CBSE CLASS 7 • MATHEMATICSPART I • CHAPTER 3

A Peek Beyond the Point

Class 7 Mathematics — Decimals, Place Value, Measurement and More

Learn how numbers can be divided into smaller units, how tenths and hundredths lead to decimal notation, and how decimals help us measure, compare, and calculate accurately.

Start Learning Practice Chapter Ganita Prakash pp. 46–80

1 unit= 10 tenths

1 tenth= 10 hundredths

Decimal PointWhole vs Fraction

0.2 = 0.20Trailing Zero Rule

Quick Answer

What is Chapter 3 — A Peek Beyond the Point about?

This chapter develops the idea of dividing whole units into smaller equal parts and extends the Indian place-value system to quantities smaller than one. Students learn tenths (1/10), hundredths (1/100), and thousandths (1/1000), decimal notation, decimal place value, measurement conversions (length, weight, and money), comparison and ordering of decimals, decimal addition and subtraction, decimal sequences, estimation, and real-world applications.

1 unit = 10 tenths

10 one-tenths make 1 whole unit (10 × 1/10 = 1).

1 tenth = 10 hundredths

10 one-hundredths make 1 tenth (10 × 1/100 = 1/10).

1 hundredth = 10 thousandths

10 one-thousandths make 1 hundredth (10 × 1/1000 = 1/100).

100 hundredths = 1 unit

100 equal hundredths combine to form 1 whole unit (100/100 = 1).

The Decimal Point ('.')

Separates whole-number integer places from fractional subunits.

Trailing Zeros Invariant

0.2 = 0.20 = 0.200 (both equal 2/10), whereas 0.02 is 2/100.

Chapter Navigation

Interactive Chapter Roadmap

8 Sections • NCERT pp. 46–80

3.1pp. 46–47

More on Decimal System

Section 3.1 • Ganita Prakash pp. 46–47

The Need for Smaller Units

Sonu's Toy & Screws

Sonu's mother was fixing a toy and trying to join two pieces with a screw. When she couldn't, Sonu asked why: his mother said the screw was not the right size. She brought another screw from her box, and the toy was fixed! To Sonu, both screws looked nearly identical, but close observation revealed they had slightly different lengths.

Key Mathematical Insight: Two objects can look almost identical yet differ by small amounts. When whole centimetre units are not accurate enough, we divide each whole unit into 10 smaller equal parts (millimetres or tenths).

Interactive Ruler & Screw Measurement

Drag the slider to adjust the screw length along the 0–4 cm ruler:

head

0 cm

1 cm

2 cm

3 cm

4 cm

2.7 cm

Length:2.7 cm

Textbook Mixed Fraction: 2 7/10 cm

Spoken Reading: two and seven-tenth centimetres (2 cm + 7/10 cm)

Textbook Measurements (pp. 47–48)

Eraser2 4/10 cm

Two and four-tenth cm

Pencil4 5/10 cm = 4 1/2 cm

Four and a half cm

Chalk Piece1 4/10 cm

One and four-tenth cm

Concept Check: Why do we divide a unit into smaller parts?

Section 3.2 • Ganita Prakash pp. 48–52

A Tenth Part & Operations with Tenths

1 unit = 10 one-tenths

Interactive Tenths Builder

Select whole units and additional tenths to see how mixed fractions, improper tenths, and decimal values align:

Whole Units:3

Tenths (1/10 each):4

Visual Part Representation:

Mixed Fraction3 4/10

Total Tenths34/10

Decimal Form3.4

Expanded Form(3 × 1) + (4 × 1/10)

Sonu's Arm Measurement (p. 50)

Regrouping

Lower Arm: 2 7/10 units | Upper Arm: 3 6/10 units

(2 + 3) + (7/10 + 6/10) = 5 + 13/10

Since 13/10 = 10/10 + 3/10 = 1 + 3/10:

5 + 1 + 3/10 = 6 3/10 units = 6.3 units

Alternative: 27/10 + 36/10 = 63/10 = 60/10 + 3/10 = 6 3/10.

