How to Use This Page
Work through each exercise in the Samacheer Kalvi textbook on your own first, then use the solutions below to verify your steps and answers. All questions from Chapter 1 (Number System — Term 2) are solved with full working. If your answer differs, trace back through the method to find where you went wrong.
Key Concepts (Quick Recap)
- Decimal notation: A decimal has a whole number part and a decimal (fractional) part separated by a decimal point — e.g., 4.56 = 4 + 0.56.
- Place value after the decimal: tenths (1/10), hundredths (1/100), thousandths (1/1000).
- Converting paise to rupees: 100 paise = ₹1, so divide paise by 100. Example: 625 paise = ₹6.25.
- Converting cm to m and km: 100 cm = 1 m, so cm ÷ 100 = m; 1,00,000 cm = 1 km, so cm ÷ 1,00,000 = km.
- Expanded form: Write each digit with its place value — e.g., 30.04 = 3 × 10 + 0 × 1 + 0 × (1/10) + 4 × (1/100).
- Comparing decimals: Start from the leftmost (highest) place value. Compare digit by digit. Pad with zeros if needed: 2.5 = 2.50.
- Fraction to decimal: Divide numerator by denominator. Example: 3/8 = 0.375.
- Decimal to fraction: Write the decimal as a fraction with a power-of-10 denominator and simplify. Example: 0.25 = 25/100 = 1/4.
- Number line: Decimals are placed between whole numbers — e.g., 0.5 is halfway between 0 and 1.
Exercise 1.1 — Decimal Notation and Place Value
Q1. Express as rupees using decimals:
(i) 4 paise
100 paise = ₹1
So 1 paise = ₹(1/100) = ₹0.01
4 paise = 4 × ₹0.01 = ₹0.04
(ii) 4 rupees 4 paise
4 rupees = ₹4.00
4 paise = 4/100 rupees = ₹0.04
Total = ₹4.00 + ₹0.04 = ₹4.04
(iii) 44 rupees 44 paise
44 rupees = ₹44.00
44 paise = 44/100 rupees = ₹0.44
Total = ₹44.00 + ₹0.44 = ₹44.44
(iv) 50 paise
50 paise = 50/100 rupees = ₹0.50
(v) 625 paise
625 paise = 625/100 rupees = ₹6.25
Q2. Express 7 cm in metres and kilometres.
In metres:
100 cm = 1 m, so 1 cm = 1/100 m
7 cm = 7/100 m = 0.07 m
In kilometres:
1,00,000 cm = 1 km, so 1 cm = 1/1,00,000 km
7 cm = 7/1,00,000 km = 0.00007 km
Q3. Write in expanded form:
(i) 30.04
Identify each digit with its place value:
- 3 is in the tens place → 3 × 10
- 0 is in the ones place → 0 × 1
- 0 is in the tenths place → 0 × (1/10)
- 4 is in the hundredths place → 4 × (1/100)
Expanded form: 30.04 = 3 × 10 + 0 × 1 + 0 × (1/10) + 4 × (1/100)
(ii) 3.04
- 3 is in the ones place → 3 × 1
- 0 is in the tenths place → 0 × (1/10)
- 4 is in the hundredths place → 4 × (1/100)
Expanded form: 3.04 = 3 × 1 + 0 × (1/10) + 4 × (1/100)
(iii) 300.04
- 3 is in the hundreds place → 3 × 100
- 0 is in the tens place → 0 × 10
- 0 is in the ones place → 0 × 1
- 0 is in the tenths place → 0 × (1/10)
- 4 is in the hundredths place → 4 × (1/100)
Expanded form: 300.04 = 3 × 100 + 0 × 10 + 0 × 1 + 0 × (1/10) + 4 × (1/100)
Q4. What is the place value of 2 in each of the following?
(i) 2.47
In 2.47, the digit 2 is in the ones place.
Place value of 2 = 2 × 1 = 2
(ii) 26.89
In 26.89, the digit 2 is in the tens place.
Place value of 2 = 2 × 10 = 20
(iii) 36.28
In 36.28, the digit 2 is in the tenths place.
Place value of 2 = 2 × (1/10) = 0.2
Exercise 1.2 — Decimals and Fractions
Q1. Express as fractions:
(i) 3.6 litres
3.6 = 3 + 0.6 = 3 + 6/10
Simplify 6/10: divide numerator and denominator by 2 → 3/5
So 3.6 litres = 3 + 3/5 = 3⅗ litres (or 18/5 litres as an improper fraction)
(ii) 9.63 mg
9.63 = 9 + 0.63 = 9 + 63/100
Since 63 and 100 have no common factors (63 = 7 × 9 = 7 × 3² and 100 = 2² × 5²), the fraction 63/100 is already in simplest form.
So 9.63 mg = 963/100 mg (as an improper fraction) or 9 63/100 mg (as a mixed fraction).
