This MCQ module is based on: Hundredths and Decimal Notation
TOPIC 8 OF 31
Hundredths and Decimal Notation
🎓 Class 7
Mathematics
CBSE
Theory
Ch 3 — A Peek Beyond the Point
⏱ ~35 min
🌐 Language: [gtranslate]
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This mathematics assessment will be based on: Hundredths and Decimal Notation
Targeting Class 7 level in Decimals, with Basic difficulty.
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3.3 A Hundredth Part
Sometimes a tenth is still not small enough. Sonu's tiny screws differed by far less than one-tenth of a centimetre. What if we divide each tenth again into 10 equal parts? Then we get 100 equal parts of one whole — and each part is called a hundredth?, written \(\frac{1}{100}\).
Definition
A hundredth is one of 100 equal parts of a whole. In symbols \(\frac{1}{100}\). Because \(\frac{1}{10}\) split into 10 equal parts gives \(\frac{1}{100}\), we have \(\frac{1}{10}=\frac{10}{100}\).From tenths to hundredths — dividing each 1/10 into 10 equal sub-parts
If a screw is \(2\frac{34}{100}\) cm long, we mean it is 2 whole centimetres plus 34 hundredths of a centimetre. Equivalently, 3 tenths + 4 hundredths = \(\frac{3}{10}+\frac{4}{100}=\frac{30+4}{100}=\frac{34}{100}\).
Note: \(\frac{1}{100}\) of a centimetre is the same length as one millimetre, since 1 cm = 10 mm and 1 mm = 10/10 ÷ 10 = 1/10 cm is wrong — actually 1 mm = 1/10 cm. Hundredths of a centimetre equal tenths of a millimetre.
3.4 Decimal Place Value
Writing \(2\frac{34}{100}\) is long. We use a compact form called the decimal?. Place a dot, called the decimal point, to the right of the ones digit. Digits after the point stand for tenths, hundredths, thousandths, and so on.
\(2\frac{34}{100} = 2.34\)
Read aloud: "two point three four" or "two and thirty-four hundredths".
| Thousands | Hundreds | Tens | Ones | • | Tenths | Hundredths | Thousandths |
|---|---|---|---|---|---|---|---|
| 1000 | 100 | 10 | 1 | • | \(\frac{1}{10}\) | \(\frac{1}{100}\) | \(\frac{1}{1000}\) |
For example, the decimal \(84.691\) breaks into \(8\times10 + 4\times1 + 6\times\frac{1}{10} + 9\times\frac{1}{100} + 1\times\frac{1}{1000}\).
Rule
Each digit's value is ten times the digit immediately to its right, and one-tenth the digit immediately to its left — the same rule as whole-number place value, extended past the decimal point.Reading decimals on the number line
Number line between 4 and 8 with arrows pointing to 5.4 and 7.2
Between 5 and 6 there are ten equal steps of size 0.1 each. So \(5.4\) sits at the fourth tick past 5. Between \(5.4\) and \(5.5\) there are ten smaller steps of \(0.01\) each.
Activity: Zooming in on the Number Line
L3 ApplyMaterials: Paper, ruler, pencil.
Predict: Between 0.5 and 0.6 on the number line, how many tiny ticks can you squeeze in so that each tick is a hundredth?
- Draw a 10 cm long line and mark 0 at the left, 1 at the right.
- Divide into 10 equal parts of 1 cm each. Label them 0.1, 0.2, ..., 0.9.
- Zoom into the segment from 0.5 to 0.6. Redraw it as a 10 cm strip below.
- Divide that strip into 10 equal parts. Label them 0.51, 0.52, ..., 0.59.
- Mark \(0.54\) and \(0.58\) on the zoomed strip.
Zooming shows visually that decimals extend to any depth. Each tenth holds ten hundredths, each hundredth holds ten thousandths — the place-value pattern is infinite.
Figure it Out
Q1. Write as a decimal: (i) \(\frac{7}{10}\) (ii) \(\frac{52}{100}\) (iii) \(3\frac{9}{100}\) (iv) \(8+\frac{3}{10}+\frac{5}{100}\).
(i) 0.7 (ii) 0.52 (iii) 3.09 (iv) 8.35.
Q2. Place value of the digit 6 in 84.691.
6 stands in the tenths place, so its value is \(\frac{6}{10}=0.6\).
Q3. Which is larger: 1.23 or 1.32?
Compare digit by digit from the left. Ones equal. Tenths: \(2<3\). So \(1.23<1.32\); 1.32 is larger.
Q4. Among 3.56, 3.65, 3.099 — which is closest to 4?
Distances from 4: 0.44, 0.35, 0.901. Smallest is 0.35. 3.65 is closest to 4.
Competency-Based Questions
Scenario: A science teacher hands out readings from a digital calliper. Four students measure the thickness of a coin as 1.84 mm, 1.8 mm, 1.804 mm and 1.840 mm.
Q1. Which two readings are exactly equal?
L3 Apply(b) — trailing zero does not change value. 1.84 = 1.840.
Q2. Arrange all four readings in ascending order and analyse whether they agree to the nearest hundredth.
L4 Analyse1.8 < 1.804 < 1.84 = 1.840. To the nearest hundredth: 1.80, 1.80, 1.84, 1.84 — the first two agree and the last two agree, but not all four.
Q3. A student claims that 1.9 is larger than 1.84 because 9 > 84 is false, but "9 hundredths is less than 84 hundredths". Evaluate this reasoning.