Honeybee Body Parts (p. 51)

Total Length

Head: 2 3/10 | Thorax: 5 4/10 | Abdomen: 7 5/10

Whole sum: 2 + 5 + 7 = 14 units

Tenths sum: 3/10 + 4/10 + 5/10 = 12/10 = 1 2/10

Total = 14 + 1 2/10 = 15 2/10 units (15.2 units)

Shylaja's Hand & Palm (p. 51): Subtraction with Regrouping

Middle Finger

Total hand length = 12 4/10 units. Palm length = 6 7/10 units.

Method (a): Split & Regroup

12 4/10 - 6 7/10

Since 4/10 < 7/10, borrow 1 unit from 12:

12 4/10 = 11 + (10/10 + 4/10) = 11 14/10

(11 - 6) + (14/10 - 7/10) = 5 7/10 units

Method (b): Improper Tenths

124/10 - 67/10

= (124 - 67) / 10

= 57/10 = 5 7/10 units

In decimal notation: 12.4 - 6.7 = 5.7 units

Interactive Ordering: Arrange in Increasing Order (p. 49)

Use the arrow buttons to arrange these 8 textbook lengths from smallest to largest:

1130/10

24/10

310 5/10

41 7/10

59/10

613 1/10

77 6/10

86 7/10

Section 3.3 • Ganita Prakash pp. 53–58

A Hundredth Part & Finer Measurements

1 unit = 100 hundredths

When a sheet of paper measuring 8 9/10 units is folded in half, its length falls between 4 4/10 and 4 5/10 units. To measure exactly between tenths, we divide each tenth into 10 smaller equal parts.

1 Unit= 10 tenths

1 Tenth= 10 hundredths

1 Unit= 100 hundredths

Interactive Zoom Ruler: 1 Unit → 10 Tenths → 100 Hundredths

Toggle the magnification to see how smaller parts emerge between whole numbers:

Zooming into 4.4 to 4.5: Divided into 10 Hundredths (each = 1/100 = 0.01)

4.40

4.41

4.42

4.43

4.44

4.45

4.46

4.47

4.48

4.49

4.50

Folded paper ends at 4.45 (read as 4 units, 4 tenths, and 5 hundredths = 4 45/100).

Three Ways to Write the Same Measurement (Textbook Wire, p. 54)

1 1/10 4/100

One and one-tenth and four-hundredths

1 14/100

One and fourteen-hundredths

114/100 = 1.14

One hundred and fourteen-hundredths

Section 3.4 • Ganita Prakash pp. 59–64

Decimal Place Value & Notation

Base-10 Extension

Why split into 10 parts every time? The Indian place-value system is based entirely on 10. Moving left multiplies by 10 (1 → 10 → 100 → 1000). To represent quantities smaller than one, we continue the same rule to the right by dividing by 10 at each step:

1000÷10→100÷10→10÷10→1 (Ones). (Point)1/10 (Tenths)÷10→1/100 (Hundredths)÷10→1/1000 (Thousandths)

Textbook Exploration: 705 vs 70.5 vs 7.05 (pp. 61–62)

705

7 hundreds + 0 tens + 5 ones

(7 × 100) + (5 × 1)

Read: “Seven hundred and five”

70.5

7 tens + 0 ones + 5 tenths

(7 × 10) + (5 × 1/10)

Read: “Seventy point five”

7.05

7 ones + 0 tenths + 5 hundredths

(7 × 1) + (5 × 1/100)

Read: “Seven point zero five”

Interactive Decimal Place Value Chart

Enter digits into each column to see how the number and expanded form update:

Hundreds (100)

Tens (10)

Ones (1)

Tenths (1/10)

Hundredths (1/100)

Thousandths (1/1000)

Resulting Decimal:70.500

Expanded Form:

(7 × 10) + (0 × 1) + (5 × 1/10) + (0 × 1/100)

Section 3.5 • Ganita Prakash pp. 64–69

Units of Measurement & Small Things in Nature

Length, Weight, Money

mm ↔ cm (÷10)

= 5.60 cm

1 cm = 10 mm

cm ↔ m (÷100)

= 0.36 m

1 m = 100 cm

g ↔ kg (÷1000)

= 0.465 kg

1 kg = 1000 g

Paise ↔ ₹ (÷100)

= ₹0.75

₹1 = 100 paise

Small Wonders in Nature (Ganita Prakash pp. 65–67)

Real-life Decimal Scales

Human Hair0.1 mm

About one-tenth of a millimetre thick, visible to the naked eye but very fine.