Q2. Convert to decimal:
(i) Three hundred three and nine hundredths
"Three hundred three" = 303
"Nine hundredths" = 9/100 = 0.09
Combined: 303 + 0.09 = 303.09
(ii) Six and fifty-five thousandths
"Six" = 6
"Fifty-five thousandths" = 55/1000 = 0.055
Combined: 6 + 0.055 = 6.055
Q3. Find the decimal form:
(i) 194 + 20 + 3 + 7/10 + 2/100
Add the whole numbers: 194 + 20 + 3 = 217
Convert fractions to decimals:
- 7/10 = 0.7
- 2/100 = 0.02
Total = 217 + 0.7 + 0.02 = 217.72
(ii) 111 + 11 + 1 + 1/10 + 1/1000
Add the whole numbers: 111 + 11 + 1 = 123
Convert fractions to decimals:
- 1/10 = 0.1
- 1/1000 = 0.001
Total = 123 + 0.1 + 0.001 = 123.101
Exercise 1.3 — Comparison of Decimals
Q1. Maya bought 5.300 kg of bananas and 3.250 kg of oranges. Diya bought 4.800 kg of apples and 4.150 kg of mangoes. Who bought more fruits (by total weight)?
Maya's total: 5.300 + 3.250 = 8.550 kg
Step-by-step addition:
Diya's total: 4.800 + 4.150 = 8.950 kg
Step-by-step addition:
Compare: 8.950 kg > 8.550 kg
Q2. Which is greater: 28 km or 42.6 km?
Compare the whole number parts:
- 28 → whole number part is 28
- 42.6 → whole number part is 42
Since 42 > 28, we immediately know 42.6 > 28.
(No need to compare decimal parts since the whole numbers are different.)
Additional comparison example: Which is greater: 12.45 or 12.5?
Whole number parts are equal: 12 = 12.
Compare tenths: 4 vs 5. Since 5 > 4, we have 12.5 > 12.45.
(Note: 12.5 = 12.50, and 50 hundredths > 45 hundredths.)
Exercise 1.4 — Number Line
Q1. Show the following numbers on a number line: 0.2, 1.8, 1.1, 2.6
Draw a number line from 0 to 3 with markings at every 0.1 (or at least every 0.5):
- 0.2: Mark 2 tenths from 0 (between 0 and 0.5, closer to 0)
- 1.1: Mark 1 tenth past 1 (just after 1)
- 1.8: Mark 8 tenths past 1 (between 1.5 and 2, closer to 2)
- 2.6: Mark 6 tenths past 2 (between 2.5 and 3, closer to 2.5)
The order on the number line from left to right: 0.2, 1.1, 1.8, 2.6
Q2. Identify the decimal numbers represented by points A, B, C, D, E, F on a number line from 0 to 4 with divisions at every 0.5.
With markings at 0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, and additional finer divisions:
Reading from left to right:
- A = 0.5 (halfway between 0 and 1)
- B = 1.2 (2 tenths past 1)
- C = 2.3 (3 tenths past 2)
- D = 2.8 (8 tenths past 2, or 2 tenths before 3)
- E = 3.4 (4 tenths past 3)
- F = 3.9 (9 tenths past 3, or just before 4)
Additional Word Problems
Q1. A ribbon is 2.5 m long. If 0.75 m is cut off, how much ribbon remains?
Remaining length = Total length − Cut length
= 2.50 − 0.75
Step-by-step subtraction:
Q2. Add: 15.75 + 23.4 + 6.125
Align decimal points and add zeros as placeholders:
Working from right to left:
- Thousandths: 0 + 0 + 5 = 5
- Hundredths: 5 + 0 + 2 = 7
- Tenths: 7 + 4 + 1 = 12 → write 2, carry 1
- Ones: 5 + 3 + 6 + 1 (carry) = 15 → write 5, carry 1
- Tens: 1 + 2 + 0 + 1 (carry) = 4
Q3. Which is greater: 0.5 or 0.05?
Method: Compare digit by digit from left.
Both have 0 in the ones place.
Compare tenths: 5 vs 0
Since 5 > 0, we have 0.5 > 0.05.
Alternative: 0.5 = 50/100 = 5/10, and 0.05 = 5/100. Clearly 5/10 > 5/100.
Q4. Convert 3/8 to a decimal.
Divide 3 by 8:
3/8 = 0.375
Q5. Multiply: 2.5 × 1.2
Step 1: Ignore decimal points and multiply: 25 × 12
Step 2: Count total decimal places in the original numbers.
- 2.5 has 1 decimal place
- 1.2 has 1 decimal place
- Total = 2 decimal places
Step 3: Place the decimal point so the result has 2 decimal places: 300 → 3.00
Multiple Choice Questions (MCQs)
Q1. The place value of 5 in 3.456 is:
(a) 5 ones (b) 5 hundredths (c) 5 tenths (d) 5 thousandths
In 3.456:
- 3 is in the ones place
- 4 is in the tenths place (4/10)
- 5 is in the hundredths place (5/100)
- 6 is in the thousandths place (6/1000)
The digit 5 is in the hundredths place. Its place value is 5 × (1/100) = 0.05.
Q2. 0.03 expressed as a fraction is:
(a) 3/10 (b) 3/1000 (c) 3/100 (d) 30/100
0.03 means 3 hundredths = 3/100.
