CBSE Class 5 Mathematics Chapter 10: Tenths and Hundredths NCERT Solutions

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NCERT Solutions PDF Class 5 PDF

CBSE Class 5 Mathematics Chapter 10, "Tenths and Hundredths," introduces students to the foundational concepts of decimals. The NCERT Solutions offer clear, step-by-step guidance for various exercises. These include converting between centimeters and millimeters, understanding decimal representations of lengths, and applying these ideas to practical situations like measuring and estimating. Students will explore how decimal numbers represent parts of a whole and their connection to metric units. The solutions aim to build a solid understanding of decimal arithmetic, which is essential for future math studies. This resource is perfect for practicing and reinforcing learning, helping students prepare for exams and gain confidence in solving problems involving decimals.

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Quick info

BoardCBSE
ClassClass 5
SubjectMathematics
Session2026
LanguageEnglish
TypeNCERT Solutions
ChapterChapter 10

Chapter summary

Chapter 10 of the CBSE Class 5 Mathematics curriculum focuses on "Tenths and Hundredths." The NCERT Solutions cover exercises that help students understand decimal notation, particularly in the context of length measurements (cm and mm). It emphasizes converting between decimal forms and fractional forms of tenths, relating decimals to millimeters, and applying these concepts to measure and compare lengths of various objects. The solutions guide students through practical measurement tasks and estimations.

Learning outcomes

  • Understand the relationship between centimeters and millimeters.
  • Interpret decimal numbers as tenths of a centimeter.
  • Convert between decimal and millimeter measurements.
  • Measure and record lengths using centimeters and millimeters.
  • Estimate and compare lengths of objects using decimal notation.

Topics covered

Paper topics

  • Understanding Tenths
  • Decimal Representation of Lengths
  • Centimeters and Millimeters
  • Converting between cm and mm
  • Measuring Objects
  • Estimating Lengths
  • Comparing Lengths using Decimals

Important topics

  • Relationship between cm and mm
  • Converting decimals to mm
  • Measuring and recording lengths
  • Understanding decimal place value for tenths

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Questions and Solutions

Question 1

What was the length of the smallest pencil you have used? How long is this pencil? Guess _____ cm Measure it using a scale. How good is your guess? We can see that Anju used a lens to make it look bigger.
Solution:

The length of the smallest pencil used can vary for each student. For example, a student might have used a pencil that was about 1 cm long.

To estimate the length of the given pencil, you can make a guess. Let's say you guess it is more than 3 cm.

After measuring the pencil accurately with a scale, you will find its actual length. If the scale shows the length to be 3.6 cm, then your guess was quite close.

Disclaimer: The actual lengths of the smallest pencil used and the given pencil will differ for each student. The measurements provided here are illustrative examples.

Question 1

What does 0.9 cm mean? It is the same as millimetres. We can also say this is nine-tenths of a cm. Right? So 30.5 cm is the same as _____ cm and ____ millimeter. About how many of the big frogs will fit on the 1 m scale? If they sit in a straight line about how many of the small frogs will cover 1 m?
Solution:

The measurement 0.9 cm means nine-tenths of a centimeter. Since 1 cm is equal to 10 millimeters (mm), 0.9 cm is the same as 9 millimeters.

To express 30.5 cm in centimeters and millimeters:

  • The whole number part, 30, represents 30 centimeters.
  • The decimal part, 0.5, represents 0.5 of a centimeter. To convert this to millimeters, we multiply by 10: 0.5 \times 10 = 5 mm.

Therefore, 30.5 cm is the same as 30 cm and 5 mm.

Now, let's consider the frogs:

Big Frogs:

  • The length of the biggest frog is given as 30.5 cm.
  • A 1-meter scale is equal to 100 cm.
  • To find how many big frogs fit on the scale, we divide the total length of the scale by the length of one frog: 100 \text{ cm} \div 30.5 \text{ cm/frog} \approx 3.27 frogs.
  • So, about 3 big frogs can fit on the 1 m scale.

Small Frogs:

  • The length of each small frog is given as 0.9 cm.
  • To find how many small frogs will cover 1 m (100 cm), we divide the total length by the length of one small frog: 100 \text{ cm} \div 0.9 \text{ cm/frog} \approx 111.11 frogs.
  • Thus, about 111 small frogs can sit in a straight line and cover 1 m.

Question 2

(1) Length of the nail — 2 cm and ____ mm or 2. ___ cm.

(2) The length of this lady finger (bhindi) is _____ cm and ____ mm. We can also write it as ____ cm.

Solution:

To answer these questions, we need to look at the images of the nail and the lady finger with their respective scales (which are not provided in the text but are implied by the questions). Assuming we have the measurements from the image:

Part (1): Length of the nail

  • Let's assume the nail's length is measured as 2 cm and 4 mm.
  • Since 1 cm = 10 mm, 4 mm is equal to 0.4 cm.
  • So, the length of the nail is 2 cm and 4 mm, which can be written as 2.4 cm.

Part (2): Length of the lady finger

  • Let's assume the lady finger's length is measured as 15 cm and 7 mm.
  • The whole part is 15 cm.
  • The decimal part is 7 mm, which is equal to 0.7 cm.
  • So, the length of the lady finger is 15 cm and 7 mm, which can be written as 15.7 cm.

Note: The actual answers depend on the specific measurements shown in the diagrams for the nail and the lady finger in the textbook.

Common mistakes

  • Confusing the relationship between cm and mm (e.g., thinking 1 cm = 100 mm).
  • Incorrectly converting decimal parts of a centimeter to millimeters.
  • Errors in estimating lengths before measuring.
  • Difficulty in accurately reading scales to the nearest tenth of a centimeter.

Revision tips

  • Practice converting lengths between cm and mm repeatedly.
  • Use a real ruler to measure various objects and write their lengths in decimal form.
  • Focus on understanding what the decimal part (tenths) represents in terms of millimeters.
  • Review the frog and pencil measurement examples to grasp the application of decimals in length.

Practice MCQs

Q1. What is 0.7 cm equivalent to in millimeters?

Q2. A length of 25.3 cm can be written as:

Q3. If a frog is 20.5 cm long, how many such frogs can fit on a 1-meter scale?

Q4. What does the digit '5' represent in the measurement 12.5 cm?

Frequently asked questions

What is the main focus of CBSE Class 5 Maths Chapter 10?

Chapter 10, 'Tenths and Hundredths,' focuses on introducing and applying the concept of decimal numbers, particularly in relation to units of length like centimeters and millimeters.

How do these NCERT Solutions help students?

These solutions provide step-by-step explanations for each question, helping students understand how to solve problems involving decimals, convert units of length, and measure objects accurately.

What is the relationship between centimeters and millimeters?

1 centimeter (cm) is equal to 10 millimeters (mm). This relationship is key to understanding decimal measurements in this chapter.

How can I use these solutions for revision?

You can use these solutions to review the concepts of tenths and hundredths, practice measurement problems, and check your understanding of decimal conversions before an exam.

Are the questions in the solutions exactly the same as the textbook?

Yes, the questions are kept the same as in the NCERT textbook, but the solutions are rewritten to be clearer and more detailed for better understanding.

Important links

Content reviewed by the NCERT Help team. Editorial Team and update policy

NCERT Solutions PDF PDF on NCERT Help. URL unchanged for search indexing.