CBSE Important Questions Class 7 Maths Chapter 3 A Peek Beyond the Point

CBSE Important Questions Class 7 Maths Chapter 3 – A Peek Beyond the Point

Class 7 Maths Chapter 3 A Peek Beyond the Point is a chapter of the new NCERT (National Council of Educational Research and Training) textbook Ganita Prakash. It introduces tenths and hundredths, the parts of a number that come after the decimal point. Students learn to read such numbers in words, to add and subtract them, to compare and arrange lengths, and to read measurements on a ruler or scale.

These CBSE important questions for Class 7 Maths Chapter 3 include writing numbers in words, sums and differences of tenths and hundredths, comparing fish lengths, number sequences, marking lengths on a scale and reading a ruler. Every question has a clear step-by-step answer in simple English, so students can practise on their own, parents can check the working, and teachers can use them in class. A free printable PDF of these important questions is also available on this page.

CBSE Important Questions Class 7 Maths Chapter 3 A Peek Beyond the Point

A Peek Beyond the Point (New NCERT)

Medium

Q.

Measure the following objects using a scale and write their measurements in centimeters (as shown earlier for the lengths of the screws): pen, sharpener, and any other object of your choice.

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A Peek Beyond the Point (New NCERT)

Medium

Q.

Identify and write the decimal numbers against the letters.

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A Peek Beyond the Point (New NCERT)

Medium

Q.

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

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A Peek Beyond the Point (New NCERT)

Medium

Q.

If you watch cricket, you might have noticed decimal-looking numbers like ‘Overs left: 5.5’. Does this mean 5 overs and 5 balls or 5 overs and 3 balls? Here, 5.5 overs means  $$5$$​$$\frac{5}{6}$$​ overs (as 1 over = 6 balls), i.e., 5 overs and 5 balls
Where else can we see such 'non-decimals' with a decimal-like notation?

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A Peek Beyond the Point (New NCERT)

Medium

Q.

Claim: If we add two decimal numbers, then the sum will always be greater than the sum of their whole number parts. Also, the sum will always be less than 2 more than the sum of their whole number parts.
What about for the sum of 25.93603259 and 8.202? 

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A Peek Beyond the Point (New NCERT)

Medium

Q.

What do you think about this claim? Verify if this is true for these numbers. Will it work for any 2 decimal numbers? (Claim: If we add two decimal numbers, then the sum will always be greater than the sum of their whole number parts. Also, the sum will always be less than 2 more than the sum of their whole number parts.)

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A Peek Beyond the Point (New NCERT)

Medium

Q.

Similarly, identify the change and write the next 3 terms for each sequence given below. Try to do this computation mentally.

(a) 4.4, 4.45, 4.5, ...

(b) 25.75, 26.25, 26.75, ...

(c) 10.56, 10.67, 10.78, ...

(d) 13.5, 16, 18.5, ...

(e) 8.5, 9.4, 10.3, ...

(f) 5, 4.95, 4.90, ...

(g) 12.45, 11.95, 11.45, ...

(h) 36.5, 33, 29.5, ....

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A Peek Beyond the Point (New NCERT)

Medium

Q.

Write the detailed place value computation for 84.691 – 77.345, and its compact form.

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A Peek Beyond the Point (New NCERT)

Medium

Q.

Which of the above is closest to 1.09 among 0.9, 1.1, 1.01, and 1.11?

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A Peek Beyond the Point (New NCERT)

Medium

Q.

Can we write$$\;\rm 1\; mm=\frac{1}{1000}\; m$$​?

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A Peek Beyond the Point (New NCERT)

Medium

Q.

Arrange these lengths in increasing order:

(a)$$\;\frac{9}{10}$$​​

(b)$$\;1 \frac{7}{10}$$​​

(c)$$\;\frac{130}{10}$$​​

(d)$$\;13 \frac{1}{10}$$​​

(e)$$\;10 \frac{5}{10}$$​​

(f)$$\;7 \frac{6}{10}$$​​

(g)$$\;6 \frac{7}{10}$$​​

(h)$$\;\frac{4}{10}$$​​

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A Peek Beyond the Point (New NCERT)

Medium

Q.

