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Samacheer Kalvi 7th Maths (Term 2) Number System Exercise Solutions

Complete Samacheer Kalvi 7th Maths Term 2 Chapter 1 Number System exercise solutions — decimals, fractions, place value, comparison, number line solved step-by-step.

Updated 12 June 202615 min read

Exercise Solutions Available

Step-by-step answers for all textbook questions in this chapter

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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

Solution

100 paise = ₹1

So 1 paise = ₹(1/100) = ₹0.01

4 paise = 4 × ₹0.01 = ₹0.04

Answer₹0.04

(ii) 4 rupees 4 paise

Solution

4 rupees = ₹4.00

4 paise = 4/100 rupees = ₹0.04

Total = ₹4.00 + ₹0.04 = ₹4.04

Answer₹4.04

(iii) 44 rupees 44 paise

Solution

44 rupees = ₹44.00

44 paise = 44/100 rupees = ₹0.44

Total = ₹44.00 + ₹0.44 = ₹44.44

Answer₹44.44

(iv) 50 paise

Solution

50 paise = 50/100 rupees = ₹0.50

Answer₹0.50

(v) 625 paise

Solution

625 paise = 625/100 rupees = ₹6.25

Answer₹6.25

Q2. Express 7 cm in metres and kilometres.

Solution

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

Answer7 cm = 0.07 m = 0.00007 km

Q3. Write in expanded form:

(i) 30.04

Solution

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)

Answer3 × 10 + 0 × 1 + 0 × (1/10) + 4 × (1/100)

(ii) 3.04

Solution
  • 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)

Answer3 × 1 + 0 × (1/10) + 4 × (1/100)

(iii) 300.04

Solution
  • 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)

Answer3 × 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

Solution

In 2.47, the digit 2 is in the ones place.

Place value of 2 = 2 × 1 = 2

Answer2 (ones place)

(ii) 26.89

Solution

In 26.89, the digit 2 is in the tens place.

Place value of 2 = 2 × 10 = 20

Answer20 (tens place)

(iii) 36.28

Solution

In 36.28, the digit 2 is in the tenths place.

Place value of 2 = 2 × (1/10) = 0.2

Answer0.2 (tenths place)

Exercise 1.2 — Decimals and Fractions

Q1. Express as fractions:

(i) 3.6 litres

Solution

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)

Answer3⅗ litres (or 18/5 litres)

(ii) 9.63 mg

Solution

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).

Answer963/100 mg (or 9 63/100 mg)

Q2. Convert to decimal:

(i) Three hundred three and nine hundredths

Solution

"Three hundred three" = 303

"Nine hundredths" = 9/100 = 0.09

Combined: 303 + 0.09 = 303.09

Answer303.09

(ii) Six and fifty-five thousandths

Solution

"Six" = 6

"Fifty-five thousandths" = 55/1000 = 0.055

Combined: 6 + 0.055 = 6.055

Answer6.055

Q3. Find the decimal form:

(i) 194 + 20 + 3 + 7/10 + 2/100

Solution

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

Answer217.72

(ii) 111 + 11 + 1 + 1/10 + 1/1000

Solution

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

Answer123.101

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)?

Solution

Maya's total: 5.300 + 3.250 = 8.550 kg

Step-by-step addition:

5.300 + 3.250 ------- 8.550

Diya's total: 4.800 + 4.150 = 8.950 kg

Step-by-step addition:

4.800 + 4.150 ------- 8.950

Compare: 8.950 kg > 8.550 kg

AnswerDiya bought more fruits (8.950 kg vs 8.550 kg)

Q2. Which is greater: 28 km or 42.6 km?

Solution

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.)

Answer42.6 km is greater

Additional comparison example: Which is greater: 12.45 or 12.5?

Solution

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.)

Answer12.5 is greater

Exercise 1.4 — Number Line

Q1. Show the following numbers on a number line: 0.2, 1.8, 1.1, 2.6

Solution

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

AnswerOn the number line, the numbers appear in order: 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.

Solution

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)
AnswerA = 0.5, B = 1.2, C = 2.3, D = 2.8, E = 3.4, F = 3.9

Additional Word Problems

Q1. A ribbon is 2.5 m long. If 0.75 m is cut off, how much ribbon remains?

