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A Peek Beyond the Point – Class 7 Mathematics notes, important questions and MCQs

NCERT Class 7 Mathematics, chapter 3. Notes, key terms, important questions with answers and MCQs.

Chapter overview

Decimals extend place value to parts smaller than one: tenths, hundredths and thousandths. They are used for money, lengths and measurements.

Decimal place value

0.1 = 1/10, 0.01 = 1/100, 0.001 = 1/1000.
In 23.45: 2 tens, 3 ones, 4 tenths, 5 hundredths.
Trailing zeros do not change value: 0.5 = 0.50.

Comparing and converting

Compare digit by digit from the left after lining up the decimal points.
Convert units: 1 cm = 10 mm, 1 m = 100 cm, 1 kg = 1000 g; 250 g = 0.25 kg.
On a number line, 0.3 lies between 0 and 1, three steps of 0.1 from 0.

Key terms

Decimal point: dot separating whole part and fractional part
Tenths: first place after the decimal point
Hundredths: the second place after the decimal point, 1/100

Formulas

0.1 = 1/10, 0.01 = 1/100

Important questions with answers

Write 3/10 and 47/100 as decimals.2 marks

3/10 = 0.3 and 47/100 = 0.47.

Convert 3 m 45 cm into metres and 2 kg 50 g into kilograms.3 marks

3 m 45 cm = 3.45 m (100 cm = 1 m). 2 kg 50 g = 2.050 kg = 2.05 kg (1000 g = 1 kg).

Riya bought a notebook for ₹35.75, a pen for ₹12.50 and an eraser for ₹4.25. She paid ₹100. Find the total cost and the change. Arrange the three prices in ascending order.5 marks

Total = 35.75 + 12.50 + 4.25 = ₹52.50. Change = 100 − 52.50 = ₹47.50. Ascending order: ₹4.25 < ₹12.50 < ₹35.75.

Quick revision

Decimals are fractions with denominators 10, 100, 1000.
Line up decimal points to compare.
1 kg = 1000 g.

Exam tips

0.6 is greater than 0.45 — compare tenths first.
Write money with two decimal places: ₹7.50.

Practice MCQs

3 tenths written as a decimal is
1. 3.0
2. 30
3. 0.03
4. 0.3
Show answer
Answer: (d) 0.3. 3/10.
Which is greater?
1. 0.45
2. 0.5
3. equal
4. cannot say
Show answer
Answer: (b) 0.5. 5 tenths > 4 tenths.
75 cm in metres is
1. 0.75 m
2. 7.5 m
3. 0.075 m
4. 75 m
Show answer
Answer: (a) 0.75 m. 75 ÷ 100.
The place value of 6 in 12.068 is
1. 6 tenths
2. 6 hundredths
3. 6 thousandths
4. 6 ones
Show answer
Answer: (b) 6 hundredths. Second place after the point.
0.5 + 0.25 equals
1. 0.30
2. 7.5
3. 0.525
4. 0.75
Show answer
Answer: (d) 0.75. Line up the decimal points.
2 kg 45 g in kilograms is
1. 2.45 kg
2. 20.45 kg
3. 2.0045 kg
4. 2.045 kg
Show answer
Answer: (d) 2.045 kg. 45 g = 0.045 kg.
Arrange in ascending order: 0.7, 0.07, 0.707, 0.077
1. 0.707, 0.7, 0.077, 0.07
2. 0.7, 0.07, 0.077, 0.707
3. 0.077, 0.07, 0.7, 0.707
4. 0.07, 0.077, 0.7, 0.707
Show answer
Answer: (d) 0.07, 0.077, 0.7, 0.707. Compare tenths, then hundredths.
Which is the largest
1. 0.65
2. 0.7
3. 0.069
4. 0.607
Show answer
Answer: (b) 0.7. 0.700 is greatest.

All chapters of Class 7 Mathematics

Written by Kundali IQ from standard, well-established facts to help with revision. This is not an official NCERT publication; always read your textbook too.