Fill in the blanks below ( mm <–> cm )

12 mm = 1.2 cm	56 mm = 5.6 cm	70 mm = ____________
____________ = 0.9 cm	134 mm = ____________	____________ = 203.6 cm

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A Peek Beyond the Point (New NCERT)

Medium

Q.

Make a place value table similar to the one above. Write each quantity in decimal form and in terms of place value and read the number:

(a) 2 ones, 3 tenths and 5 hundredths

(b) 1 ten and 5 tenths

(c) 4 ones and 6 hundredths

(d) 1 hundred, 1 one and 1 hundredth

(e)$$\rm \;\frac{8}{100}\; and\; \frac{9}{10}$$​​

(f)$$\;\frac{5}{100}$$​​

(g)$$\;\frac{1}{10}$$​​

(h)$$\rm \;2 \frac{1}{100^{\prime}}, 4 \frac{1}{10}\;and\;7 \frac{1}{1000}$$​​

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A Peek Beyond the Point (New NCERT)

Medium

Q.

We can ask similar questions about fractional parts:
(a) How many hundredths make one unit?
(b) How many tenths make one unit?
(c) How many tenths make one hundredth?
(d) How many hundredths make one tenth?

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A Peek Beyond the Point (New NCERT)

Medium

Q.

We can ask similar questions about fractional parts:
(a) How many thousandths make one unit?
(b) How many thousandths make one tenth?
(c) How many thousandths make one hundredth?
(d) How many tenths make one ten?
(e) How many hundredths make one ten?

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A Peek Beyond the Point (New NCERT)

Medium

Q.

Can we extend this further?

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A Peek Beyond the Point (New NCERT)

Medium

Q.

How many one-hundredths make one-tenth? Can we also say that the length is 4 units and 45 one-hundredths? (Length is 4 units and 4 one-tenths and 5 one-hundredths)

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A Peek Beyond the Point (New NCERT)

Medium

Q.

Observe the given sequences of numbers. Identify the change after each term and extend the pattern:

(a)$$\;4,\,4 \frac{3}{10}, \,4 \frac{6}{10},\;\;...........$$​​

(b)$$\;8 \frac{2}{10}, \;8 \frac{7}{10}, \,9 \frac{2}{10},\;\;...........$$​​

(c)$$\;7 \frac{6}{10},\, 8 \frac{7}{10},\;\;...........$$​​

(d)$$\;5 \frac{7}{10}, \,5 \frac{4}{10}, \;\;...........$$​​

(e)$$\;13 \frac{5}{10},\; 13,\;12 \frac{5}{10},\;\;...........$$​​

(f)$$\;11 \frac{5}{10},\, 10 \frac{4}{10}, \,9 \frac{3}{10},\;\;...........$$​​

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A Peek Beyond the Point (New NCERT)

Medium

Q.

Arrange the following lengths in increasing order:$$\;4 \frac{1}{10}, \,\frac{4}{10},\, \frac{41}{10},\, 41 \frac{1}{10}.$$​​

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A Peek Beyond the Point (New NCERT)

Medium

Q.

Write the following fractions in decimal form:

(a)$$\;\frac{1}{2}$$​​

(b)$$\;\frac{3}{2}$$​​

(c)$$\;\frac{1}{4}$$​​

(d)$$\;\frac{3}{4}$$​​

(e)$$\;\frac{1}{5}$$​​

(f)$$\;\frac{4}{5}$$​​

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Q1. Write the given lengths in words.
(i) 2 + 1/10 + 5/100
(ii) 6 + 19/100
(iii) 118/100

Answer: (i) 2 + 1/10 + 5/100: Two and one-tenth and five-hundredths
(ii) 6 + 19/100: Six and nineteen-hundredths
(iii) 118/100: One hundred and eighteen-hundredths

Q2. Find the sum and the difference for the following.
(i) 15 + 6/10 + 15/100 and 13 + 2/10 + 1/100 (sum)
(ii) 8 + 15/100 and 2 + 3/100 (difference)

Answer: (i) Add the whole numbers, the tenths and the hundredths separately:
(15 + 13) + (6/10 + 2/10) + (15/100 + 1/100) = 28 + 8/10 + 16/100
16/100 = 10/100 + 6/100 = 1/10 + 6/100, so the sum = 28 + 9/10 + 6/100
(ii) (8 − 2) + (15/100 − 3/100) = 6 + 12/100
The difference = 6 + 12/100

Q3. A Celestial Pearl Danio's length is 3 6/10 cm, and the length of the Philippine Goby is 7/10 cm. What is the difference in their lengths?