Solution

Remaining length = Total length − Cut length

= 2.50 − 0.75

Step-by-step subtraction:

2.50 − 0.75 ------- 1.75
WorkingBorrow 1 from the 5 in tenths place (making it 4), then 10 − 5 = 5 in hundredths. Then 4 − 7: borrow from 2 (making it 1), then 14 − 7 = 7 in tenths. Finally 1 − 0 = 1 in ones.
Answer1.75 m of ribbon remains

Q2. Add: 15.75 + 23.4 + 6.125

Solution

Align decimal points and add zeros as placeholders:

15.750 + 23.400 + 6.125 -------- 45.275

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
Answer45.275

Q3. Which is greater: 0.5 or 0.05?

Solution

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.

Answer0.5 is greater than 0.05

Q4. Convert 3/8 to a decimal.

Solution

Divide 3 by 8:

0.375 ------ 8 ) 3.000 24 (8 × 3 = 24) --- 60 56 (8 × 7 = 56) --- 40 40 (8 × 5 = 40) -- 0

3/8 = 0.375

Answer0.375

Q5. Multiply: 2.5 × 1.2

Solution

Step 1: Ignore decimal points and multiply: 25 × 12

25 × 12 ---- 50 (25 × 2) 250 (25 × 10) ---- 300

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

Answer3.00 (or 3)

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

Solution

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.

Answer(b) 5 hundredths

Q2. 0.03 expressed as a fraction is:

(a) 3/10  (b) 3/1000  (c) 3/100  (d) 30/100

Solution

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).

Answer(c) 3/100

Q3. Which is greater: 1.09 or 1.9?

(a) 1.09  (b) 1.9  (c) Both are equal  (d) Cannot be compared

Solution

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.

Answer(b) 1.9

Q4. 2.5 + 3.75 equals:

(a) 5.25  (b) 6.75  (c) 6.25  (d) 5.75

Solution
2.50 + 3.75 ------ 6.25

Working from right: 0 + 5 = 5, 5 + 7 = 12 (write 2, carry 1), 2 + 3 + 1 = 6.

Answer(c) 6.25

Q5. 5.00 − 2.83 equals:

(a) 2.17  (b) 3.17  (c) 2.83  (d) 3.83

Solution
5.00 − 2.83 ------ 2.17

Working from right: 0 − 3: borrow, 10 − 3 = 7. Then 9 − 8 = 1. Then 4 − 2 = 2.

Answer(a) 2.17

True or False

1. 0.5 = 0.50

Solution

0.5 = 5/10 = 50/100 = 0.50. Adding a trailing zero after the decimal does not change the value.

AnswerTrue

2. In 6.07, the digit 7 is in the tenths place.

Solution

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.

AnswerFalse (7 is in the hundredths place)

3. The decimal 0.4 is equal to 4/10.

Solution

0.4 = 4/10. This is correct by definition of decimal notation.

Simplifying: 4/10 = 2/5.

AnswerTrue

4. 3.2 > 3.19

Solution

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)

AnswerTrue

5. 0.01 is greater than 0.1.

Solution

0.01 = 1/100 and 0.1 = 1/10 = 10/100.

Since 1/100 < 10/100, we have 0.01 < 0.1.

AnswerFalse (0.01 is less than 0.1)

Fill in the Blanks

1. The decimal 0.25 is equal to the fraction ___.

Solution

0.25 = 25/100

Simplify: 25/100 = (25 ÷ 25)/(100 ÷ 25) = 1/4

Answer1/4

2. In 12.34, the digit 3 is in the ___ place.

Solution

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)
Answertenths

3. 7 cm = ___ m.

Solution

1 m = 100 cm, so 7 cm = 7/100 m = 0.07 m.

Answer0.07

4. To compare decimals, start from the ___ place.

Solution

When comparing decimal numbers, always start from the leftmost (highest) place value and compare digit by digit moving right.

Answerleftmost (or ones)

5. 625 paise = ₹___.

Solution

100 paise = ₹1

625 paise = 625/100 rupees = ₹6.25

Answer6.25

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)

Frequently Asked Questions

Start from the leftmost digit and compare each place value. If the whole number parts differ, the larger whole number gives the larger decimal. If whole parts are equal, compare tenths, then hundredths, and so on.