L5 EvaluateThe student confuses place values. In 1.9 the 9 is in the tenths place, not hundredths. 1.9 = 1.90 = 90 hundredths after the point; 1.84 = 84 hundredths. So 1.9 > 1.84. The reasoning is wrong; the conclusion should be the opposite.
Q4. Design a decimal "zoom" strip: starting between 2 and 3, show exactly where 2.7, 2.74 and 2.748 would fall, using three increasing levels of zoom.
L6 CreateLevel 1: 2 to 3 split into tenths; mark 2.7 at the seventh tick. Level 2: 2.7 to 2.8 split into hundredths; mark 2.74 at the fourth tick. Level 3: 2.74 to 2.75 split into thousandths; mark 2.748 at the eighth tick.
Assertion–Reason Questions
A: 0.50 and 0.5 represent the same number.
R: Adding a zero after the last digit past the decimal point adds a term of the form \(0\times\frac{1}{10^n}\), which is zero.
R: Adding a zero after the last digit past the decimal point adds a term of the form \(0\times\frac{1}{10^n}\), which is zero.
(a) — Both true; R explains why trailing zeros don't change value.
A: The decimal 1.009 is greater than 1.09.
R: In decimal comparison, the number with more digits after the decimal point is always larger.
R: In decimal comparison, the number with more digits after the decimal point is always larger.
(d) — A is false (\(1.009 < 1.090\)); R is a common misconception, also false. Comparison is digit-by-digit after aligning.
Frequently Asked Questions
What is a hundredth in Class 7 Maths?
A hundredth is one of 100 equal parts of a whole, written as 0.01 or 1/100. Seven hundredths is 0.07 or 7/100. NCERT Class 7 Ganita Prakash Chapter 3 explains hundredths after tenths to build a full place-value picture.
How is 0.45 read aloud?
0.45 is read as 'zero point four five' or 'forty-five hundredths'. The 4 is in the tenths place and the 5 is in the hundredths place, so 0.45 = 4/10 + 5/100 = 45/100. NCERT Class 7 Chapter 3 uses this reading.
What does decimal notation mean?
Decimal notation writes numbers using a decimal point to separate whole and fractional parts. It uses base-10 positions extending rightwards as tenths, hundredths, thousandths. NCERT Class 7 Ganita Prakash Chapter 3 treats notation as a compact way to express fractions with power-of-ten denominators.
How do you convert 3/100 to decimal?
3/100 is 3 hundredths. Place 3 in the hundredths column: 0.03. If the fraction were 30/100, it would be 0.30 or 0.3 (three tenths). NCERT Class 7 Chapter 3 shows this conversion step by step.
What is the difference between 0.5 and 0.05?
0.5 is five tenths = 5/10 = 1/2. 0.05 is five hundredths = 5/100 = 1/20. So 0.5 is ten times 0.05. Misreading place value causes errors. NCERT Class 7 Ganita Prakash Chapter 3 highlights this distinction.
How many hundredths are in one tenth?
One tenth equals ten hundredths: 0.1 = 0.10 = 10/100. Moving one place to the right divides by 10. NCERT Class 7 Ganita Prakash Chapter 3 uses place-value grids to make this clear.
Frequently Asked Questions — A Peek Beyond the Point
What is Hundredths and Decimal Notation in NCERT Class 7 Mathematics?
Hundredths and Decimal Notation is a key concept covered in NCERT Class 7 Mathematics, Chapter 3: A Peek Beyond the Point. This lesson builds the student's foundation in the chapter by explaining the core ideas with worked examples, definitions, and step-by-step methods aligned to the CBSE curriculum.
How do I solve problems on Hundredths and Decimal Notation step by step?
To solve problems on Hundredths and Decimal Notation, follow the NCERT method: identify the given quantities, choose the relevant formula or theorem, substitute values carefully, and simplify. Class 7 exercises gradually increase in difficulty — start with solved NCERT examples before attempting exercise questions, and always verify your answer by substitution or diagram.
What are the most important formulas for Chapter 3: A Peek Beyond the Point?
The essential formulas of Chapter 3 (A Peek Beyond the Point) are listed in the chapter summary and highlighted throughout the lesson in formula boxes. Memorise them and practise at least 2–3 problems per formula. CBSE board exams frequently test direct application as well as combined use of multiple formulas from this chapter.
Is Hundredths and Decimal Notation important for the Class 7 board exam?
Hundredths and Decimal Notation is part of the NCERT Class 7 Mathematics syllabus and appears in CBSE board exams. Questions typically include short-answer, long-answer, and competency-based items. Review the NCERT examples, exercise questions, and previous-year board problems on this topic to prepare confidently.
What mistakes should students avoid in Hundredths and Decimal Notation?
Common mistakes in Hundredths and Decimal Notation include skipping steps, misapplying formulas, sign errors, and losing track of units. Write each step clearly, double-check algebraic manipulations, and re-read the question after solving to verify that your answer matches what was asked.
Where can I find more NCERT practice questions on Hundredths and Decimal Notation?
End-of-chapter NCERT exercises for Hundredths and Decimal Notation cover all difficulty levels tested in CBSE exams. After completing them, try the examples again without looking at the solutions, attempt the NCERT Exemplar questions for Chapter 3, and solve at least one previous-year board paper to consolidate your understanding.
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