Tenths and Hundredths – Complete Guide For Class 5 Math Chapter 10

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The chapter Tenths and Hundredths introduces students to the concept of decimals through practical, real-life examples. It focuses on helping students understand how decimals, particularly tenths and hundredths, are used in everyday situations like measuring lengths, handling money, and expressing smaller parts of a whole. Students learn to convert fractions into decimals, understand place value, and perform operations such as adding and subtracting decimals. Through relatable exercises, students apply these concepts in activities like reading measuring tapes and managing money, building a solid foundation for understanding decimals in both mathematical and real-world contexts.

What are Tenths and Hundredths?

Tenths and hundredths are decimal values that represent parts of a whole, with tenths dividing a whole into 10 equal parts (0.1) and hundredths dividing it into 100 equal parts (0.01). The chapter – “Tenths And Hundredths” begins with an introduction to tenths and hundredths, laying the foundation for understanding decimals.

• Tenths: When a whole is divided into ten equal parts, each part is called one-tenth. It is written as 0.1. We read it as zero point one centimeter. So one is the same as 0.1 cm.

For example, if a pencil is 3 cm and 6 mm long, we can write the length as 3.6 cm (which is 3 whole centimeters and 6-tenths of a centimeter or 6 mm).

• Hundredths: When a whole is divided into 100 equal parts, each part is called one-hundredth. It is written as 0.01. 

For example, 99 paise is the same as ₹0.99, where ₹1 is divided into 100 equal parts, each part representing one-hundredth of a rupee.

Connecting Decimals to Daily Life

The chapter – “Tenths And Hundredths” connects decimals to real-life scenarios, such as measuring the length of objects. 

For instance, students are asked to guess the lengths of pencils, candles, and fingers in both centimeters and millimeters, allowing them to practice using decimals in measurement.

Example activities include:

• Guessing and measuring: Estimating the lengths of objects like pencils, candles, and nails, and converting those measurements into decimals.

Our Eyes Get Confused?

Examples of Gussing the measurement

Which line is longer? A or B? Measure each line and write how long it is in centimeters. How good is your guess?

Which line is longer? C or D ? Measure each line. How good is your guess?

Whose Tail is the Longest?

Guess whose tail is the longest. Now measure the tails. How good is your guess?

• Using a ruler: Students measure objects in centimeters and millimeters and then express the measurements as decimals. For instance, 30.5 cm means 30 cm and 5 mm.

Understanding through Examples: Frogs of Different Lengths

The chapter – “Tenths And Hundredths” includes a comparison of frogs of different lengths. For example:

• Gold Frogs: One of the smallest frogs in the world, with a length of only 0.9 cm (9 millimeters).
• Bull Frogs: One of the largest frogs, with a length of 30.5 cm.

This comparison helps students understand how decimals work when talking about parts of a centimeter.

The Decimal System in Money

Decimals are closely connected to our everyday experience with money. 

The chapter – “Tenths And Hundredths” emphasizes the use of decimals in currency, where 1 rupee is divided into 100 paise. A few key ideas include:

• 1 paisa as a hundredth of a rupee: This is written as ₹0.01. Similarly, ₹0.50 (fifty paise) is half of a rupee.
• Adding and subtracting decimals: For example, if something costs ₹32.99, it is slightly less than ₹33. This introduces the idea that ₹0.99 is 99 paise, almost a full rupee.

Practice Time with Decimal Operations

Several activities in the chapter – “Tenths And Hundredths” encourage students to practice:

1. Comparing prices and measurements: They work with decimal numbers like ₹32.99 and ₹120.50, understanding how decimals affect monetary transactions.
2. Solving word problems: Students solve problems related to purchases and costs, such as calculating the total price of items or figuring out how much change should be returned.

Example: Arun wanted to buy a soap. He has a five-rupee coin, 2 one-rupee coins, and 4 half-rupee coins. Write in rupees what money he will get back.

Solution: calculate the total money Arun has:

• A five-rupee coin = ₹5
• 2 one-rupee coins = 2 × ₹1 = ₹2
• 4 half-rupee coins = 4 × ₹0.50 = ₹2

         So, the total amount Arun has is:

₹5+₹2+₹2 = ₹9

If the price of the soap is less than ₹9, then the amount he will get back will depend on the price of the soap.

Visualizing Decimals with Grids

The chapter – “Tenths And Hundredths” introduces students to the idea of visualizing decimals using grids. 

A grid is divided into 100 equal parts, each representing one-hundredth (0.01) of the total area. 

Students color different parts of the grid to represent various decimals. For example:

• 10 out of 100 boxes colored: Represents 0.10, which is also 1/10.
• 45 out of 100 boxes colored: Represents 0.45, or 45/100.

Make a nice design by coloring 0.45 part of this square red.

This activity helps students connect fractions to decimals visually and understand how decimals work on a hundredth scale.

Real-Life Applications Of Decimals

• Measuring Lengths in Sports

Decimals are commonly used when measuring Lengths and Distances. 

For instance, they are useful in measuring the length of a long jump or the chest size of a wrestler. These measurements are typically recorded in meters.

Since 1 meter equals 100 centimeters, one centimeter is represented as 1/100 of a meter.

• Shopping and Currency

  Decimals also help us to measure the currency of different countries.

The chapter – “Tenths And Hundredths” includes several examples of how decimals are used in shopping. 

For example, students are given shopping scenarios where prices are listed in decimal form.

They calculate the total cost, practice placing the decimal correctly, and use subtraction to figure out how much change they should receive after a purchase.

Practice with Temperature

A fun exercise in the chapter – “Tenths And Hundredths” involves comparing temperatures in different cities. Students learn how decimals are used to represent temperatures (e.g., 35.1°C) and practice basic decimal subtraction by comparing the differences in temperatures at different times of the day.

This exercise introduces the practical use of decimals in scientific measurements.

Conclusion: The Importance of Decimals

The chapter “Tenths and Hundredths,” helps students build a solid understanding of decimals, which are crucial in real-life scenarios like shopping, money transactions, and measurements. The chapter – “Tenths And Hundredths” makes learning fun and interactive through measurement exercises, comparisons, and practical word problems. By the end of the chapter – “Tenths And Hundredths”, students will be comfortable working with decimals, converting between fractions and decimals, and applying these concepts in everyday life.

In conclusion, the chapter “Tenths and Hundredths” plays a vital role in helping students understand the significance of decimals in everyday life. Whether measuring lengths, handling money, or working with fractions, the chapter – “Tenths And Hundredths” introduces these concepts in a relatable and practical way. Through engaging activities, students can master the basics of tenths and hundredths, ensuring a strong foundation for future mathematical concepts. By the end of the chapter – “Tenths And Hundredths”, students will have gained the confidence to apply decimals in real-world situations. Keep practicing with iPrep’s resources to solidify your understanding of this essential topic.