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Solutions

Overview

Step-by-step NCERT solutions for A Peek Beyond the Point (Chapter 3, NCERT Class 7 Mathematics) — every question and answer worked out in full, not just the final result. You can also read the A Peek Beyond the Point textbook chapter.

Solved

What these solutions cover

All 47 questions in A Peek Beyond the Point are solved in the PDF. Here's what's inside, exercise by exercise:

Measure Objects and Write Lengths

  1. Write the measurements of the objects shown in the picture (eraser, pencil, chalk placed above a ruler).

Lengths in Two Ways and Increasing Order

  1. Arrange the following lengths in increasing order:
    • (a) 9/10,
    • (b) 1 7/10,
    • (c) 130/10,
    • (d) 13 1/10,
    • (e) 10 5/10,
    • (f) 7 6/10,
    • (g) 6 7/10,
    • (h) 4/10.
  2. Arrange the following lengths in increasing order: 4 1/10, 4/10, 41/10, 41 1/10.
  3. The lengths of the body parts of a honeybee are given. Find its total length. Head: 2 3/10 units, Thorax: 5 4/10 units, Abdomen: 7 5/10 units.
  4. The length of Shylaja's hand is 12 4/10 units and her palm is 6 7/10 units. What is the length of the longest (middle) finger?
  5. A Celestial Pearl Danio's length is 2 4/10 cm, and the length of a Philippine Goby is 9/10 cm. What is the difference in their lengths?
  6. Observe the given sequences of numbers. Identify the change after each term and extend the pattern with 4 more terms:
    • (a) 4, 4 3/10, 4 6/10, …
    • (b) 8 2/10, 8 7/10, 9 2/10, …
    • (c) 7 6/10, 8 7/10, …
    • (d) 5 7/10, 5 3/10, …
    • (e) 13 5/10, 13, 12 5/10, …
    • (f) 11 5/10, 10 4/10, 9 3/10, …

Number Line Readings and Longest-Shortest

  1. Observe the figure. Notice the markings and the corresponding lengths written in the boxes when measured from 0. Fill the lengths in the empty boxes. (A number line with markings at 0, 1/10, 2/10, 1, 1 3/10, 2, showing 1/100, 20/100, 99/100, 130/100 in boxes.)
  2. For the lengths shown below write the measurements and read out the measures in words. (Four wires of different lengths shown against rulers.)
  3. In each group, identify the longest and the shortest lengths.
    • (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.
  4. 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.

Place Value Table and Decimal Notation

  1. How many thousandths make:
    • (a) one unit,
    • (b) one tenth,
    • (c) one hundredth,
    • (d) one ten,
    • (e) one hundred?
  2. Make a place value table. 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) 8/100 and 9/10,
    • (f) 5/100,
    • (g) 1/10,
    • (h) 2 1/100, 4 1/10, and 7 7/1000.
  3. Write these quantities in decimal form:
    • (a) 234 hundredths,
    • (b) 105 tenths.

Units of Measurement

  1. Fill in the blanks (mm ↔ cm): 12 mm = 1.2 cm, 56 mm = 5.6 cm, 70 mm = ___, ___ = 0.9 cm, 134 mm = ___, ___ = 203.6 cm.
  2. Fill in the blanks (cm ↔ m): 36 cm = ___, 50 cm = ___, ___ = 0.89 m, 4 cm = ___, 325 cm = ___, ___ = 2.07 m.
  3. How many mm does 1 metre have? Can we write 1 mm = 1/1000 m?
  4. Fill in the blanks (g ↔ kg): 465 g = ___, 68 g = ___, 1560 g = ___, 704 g = ___, ___ = 0.56 kg, ___ = 2.5 kg.
  5. Fill in the blanks (rupee ↔ paise): 10 p = ___, ___ p = ₹0.05, ___ p = ₹0.36, ___ = ₹0.50, 99 p = ___, 250 p = ___.

Locating and Comparing Decimals

  1. Name all the divisions between 1 and 1.1 on the number line.
  2. Identify and write the decimal numbers against the letters A, B, C, D on the number line (marks near 5, 5.1, 5.3, 5.4).
  3. Can you tell which of 0.2, 0.20, 0.200, 0.02, 0.002 is the smallest and which is the largest?
  4. Which of these are the same: 4.5, 4.05, 0.405, 4.050, 4.50, 4.005, 04.50?
  5. Identify the decimal number denoted by '?' in the last number line of Figure (b), where the innermost number line runs between 3.05 and 3.06.
  6. In the number line from 5 to 10, what decimal numbers do boxes 'a', 'b', and 'c' denote? (b = 7.5 is given.)
  7. Using similar reasoning find the decimal numbers in boxes d, e (between 8 and 8.1) and f, g, h (between 4.3 and 4.8).
  8. Which decimal number is greater?
    • (a) 1.23 or 1.32,
    • (b) 3.81 or 13.800,
    • (c) 1.009 or 1.090.
  9. Consider 0.9, 1.1, 1.01, 1.11.
    • (a) Which is closest to 1.09?
    • (b) Which among 3.56, 3.65, 3.099 is closest to 4?
    • (c) Which among 0.8, 0.69, 1.08 is closest to 1?