Answer: Length of the Celestial Pearl Danio = 3 6/10 cm = 36/10 cm
Length of the Philippine Goby = 7/10 cm
Difference = 36/10 − 7/10 = 29/10 cm = 2 9/10 cm

Q4. Arrange the given lengths in ascending order.
7 6/10, 6 7/10, 130/10, 13 1/10

Answer: Write all the lengths as fractions with denominator 10:
7 6/10 = 76/10, 6 7/10 = 67/10, 130/10 stays 130/10, 13 1/10 = 131/10
When the denominators are the same, the fraction with the smaller numerator is smaller. Arranging the numerators: 67, 76, 130, 131.
So the ascending order is 6 7/10, 7 6/10, 130/10, 13 1/10.

Q5. In the given sequence, identify the change after each term and write the next three terms.
13 6/10, 12 5/10, 11 4/10

Answer: 13 6/10 − 12 5/10 = 1 1/10 and 12 5/10 − 11 4/10 = 1 1/10. So each term is 1 1/10 less than the term before it (the whole number goes down by 1 and the tenths go down by 1).
The next three terms are 10 3/10, 9 2/10 and 8 1/10.
The sequence is 13 6/10, 12 5/10, 11 4/10, 10 3/10, 9 2/10, 8 1/10.

Q6. We can ask similar questions about fractional parts:
(a) How many hundredths make one unit?
(b) How many tenths make one unit?
(c) How many tenths make one hundredth?
(d) How many hundredths make one tenth?

Answer: (a) Since 1/100 × 100 = 1, 100 hundredths make one unit.
(b) Since 1/10 × 10 = 1, 10 tenths make one unit.
(c) Since 1/10 × 1/10 = 1/100, one-tenth of a tenth makes one hundredth.
(d) Since 1/100 × 10 = 1/10, 10 hundredths make one tenth.

Q7. Find the sums and differences:
(a) 3/10 + 3 + 4/100
(b) (9 + 5/10 + 7/100) + (2 + 1/10 + 3/100)
(c) (15 + 6/10 + 4/100) + (14 + 3/10 + 6/100)
(d) (7 + 7/100) − (4 + 4/100)
(e) (8 + 6/100) − (5 + 3/100)
(f) (12 + 6/10 + 2/100) − (9/10 + 9/100)

Answer: (a) 3/10 = 30/100, so 3 + 30/100 + 4/100 = 3 + 34/100 = 3 34/100
(b) (9 + 2) + (5/10 + 1/10) + (7/100 + 3/100) = 11 + 6/10 + 10/100 = 11 + 6/10 + 1/10 = 11 + 7/10 = 11 7/10
(c) (15 + 14) + (6/10 + 3/10) + (4/100 + 6/100) = 29 + 9/10 + 10/100 = 29 + 9/10 + 1/10 = 29 + 1 = 30
(d) (7 − 4) + (7/100 − 4/100) = 3 + 3/100 = 3 3/100
(e) (8 − 5) + (6/100 − 3/100) = 3 + 3/100 = 3 3/100
(f) 12 + 6/10 + 2/100 = 12 + 62/100 and 9/10 + 9/100 = 99/100. Since 62/100 is less than 99/100, borrow 1 from 12: 11 + 162/100 − 99/100 = 11 + 63/100 = 11 63/100

Q8. Solve this by converting to hundredths: 25 9/10 − (6 + 4/10 + 7/100)

Answer: 25 9/10 = 25 90/100 (because 9/10 = 90/100)
6 + 4/10 + 7/100 = 6 + 40/100 + 7/100 = 6 47/100
25 90/100 − 6 47/100 = (25 − 6) + (90/100 − 47/100) = 19 + 43/100 = 19 43/100

Q9. (a) What will be the sum of 15 + 3/10 + 4/100 and 2 + 6/10 + 8/100?
(b) Are both these methods different?