0.1 mm = 0.01 cm

Newspaper Page0.05 – 0.08 mm

Standard newsprint paper ranges between 5 to 8 hundredths of a millimetre in thickness.

0.05 mm to 0.08 mm

Mustard Seed1 – 2 mm

A common kitchen spice seed measuring 1 to 2 millimetres across.

1 mm to 2 mm (0.1 cm to 0.2 cm)

Carabera Bruni Ant0.8 – 1 mm

The smallest ant species discovered so far, found in Sri Lanka and China.

0.8 mm = 0.08 cmSri Lanka & China

Acmella Nana Land Snail0.7 mm

The smallest land snail species discovered on Earth, having a tiny translucent shell of just 0.7 mm diameter.

0.7 mm = 0.07 cmMalaysia

Hummingbird Egg1.3 cm long × 0.9 cm wide

The tiny egg of a hummingbird, about the size of a pea.

13 mm × 9 mm

Philippine Goby0.9 cm

One of the world's smallest freshwater fish, found in the Philippines and Southeast Asia.

0.9 cm = 9 mmPhilippines & Southeast Asia

Irukandji Jellyfish0.5 – 2.5 cm bell

Extremely small but lethal marine stinger from northern Australian waters.

5 mm to 25 mm bell, tentacles up to 1 mAustralia

Star-sucker Pygmy Octopus (Wolfi)1 – 2.5 cm, < 1 g

The smallest known octopus species, weighing less than a single gram.

10 mm to 25 mm, weight < 0.001 kgPacific Ocean

The 11.111 kg Rice Heaps (p. 68)

Consecutive heaps: 10 kg + 1 kg + 0.1 kg (100 g) + 0.01 kg (10 g) + 0.001 kg (1 g) = 11.111 kg.

10 + 1 + 1/10 + 1/100 + 1/1000 = 11.111 kg

Section 3.6 • Ganita Prakash pp. 69–73

Locating, Comparing & The Zero Dilemma

Number Lines & Precision

There is Zero Dilemma! (Textbook p. 70)

Sonu says that 0.2 can also be written as 0.20 and 0.200. Zara thinks putting zeros on the right alters the value. Who is right?

Decimal	Tenths	Hundredths	Thousandths	Fraction Value
0.2	2	-	-	2/10
0.20	2	0	-	20/100 = 2/10
0.200	2	0	0	200/1000 = 2/10
0.02	0	2	-	2/100 (10x smaller!)
0.002	0	0	2	2/1000 (100x smaller!)

Conclusion: Sonu is right! 0.2 = 0.20 = 0.200 because they all denote 2 tenths. But 0.02 and 0.002 are completely different values.

Place-by-Place Decimal Comparator

Compare two decimal numbers step-by-step to see where their digits first differ:

Number A:

Number B:

Comparison Result:6.456 < 6.465

Comparison rule from textbook p. 72: Start at highest place value. If equal, move to the next smaller place value until a difference is found. The number with the larger digit at this first differing position is greater.

Digit Placement Challenge (Textbook p. 73)

Target: 25

Use the digits 4, 1, 8, 2, and 5 exactly once to form a decimal number __ __ . __ __ __ as close as possible to 25:

Your number: 25.148 | Distance from 25: 0.148

Section 3.7 • Ganita Prakash pp. 74–76

Addition, Subtraction & Decimal Sequences

Column Alignment & Patterns

Real-Life Application: Priya and Shylaja's Cloth (p. 74)

Priya requires 2.7 m of cloth for her skirt, and Shylaja requires 3.5 m for her kurti.

Total cloth needed = 2.7 m + 3.5 m = 6.2 m

Difference = 3.5 m - 2.7 m = 0.8 m

Column Addition Visualizer (p. 75)

75.345 + 86.691

Term A:

Term B:

Carries: 1 1 1

75.345

+ 86.691

= 162.036

Textbook exact: 75.345 + 86.691 = 162.036 (regrouping from thousandths to hundreds).

