Tenths And Hundredths Class 5 Notes Maths Chapter 10

Measuring Length

Length is the measurement of the longest distance from one end of an object to the other. Different units are used to measure shorter and longer lengths.

Shorter lengths are measured in:

• Centimetres (cm)
• Millimetres (mm)
• Decimetres (dm)

Longer lengths are measured in:

• Metres (m)
• Kilometres (km)
• Decametres (dam)
• Hectometres (hm)

The standard unit of length is the metre (m). To understand the relationship between different units:

• 1 metre (m) is equal to 100 centimetres (cm).
• 1 kilometre (km) is equal to 1000 metres (m).

Unit of the Length Conversion Table  

• Observe the above-mentioned conversion table. It is clear that when we move from one metric unit to another to the right, the value of the metric unit becomes ten times smaller, which is one-tenth. 
• When we move from one metric unit to another to the left in the metric chart, the value of the metric unit becomes ten times bigger.
• From the length conversion chart, different units of lengths and their equivalents are given below : 
  • 1 m = 10 dm = 1000 mm = 100 cm 
  • 1 dm = 10 cm 
  • 1 dm = 0.1 m 1 cm = 0.01 m
  • 1 mm = 0.001 m 
  • 1 km = 10 hm = 1000 m 
  • 1 hm = 10 dam = 100 m 
  • 1 dam = 10 m

Example 1: What does 0.9 cm me and convert the value into millimetres. 

Sol: We know that 1 m = 100 cm
1 cm has 10 equal parts and each part is equal to one-tenth of a centimetre.
1 millimetre is nothing but one-tenth of a centimetre.
1 mm = 1/10 cm = 0.1 cm
Hence 0.9 cm is the same as 9 millimetres.

Example 2: The school at Malappuram has its sports day. Teena jumped 3.50 m, Meena jumped 4.05 m, Rehana jumped 4.50 m, Anu jumped 3.05 m and Amina jumped 3.35 m. How far had everyone jumped in terms of metres and cm 

Sol: We know that 1 m = 100 cm
So we can write the numbers again as
Teena jumped 3 metres and 50 centimetres
Meena jumped 4 metres and 5 centimetres
Rehana jumped 4 metres and 50 centimetres
Anu jumped 3 metres and 5 centimetres
Amina jumped 3 metres and 35 centimetres. 

Example 3: Rewrite the following values in metres. 
3 metre 45 centimetre , 99 centimetre and 1 metre and 5 centimetre

Sol: We know that 1 m = 100 cm
1 cm = 0.01 m and 1 mm = 0.001 m
Now the following values can be rewritten in metres as
3 metre 45 centimetre = 3.45 m
99 centimetre = 0.99 m
1 metre and 5 centimetre = 1.05 m

Example 4: Dinesh’s mother while measuring his height said that he has to grow 45 cm more to reach 2 m height. What is Dinesh’s height in metres? 

Sol: From the question, we can say that to reach 2 m height, Dinesh has to grow 45 cm more
Dinesh's height = 2 m - 45 cm
We know that 1 m = 100 cm, hence
Dinesh's height = 200 cm - 45 cm  = 155 cm
Hence, Dinesh height is 155 cm =  1 m 55 cm

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Measurement of Capacity

• Capacity refers to the amount of liquid a container can hold, and it is measured using different units. The standard unit for measuring capacity is a litre (L). Other units include millilitres (mL), centilitres (cL), decilitres (dL), hectolitres (hL), and kilolitres (kL).
• Large volumes of liquid, such as those found in buckets, are typically measured in litres. On the other hand, smaller amounts of liquid, like coffee in a cup or water in a small bottle, are measured in millilitres.

Measurement Units of Capacity Related To Each Other in a Place Value System.

• The concept of a place value system for capacity is very similar to length conversion. 
• As L is the basic unit of measurement of capacity, all the other metric units are derived from L. It is clear that when we move from one metric unit to another to the left, the value of the metric units becomes ten times bigger. 
• Similarly, when we move from one metric unit to another to the right, the value becomes ten times smaller. The table given below has summarised the same.
  

Example 5: A water tank had a total capacity of 2500 Litres of water. During the daytime, 950 L 350 mL of water is pumped out of the tank. How much amount of water is left in the tank? 

Ans: From the given information we can say that
The total capacity of the tank = 2500 Litres
Total water pumped out during the daytime = 950 L 350 mL,
Therefore, water left in the tank = 2500 L - 950 L 350 mL = 1549  L= 65 mL 

Example 6: The quantity in one Dettol hand sanitiser bottle is 500 mL. What is the quantity present in 12 dozen such bottles? 

Ans: One Dettol hand sanitiser bottle contains 500 mL
We know that a dozen is nothing but a group or set of twelve.
Therefore 12 x 12 bottles contains Dettol hand sanitizer= 500 mL x 12 x 12
= 500 mL x 144
= 72000 mL or 72 litres.
Therefore a dozen of Dettol hand sanitisers have a total of 72 litres worth of hand sanitiser liquid in them. 

Introduction to Money

• Money is an essential part of our daily lives as it helps people buy goods and services. It is also called currency. Each country has its own currency, which has a specific value that can be different from other countries. For example, the value of money in India is not the same as in Sri Lanka.
• Indian Currency. In India, the currency is called the Indian rupee, which is represented by the symbol ₹. According to Indian currency standards, 1 rupee is equal to 100 paisa. This means that 1 paisa is 1/100th of a rupee, or 0.01 rupee.

Example 6: If Arun wants to buy a notebook costing ₹45.50, and he pays with a hundred-rupee note, he should receive ₹54.50 back.

Sol: The cost of the notebook is ₹45.50.
If Arun pays with a ₹100 note
The change he should receive is ₹100 - ₹45.50 = ₹54.50.

Example 7 : How much money in Indian rupees will Riya's father earn if he is paid 1200 Dirham, considering 1 Dirham = ₹10.50?

Sol: To find the total amount in Indian rupees, multiply the amount in Dirham by the conversion rate: 1200 Dirham × ₹10.50 = ₹12,600.

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Understanding Temperature

Temperature measures how hot or cold something is. It is expressed in degrees, with the most common scales being degrees Celsius (°C) and degrees Fahrenheit (°F).Thermometers are the tools used to measure the temperature of an object.

Example 8: What is the difference in temperature between the day and night in Bangalore, if the night temperature is 19°C and the day temperature is 27°C?

Sol: Subtract the night temperature from the day temperature: 27°C - 19°C = 8°C difference.

Example 9: In Chicago, during winter the temperature averages around 2°C. On a particular winter day, the temperature dropped 7°C below this average. What was the temperature on that day?

Sol: The average winter temperature in Chicago is noted as 2°C. If the temperature decreases by 7°C, the temperature on that day would be 2°C - 7°C = -5°C.