Simplifying: 3/100 is already in lowest terms (3 and 100 share no common factor other than 1).
Q3. Which is greater: 1.09 or 1.9?
(a) 1.09 (b) 1.9 (c) Both are equal (d) Cannot be compared
Compare digit by digit:
- Ones place: 1 = 1 (equal)
- Tenths place: 0 vs 9 → 9 > 0
Since 9 > 0 in the tenths place, 1.9 > 1.09.
Note: 1.9 = 1.90, and 1.90 > 1.09.
Q4. 2.5 + 3.75 equals:
(a) 5.25 (b) 6.75 (c) 6.25 (d) 5.75
Working from right: 0 + 5 = 5, 5 + 7 = 12 (write 2, carry 1), 2 + 3 + 1 = 6.
Q5. 5.00 − 2.83 equals:
(a) 2.17 (b) 3.17 (c) 2.83 (d) 3.83
Working from right: 0 − 3: borrow, 10 − 3 = 7. Then 9 − 8 = 1. Then 4 − 2 = 2.
True or False
1. 0.5 = 0.50
0.5 = 5/10 = 50/100 = 0.50. Adding a trailing zero after the decimal does not change the value.
2. In 6.07, the digit 7 is in the tenths place.
In 6.07:
- 6 is in the ones place
- 0 is in the tenths place
- 7 is in the hundredths place
The digit 7 is in the hundredths place, not the tenths place.
3. The decimal 0.4 is equal to 4/10.
0.4 = 4/10. This is correct by definition of decimal notation.
Simplifying: 4/10 = 2/5.
4. 3.2 > 3.19
Compare: 3.2 vs 3.19
3.2 = 3.20 (adding trailing zero for easy comparison)
3.20 > 3.19 (since 20 hundredths > 19 hundredths)
5. 0.01 is greater than 0.1.
0.01 = 1/100 and 0.1 = 1/10 = 10/100.
Since 1/100 < 10/100, we have 0.01 < 0.1.
Fill in the Blanks
1. The decimal 0.25 is equal to the fraction ___.
0.25 = 25/100
Simplify: 25/100 = (25 ÷ 25)/(100 ÷ 25) = 1/4
2. In 12.34, the digit 3 is in the ___ place.
In 12.34:
- 1 is in the tens place
- 2 is in the ones place
- 3 is in the tenths place (3/10)
- 4 is in the hundredths place (4/100)
3. 7 cm = ___ m.
1 m = 100 cm, so 7 cm = 7/100 m = 0.07 m.
4. To compare decimals, start from the ___ place.
When comparing decimal numbers, always start from the leftmost (highest) place value and compare digit by digit moving right.
5. 625 paise = ₹___.
100 paise = ₹1
625 paise = 625/100 rupees = ₹6.25
Common Mistakes
1. Confusing tenths place (1/10) with hundredths place (1/100) — In 6.07, the 0 is in tenths and 7 is in hundredths. Students often reverse these, saying 7 is in tenths.
2. Not aligning decimal points when adding or subtracting — Always write numbers with decimal points aligned vertically. For example, adding 2.5 and 3.75 requires writing 2.50 + 3.75, not misaligning the digits.
3. Forgetting to add zeros as placeholders — When comparing 2.5 and 2.05, you must write 2.50 to see that 2.50 > 2.05. Treating both as having the same number of decimal places makes comparison straightforward.
4. Misplacing the decimal point when converting fractions to decimals — 3/8 = 0.375, not 3.8 or 0.38. Always perform the long division carefully and place the decimal point correctly.
5. Thinking 0.05 > 0.5 because 5 > 5 — This ignores place value. 0.5 has 5 in the tenths place (5/10), while 0.05 has 5 in the hundredths place (5/100). Since 5/10 > 5/100, we get 0.5 > 0.05.
6. Forgetting unit conversions — 1 metre = 100 cm and 1 km = 1,00,000 cm. When converting 7 cm to km, it is 7/1,00,000 = 0.00007 km, NOT 0.0007 km.
Exam Checklist
- [ ] Decimal notation and place value: identify tenths, hundredths, thousandths places
- [ ] Converting between fractions and decimals: fraction → decimal (divide), decimal → fraction (write as fraction with power-of-10 denominator, simplify)
- [ ] Comparing and ordering decimals: align decimal points, pad with zeros, compare left to right
- [ ] Addition and subtraction of decimals: align decimal points, add/subtract column by column
- [ ] Number line representation of decimals: position decimals between whole numbers
- [ ] Converting units: cm to m (÷100), cm to km (÷1,00,000), paise to rupees (÷100)
- [ ] Expanded form: writing each digit with its place value
Internal Links
- [Term 2 Measurements Solutions](/school/tamil-nadu-state-board/class/7/maths/solutions/term-2-measurements-exercise-solutions)
- [Term 2 Algebra Solutions](/school/tamil-nadu-state-board/class/7/maths/solutions/term-2-algebra-exercise-solutions)
- [All Class 7 Maths Solutions](/school/tamil-nadu-state-board/class/7/maths/solutions)
- [Class 7 Maths Subject Guide](/school/tamil-nadu-state-board/class/7/maths)