Column Subtraction Visualizer (p. 75)

84.691 - 77.345

Minuend:

Subtrahend:

Borrowing applied

84.691

- 77.345

= 7.346

Textbook exact: 84.691 - 77.345 = 7.346 (with borrow across ones).

Textbook Decimal Sequences & Rules (p. 76)

4.4, 4.45, 4.5, ...Rule: +0.05Next: 4.55, 4.60, 4.65

25.75, 26.25, 26.75, ...Rule: +0.50Next: 27.25, 27.75, 28.25

10.56, 10.67, 10.78, ...Rule: +0.11Next: 10.89, 11.00, 11.11

13.5, 16.0, 18.5, ...Rule: +2.50Next: 21.0, 23.5, 26.0

8.5, 9.4, 10.3, ...Rule: +0.90Next: 11.2, 12.1, 13.0

5.0, 4.95, 4.90, ...Rule: -0.05Next: 4.85, 4.80, 4.75

12.45, 11.95, 11.45, ...Rule: -0.50Next: 10.95, 10.45, 9.95

36.5, 33.0, 29.5, ...Rule: -3.50Next: 26.0, 22.5, 19.0

Sonu's Estimation Rule (p. 76)

When adding two decimal numbers like 25.936 + 8.202:

Lower bound: Sum of whole number parts = 25 + 8 = 33.
Upper bound: 2 more than whole parts sum = 25 + 1 + 8 + 1 = 35.
Actual sum = 34.138 (falls directly in the estimated range [33, 35]!).

Section 3.8 • Ganita Prakash pp. 76–80

More on the Decimal System: Disasters, Deceptions & History

Real-World Precautions

Deceptive Decimal Notations (pp. 77–78)

4.5 Hours Post Noon

Does 4.5 hours mean 4:05 or 4:50? Neither!

0.5 hour = 5/10 × 60 min = 30 min.
Arrival time: 4:30 p.m.

2 ft 5 inches vs 2.5 ft

A carpenter builds a door 2.5 ft wide for a 2 ft 5 inch opening. Why won't it shut?

1 ft = 12 inches.
0.5 ft = 6 inches.
Door = 2 ft 6 in > 2 ft 5 in!

Cricket Overs (5.5)

In cricket, 5.5 overs does NOT mean 5.5 in base-10!

1 over = 6 balls.
5.5 = 5 overs and 5 balls (5 5/6 overs). Next ball makes it 6.0 overs, not 5.6!

Real-World Decimal Disasters (p. 77)

2013Netherlands

Amsterdam Housing Benefits Overpayment

The Amsterdam City Council mistakenly disbursed €188 million instead of the intended €1.8 million. A software glitch processed benefits in euro cents (1/100 of a euro) without converting them back to euros, multiplying payouts by roughly 100 times.

Lesson: Always verify units of measure when handling financial and mathematical databases.

1983Canada

The 'Gimli Glider' Air Canada Flight 143

A Boeing 767 ran completely out of fuel at 41,000 feet mid-flight because ground personnel miscalculated fuel loading in pounds instead of kilograms (1 lb ≈ 0.453 kg). The aircraft received roughly half the fuel required, forcing the pilot to execute an unpowered deadstick glide to an abandoned airfield.

Lesson: Unit confusion between imperial and metric decimal systems can have life-threatening consequences.

Ongoing WarningHealthcare Worldwide

Medication Dosing Errors

Misreading 0.05 mg as 0.5 mg multiplies a drug dose tenfold (1000% overdose). Pediatric and critical-care medicine now strictly mandate leading zeros (always write 0.5 mg, never .5 mg) and decimal verification to prevent fatal overdoses.

Lesson: Decimal place value accuracy is critical in healthcare and pharmacology.

A Pinch of History — Decimal Notation Over Time (p. 78)

8th Century CE • Śhrīdharāchārya (India)

Pioneered early systematic operations on decimal fractions (fractions with denominators 10, 100, 1000) in influential treatises on arithmetic and algebra.

c. 950 CE • Abūl Ḥassan al-Uqlīdisī (Damascus (Syria))

Wrote 'Kitāb al-Fuṣūl fī al-Ḥisāb al Hindī' (The Book of Chapters on Indian Arithmetic). Used a vertical tick/stroke above digits to separate whole numbers from decimal fractions, writing 0.059375 as 0'059375.