Answer: (a) Method 1 (adding the parts separately):
(15 + 2) + (3/10 + 6/10) + (4/100 + 8/100) = 17 + 9/10 + 12/100
12/100 = 10/100 + 2/100 = 1/10 + 2/100, so the sum = 17 + 9/10 + 1/10 + 2/100 = 17 + 10/10 + 2/100 = 17 + 1 + 2/100 = 18 2/100
Method 2 (column method): write the numbers one below the other, add hundredths (4 + 8 = 12), tenths (3 + 6 = 9) and units (15 + 2 = 17). Carry 10 hundredths to the tenths (10 tenths), then carry 10 tenths to the units: 18 2/100.
(b) No, both methods use the same logic and give the same answer. They differ only in layout: Method 1 is written across the page, Method 2 is written in columns like we do for whole numbers.

Q10. In each group, identify the longest and the shortest lengths. Mark each length on the scale.
(a) 3/10, 3/100, 33/100
(b) 3 1/10, 30/10, 1 3/10
(c) 45/100, 54/100, 5/10, 4/10
(d) 3 6/10, 3 6/100, 3 6/10 6/100
(e) 8/10 2/100, 9/100, 1 8/100
(f) 7 3/10 5/100, 7 5/10, 7 41/100
(g) 65/10 15/100, 5 87/100, 5 7/100

(a) 3/10, 3/100, 33/100 3/10 = 30/100. Comparing 30/100, 3/100 and 33/100: longest length = 33/100, shortest length = 3/100.

(b) 3 1/10, 30/10, 1 3/10 3 1/10 = 31/10, 30/10 = 3, 1 3/10 = 13/10. Longest length = 3 1/10, shortest length = 1 3/10.

(c) 45/100, 54/100, 5/10, 4/10 5/10 = 50/100 and 4/10 = 40/100. Longest length = 54/100, shortest length = 40/100 (that is, 4/10).

(d) 3 6/10, 3 6/100, 3 6/10 6/100 3 6/10 = 36/10, 3 6/100 = 30/10 + 6/100, 3 6/10 6/100 = 36/10 + 6/100. Largest number = 3 6/10 6/100, smallest number = 3 6/100.

(e) 8/10 2/100, 9/100, 1 8/100 8/10 + 2/100 = 82/100, 9/100 and 1 8/100 = 108/100. Largest number = 1 8/100, smallest number = 9/100.

(f) 7 3/10 5/100, 7 5/10, 7 41/100 7 3/10 5/100 = 7 35/100, 7 5/10 = 7 50/100, 7 41/100. Largest number = 7 5/10, smallest number = 7 3/10 5/100.

(g) 65/10 15/100, 5 87/100, 5 7/100 65/10 + 15/100 = 66/10 + 5/100 = 6 65/100, 5 87/100 and 5 7/100. Largest number = 65/10 15/100, smallest number = 5 7/100.

Q11. For the lengths shown below, write the measurements and read out the measures in words.

Answer: First ruler: 5 3/10 7/100 = Five and three-tenths and seven-hundredths.
Second ruler: 15 3/100 = Fifteen and three-hundredths.

Q12. Observe the figure below. Notice the markings and the corresponding lengths written in the boxes when measured from 0. Fill the lengths in the empty boxes.

Answer: The distance from 0 to 1 is divided into 100 small parts, so each small mark is 1/100. Counting the marks from 0, the empty boxes are 55/100, 155/100, 164/100, 202/100 and 240/100.

Related Study Material on Extramarks

• CBSE Important Questions Class 7 Maths Chapter 1
• CBSE Important Questions Class 7 Maths Chapter 2
• CBSE Important Questions Class 7 Maths Chapter 4
• CBSE Important Questions Class 7 Maths Chapter 5
• CBSE Important Questions Class 7 Maths Chapter 6
• CBSE Important Questions Class 7 Maths Chapter 7
• CBSE Important Questions Class 7 Maths Chapter 8
• CBSE Important Questions Class 7 Maths Chapter 9
• CBSE Important Questions Class 7 Maths Chapter 10
• CBSE Important Questions Class 7 Maths Chapter 11