The International System of Units (SI) defines seven base units from which all other SI units are derived. In this section, we will discuss more metric units of length, mass and capacity. Let's begin with the topic.
Metric units of length, mass and capacity
What is Measurement?
The word “measurement” is used in mathematics to describe the process of assigning a number to a variable. Measurement can be an abstract concept or it can be as simple as counting. When we measure something, we are assigning numbers to that thing and this allows us to quantify it and compare it with other things. Measurement is an important part of mathematics and has been used for centuries. It is also closely related to geometry, which deals with lengths and distances.
Measurement is an assignment of numbers to a magnitude or distance. A measurement can be classified as either a physical measurement or a mathematical measurement. Physical measurements are taken with the help of instruments such as rulers, thermometers, and scales. Mathematical measurements are taken by calculations on numbers. We have learned about what measurement is, now let's move further to other topics.
Define Length, Mass and Capacity
The term Length, in mathematics, refers to the distance between two points, or the measure of a line segment. This measurement is usually given in the form of a number. This number can be measured in either centimetres or inches. It can also be measured by using a ruler and measuring from point A to point B. SI unit of length is m(metre).
Mass is a measure of how much matter an object contains. It is measured in kilograms. Mass can be thought of as the amount of matter in an object, but it is the amount of matter per unit volume. The SI unit for mass is the kilogram (kg).
The capacity of a container is its volume or the amount of space it has. The term capacity is used for measuring the volume of a liquid. The amount of liquid that any container can hold is called its capacity. A fluid ounce is the smallest unit of measuring capacity and the gallon is the largest unit.
Length, Weight, Capacity Chart
Here the length, weight, and capacity chart have been described, which are as follows:
Solved Examples of Measures of Length, Mass and Capacity
Here examples related to metric units of length, mass and capacity, have been described, which are as follows;
Example- Convert 0.725 Kilometres to Metres.
Ans: Given us, 0.725 Kilometres
We know that 1 kilometre = 1000 metre
So, 0.725 Kilometres= $0.725 \times 1000$ metre
= 725 metre
Therefore 0.725 Kilometres equals 725 metres.
Example- Convert 52 litres to cl.
Ans: Given us, 52 litres
We know that 1 L = 100 cL
So, 52 litres = $52 \times 100$ cL
= 5200 cL
Therefore 52 litres equals 5200 cL.
Example- Convert 58.26 kg to gms.
Ans: Given us, 58.26 kg
We know that 1 kg = 1000 gm
So, 58.26 kg = $58.26 \times 1000$ gm
= 58260 gm
Therefore 58.26 kg equals 58260 gm.
Practice Problems
Here are some practice problems related to metric units of length mass and capacity, which are as follows;
Q1. Convert 1.45 kilometres to metres.
Ans. 1450 metres.
Q2. Convert 6.14 litres to cl.
Ans. 614 cl.
Q3. Convert 18.9 kg. to gms.
Ans. 18900 gms.
Q4. Convert 7 cm to m.
Ans. 0.07 m.
Q5. Convert 845 gm. to kg.
Ans. 0.845 kg.
Summary
The section concludes that there are four different types of measures of length, mass, and capacity. We have learned about what measurement is, and the definition of length, mass and capacity. There are many different units of measurement for length, mass and capacity, which are discussed using length, weight, and capacity charts. We have also seen how these units are used in the real world to measure things. Apart from this, here we have also seen some examples related to metric units of length, mass and capacity. Along with this, related practice problems have also been given, which helps to understand this topic better.
FAQs on Measures of Length Mass and Capacity in Mathematics
1. What are measures of length, mass, and capacity?
Measures of length, mass, and capacity are standard units used to measure distance, weight, and volume of liquids respectively.
- Length measures how long or tall something is (e.g., metre, centimetre, kilometre).
- Mass measures how heavy an object is (e.g., gram, kilogram).
- Capacity measures how much liquid a container can hold (e.g., litre, millilitre).
2. What are the standard units of length in the metric system?
The standard metric units of length are millimetre (mm), centimetre (cm), metre (m), and kilometre (km).
- 10 mm = 1 cm
- 100 cm = 1 m
- 1000 m = 1 km
3. How do you convert units of length?
To convert units of length in the metric system, multiply or divide by powers of 10.
- To convert metres to centimetres, multiply by 100.
- To convert centimetres to metres, divide by 100.
- To convert kilometres to metres, multiply by 1000.
4. What are the standard units of mass in maths?
The standard metric units of mass are milligram (mg), gram (g), and kilogram (kg).
- 1000 mg = 1 g
- 1000 g = 1 kg
5. How do you convert kilograms to grams?
To convert kilograms to grams, multiply the number of kilograms by 1000.
- Formula: grams = kilograms × 1000
6. What is capacity and how is it measured?
Capacity is the measure of how much liquid a container can hold, and it is measured in litres (L) and millilitres (mL).
- 1000 mL = 1 L
7. How do you convert litres to millilitres?
To convert litres to millilitres, multiply the number of litres by 1000.
- Formula: millilitres = litres × 1000
8. What is the difference between mass and weight?
The difference between mass and weight is that mass is the amount of matter in an object, while weight is the force of gravity acting on it.
- Mass is measured in grams (g) or kilograms (kg).
- Weight is measured in newtons (N).
9. Can you give an example of a word problem on measures of length, mass, or capacity?
A typical word problem involves converting units before performing calculations.
- Example: A bottle contains 2 L of juice. How many millilitres is this?
- Step 1: Use the conversion 1 L = 1000 mL.
- Step 2: 2 × 1000 = 2000 mL.
10. What are common mistakes when converting units of length, mass, and capacity?
Common mistakes when converting metric units include multiplying instead of dividing and forgetting conversion factors.
- Not remembering that 1000 g = 1 kg or 1000 mL = 1 L.
- Moving the decimal point in the wrong direction.
- Mixing up units like metre and millimetre.