15th Century • European & Middle-Eastern Mathematicians (Global)

Experimented with multiple notations: different ink colours, horizontal bars, and superscripts (writing 0.36 as 36² to indicate 2 decimal places).

16th – 17th Century • John Napier & Christopher Clavius (Scotland & Germany)

Adopted the dot/period ('.') to separate integer parts from decimal fractions, giving rise to modern decimal point notation in English-speaking nations.

Late 16th Century • François Viète (France)

Advocated the comma (',') as a separator. Many European and South American countries still use commas for decimals (e.g. 1 000,5).

Interactive Lab

The Decimal Laboratory

8 Hands-on Experiments

Build Your Own Decimal

Choose units, tenths, and hundredths:

Whole Units: 33 ones = 3

Tenths: 44 tenths = 0.4

Hundredths: 77 hundredths = 0.07

Combined Decimal:3.47

Three point four seven (3 47/100)

Practice Zone

Chapter 3 Practice Zone (30 Questions)

Foundation → Application → Challenge

13.1 The Need for Smaller Units

pp. 46–47

Why do we divide a whole centimetre into 10 smaller equal parts on a ruler?

23.2 A Tenth Part

p. 48

How many one-tenths make 1 whole unit?

33.2 A Tenth Part

p. 49

Convert 34 one-tenths (34/10) into a mixed fraction. What is the whole number part?

43.3 A Hundredth Part

p. 53

How many one-hundredths make one-tenth?

53.4 Decimal Place Value

p. 62

What does the decimal point ('.') separate?

63.4 Decimal Place Value

p. 63

How is the decimal 0.274 read in words according to standard mathematical convention?

73.5 Units of Measurement

p. 65

Convert 56 mm into centimetres. Enter the decimal number (e.g. 5.6):

83.5 Units of Measurement

p. 66

Convert 36 cm into metres. Enter the decimal value (e.g. 0.36):

93.5 Units of Measurement

p. 67

Convert 465 g into kilograms. Enter the decimal value:

103.5 Units of Measurement

p. 68

Convert 75 paise into rupees. Enter the decimal value:

Caution Zone

10 Common Mistakes Students Make

Pitfalls & Remedies

1. Thinking more decimal digits means a larger number

Wrong Thinking:0.198 is bigger than 0.7 because 198 is bigger than 7.

Why it is wrong: Decimal values are determined place-by-place from left to right. In 0.7, the tenths digit is 7. In 0.198, the tenths digit is only 1. 7 tenths (700 thousandths) is much greater than 1 tenth (198 thousandths).

Correct Idea:Always compare place values starting with tenths, then hundredths, then thousandths.

Example: 0.7 > 0.198 because 7/10 > 1/10.

2. Confusing 0.2 and 0.02

Wrong Thinking:0.2 and 0.02 have the same number 2, so they must be equal.

Why it is wrong: The position of the 2 determines its value: in 0.2, the 2 is in the tenths place (value = 2/10). In 0.02, the 2 is in the hundredths place (value = 2/100). 2 tenths is 10 times larger than 2 hundredths.

Correct Idea:A zero immediately after the decimal point pushes the non-zero digit to a 10-times smaller place value.

Example: 0.2 = 20/100, while 0.02 = 2/100. Thus, 0.2 = 10 × 0.02.

3. Interpreting 4.5 hours as 4 hours 5 minutes or 4:50

Wrong Thinking:4.5 hours means 4 hours and 5 minutes, or 4 hours 50 minutes.

Why it is wrong: Time is not based on powers of 10! An hour has 60 minutes. Therefore, 0.5 hours = 5/10 of 60 minutes = 30 minutes.

Correct Idea:Multiply the decimal fractional part by 60 to convert hours to minutes.

Example: 4.5 hours = 4 hours + 0.5 × 60 min = 4 hours 30 minutes (4:30).

4. Ignoring units during measurement conversion

Wrong Thinking:5 mm is 5.0 cm.

Why it is wrong: Since 1 cm = 10 mm, each mm is 1/10 of a cm (0.1 cm). Therefore 5 mm is 5/10 cm = 0.5 cm, not 5 cm.

Correct Idea:To convert millimetres to centimetres, divide by 10 (shift decimal point 1 place left).

Example: 12 mm = 1.2 cm, 56 mm = 5.6 cm, 70 mm = 7.0 cm.

5. Misaligning decimal points during addition and subtraction

Wrong Thinking:Adding 18 + 8.8 by aligning right: 18 + 8.8 = 26.6 or 10.6.

Why it is wrong: You must align corresponding place values (tens with tens, ones with ones, tenths with tenths). 18 is 18.0.

Correct Idea:Line up the decimal points vertically before adding or subtracting.

Example: 18.0 + 8.8 = 26.8; 17.00 - 0.05 = 16.95.

6. Forgetting to regroup across the decimal point

Wrong Thinking:In 12.4 - 6.7, since 7 > 4, just write 7 - 4 = 3, so 6.3.

Why it is wrong: You cannot simply subtract the smaller digit from the larger when the subtrahend digit is larger! You must regroup 1 whole unit into 10 tenths, turning 12.4 into 11 units and 14 tenths.

Correct Idea:Borrow 1 from the ones column: 1 unit = 10 tenths.

Example: 11 units and 14 tenths - 6 units and 7 tenths = 5 units and 7 tenths = 5.7.

7. Reading 7.05 as 'seven point fifty' or 'seven point five'

Wrong Thinking:7.05 is pronounced 'seven point five' or 'seven point fifty'.

Why it is wrong: 7.05 means 7 units and 5 hundredths. 7.5 means 7 units and 5 tenths (which is 7.50). Saying 'point five' confuses 5 hundredths with 5 tenths (10 times larger).

Correct Idea:Read each digit after the decimal point individually: 'seven point zero five'.

Example: 7.05 is 'seven point zero five'. 7.50 is 'seven point five zero'.

8. Treating cricket overs '5.5' as a decimal number

Wrong Thinking:If a bowler bowls 5.5 overs and bowls 1 more ball, they have bowled 5.6 overs.

Why it is wrong: In cricket notation, the number after the dot counts balls (out of 6), not tenths! 5.5 means 5 overs and 5 balls (5 5/6 overs). 1 more ball completes the 6th over, so it becomes 6.0 overs, not 5.6.

Correct Idea:Cricket over notation is shorthand, not a base-10 decimal fraction.

Example: 5.5 overs + 1 ball = 6.0 overs (never 5.6 overs in cricket).

9. Believing trailing zeros alter decimal values

Wrong Thinking:0.20 is larger than 0.2 because 20 is larger than 2.

Why it is wrong: 0.2 means 2 tenths. 0.20 means 2 tenths and 0 hundredths, which is the exact same amount: 2/10 = 20/100.

Correct Idea:Adding zeros to the very right of the last non-zero decimal digit does not change its mathematical value.

Example: 0.2 = 0.20 = 0.200 = 0.2000.

10. Assuming 2 ft 5 inches equals 2.5 feet

Wrong Thinking:A door of opening 2 ft 5 inches will fit a door made 2.5 ft wide.

Why it is wrong: 1 foot = 12 inches, not 10 inches! 0.5 feet = 1/2 of 12 inches = 6 inches. Therefore 2.5 ft = 2 ft 6 inches, which is 1 inch wider than 2 ft 5 inches!

Correct Idea:Decimal notation only aligns with units when the subunit is base-10.

Example: 2.5 ft = 2 ft 6 inches. The door won't shut!

Chapter Summary

Essential Concepts & Formulas Cheat Sheet

Ganita Prakash p. 80

1. Subdivision of Units

Splitting units into smaller equal parts allows more exact measurements when whole numbers are not enough.

2. Base-10 Hierarchy

1 unit = 10 tenths = 100 hundredths = 1000 thousandths. Moving right divides by 10 at every position.

3. Decimal Point Separator

The dot (‘.’) clearly separates whole integer place values from fractional decimal subunits.

4. Invariant Trailing Zeros

0.2 = 0.20 = 0.200 (both represent 2 tenths). Extra trailing zeros to the far right don't change the value.

5. Place-by-Place Comparison

Compare from left to right. The number with the larger digit at the first differing position is greater.

6. Column Alignment in Operations

Always align decimal points vertically when adding or subtracting to keep identical place values together.

Final Assessment

Final Chapter Quiz (15 Questions)

Comprehensive Mastery Evaluation

Question 1 of 15Tenths and Hundredths

If 1 unit is divided into 100 equal parts, what is the value of 45 such parts?

Question 2 of 15Tenths and Hundredths

Which of the following is equivalent to 1 14/100?

Question 3 of 15Tenths and Hundredths

How many thousandths make one hundredth?

Question 4 of 15Decimal Place Value

What is the place value of the digit 5 in the number 70.5?

Question 5 of 15Decimal Place Value

Convert 234 hundredths into decimal form:

Question 6 of 15Decimal Place Value

What is the decimal form of: 10 tens, 10 ones, 10 tenths, and 10 hundredths?

Question 7 of 15Measurement Conversions

A pencil has a length of 134 mm. What is its length in centimetres?

Question 8 of 15Measurement Conversions

A packet of baking powder weighs 68 g. What is its weight in kilograms?

Question 9 of 15Comparing Decimals

Which of the following comparisons is FALSE?

Question 10 of 15Comparing Decimals

Arrange in descending order: 11.01, 1.011, 1.101, 11.10, 1.01

Question 11 of 15Addition and Subtraction

Evaluate: 29.19 + 9.91

Question 12 of 15Addition and Subtraction

Evaluate: 34.505 - 18.1

Question 13 of 15Decimal Sequences

Find the missing term in the sequence: 10.56, 10.67, 10.78, ____, 11.00

Question 14 of 15Real-Life Applications

Tinku weighed 35.75 kg in January and 34.50 kg in February. Did he gain or lose weight, and by how much?

Question 15 of 15Decimal Reasoning

Will a decimal number with more digits always be greater than a decimal number with fewer digits?

Frequently Asked Questions

Chapter 3 Questions & Answers

15 Accordion FAQs

What is Chapter 3 — A Peek Beyond the Point about?

Interactive Chapter Roadmap

The Need for Smaller Units

A Tenth Part

A Hundredth Part

Decimal Place Value

Units of Measurement

Locating & Comparing

Addition & Subtraction

More on Decimal System

The Need for Smaller Units

Interactive Ruler & Screw Measurement

Textbook Measurements (pp. 47–48)

Concept Check: Why do we divide a unit into smaller parts?

A Tenth Part & Operations with Tenths

Interactive Tenths Builder

Sonu's Arm Measurement (p. 50)

Honeybee Body Parts (p. 51)

Shylaja's Hand & Palm (p. 51): Subtraction with Regrouping

Interactive Ordering: Arrange in Increasing Order (p. 49)

A Hundredth Part & Finer Measurements

Interactive Zoom Ruler: 1 Unit → 10 Tenths → 100 Hundredths

Three Ways to Write the Same Measurement (Textbook Wire, p. 54)

Decimal Place Value & Notation

Textbook Exploration: 705 vs 70.5 vs 7.05 (pp. 61–62)

Interactive Decimal Place Value Chart

Units of Measurement & Small Things in Nature

Small Wonders in Nature (Ganita Prakash pp. 65–67)

Locating, Comparing & The Zero Dilemma

There is Zero Dilemma! (Textbook p. 70)

Place-by-Place Decimal Comparator

Digit Placement Challenge (Textbook p. 73)

Addition, Subtraction & Decimal Sequences

Column Addition Visualizer (p. 75)

Column Subtraction Visualizer (p. 75)

Textbook Decimal Sequences & Rules (p. 76)

More on the Decimal System: Disasters, Deceptions & History

Deceptive Decimal Notations (pp. 77–78)

Real-World Decimal Disasters (p. 77)

A Pinch of History — Decimal Notation Over Time (p. 78)

The Decimal Laboratory

Build Your Own Decimal

Chapter 3 Practice Zone (30 Questions)

10 Common Mistakes Students Make

Essential Concepts & Formulas Cheat Sheet

Final Chapter Quiz (15 Questions)

Chapter 3 Questions & Answers