Addition and Subtraction of Decimals

  1. Find the sums:
    • (a) 5.3 + 2.6,
    • (b) 18 + 8.8,
    • (c) 2.15 + 5.26,
    • (d) 9.01 + 9.10,
    • (e) 29.19 + 9.91,
    • (f) 0.934 + 0.6,
    • (g) 0.75 + 0.03,
    • (h) 6.236 + 0.487.
  2. Find the differences:
    • (a) 5.6 − 2.3,
    • (b) 18 − 8.8,
    • (c) 10.4 − 4.5,
    • (d) 17 − 16.198,
    • (e) 17 − 0.05,
    • (f) 34.505 − 18.1,
    • (g) 9.9 − 9.09,
    • (h) 6.236 − 0.487.
  3. Continue this sequence and write the next 3 terms: 4.4, 4.8, 5.2, 5.6, 6.0, …
  4. Identify the change and write the next 3 terms for each sequence:
    • (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, …

More on the Decimal System — Figure it Out

  1. Convert the following fractions into decimals:
    • (a) 5/100,
    • (b) 16/1000,
    • (c) 12/10,
    • (d) 254/1000.
  2. Convert the following decimals into a sum of tenths, hundredths and thousandths:
    • (a) 0.34,
    • (b) 1.02,
    • (c) 0.8,
    • (d) 0.362.
  3. What decimal number does each letter represent in the number line (from 6.4 to 6.6, with marks at a, c, b)?
  4. Arrange the following quantities in descending order:
    • (a) 11.01, 1.011, 1.101, 11.10, 1.01
    • (b) 2.567, 2.675, 2.768, 2.499, 2.698
    • (c) 4.678 g, 4.595 g, 4.600 g, 4.656 g, 4.666 g
    • (d) 33.13 m, 33.31 m, 33.133 m, 33.331 m, 33.313 m.
  5. Using the digits 1, 4, 0, 8, and 6 make:
    • (a) the decimal number closest to 30,
    • (b) the smallest possible decimal number between 100 and 1000.
  6. Will a decimal number with more digits be greater than a decimal number with fewer digits?
  7. Mahi purchases 0.25 kg of beans, 0.3 kg of carrots, 0.5 kg of potatoes, 0.2 kg of capsicums, and 0.05 kg of ginger. Calculate the total weight.
  8. Pinto supplies 3.79 L, 4.2 L, and 4.25 L of milk in the first three days. In 6 days, he supplies 25 litres. Find the total quantity supplied in the last three days.
  9. Tinku weighed 35.75 kg in January and 34.50 kg in February. Has he gained or lost weight? How much is the change?
  10. Extend the pattern: 5.5, 6.4, 6.39, 7.29, 7.28, 8.18, 8.17, ___, ___
  11. How many millimeters make 1 kilometer?
  12. Indian Railways offers optional travel insurance at 45 paise per passenger. If 1 lakh people opt for insurance in a day, what is the total insurance fee paid?
  13. Which is greater?
    • (a) 10/1000 or 1/10,
    • (b) one-hundredth or 90 thousandths,
    • (c) one-thousandth or 90 hundredths.
  14. Write the decimal forms of the quantities mentioned (example given: 87 ones, 5 tenths and 60 hundredths = 88.10): (b) 12 tens and 12 tenths, (c) 10 tens, 10 ones, 10 tenths, and 10 hundredths, (d) 25 tens, 25 ones, 25 tenths, and 25 hundredths.
  15. Write the following fractions in decimal form:
    • (a) 1/2,
    • (b) 3/2,
    • (c) 1/4,
    • (d) 3/4,
    • (e) 1/5,
    • (f) 4/5.
Sample

Worked examples

3 questions from A Peek Beyond the Point, solved step by step.

Lengths in Two Ways and Increasing Order

Arrange the following lengths in increasing order: 4 1/10, 4/10, 41/10, 41 1/10.

Convert each to decimal:

4 1/10 = 4.1, 4/10 = 0.4, 41/10 = 4.1, 41 1/10 = 41.1

Note: 4 1/10 = 4.1 and 41/10 = 4.1 are equal.

Arranging in increasing order: 0.4 < 4.1 = 4.1 < 41.1

Answer: 4/10 < 4 1/10 = 41/10 < 41 1/10

Place Value Table and Decimal Notation

Write these quantities in decimal form: (a) 234 hundredths, (b) 105 tenths.

(a) 234 hundredths = 234/100 = 200/100 + 30/100 + 4/100 = 2 + 3/10 + 4/100 = 2.34

(b) 105 tenths = 105/10 = 100/10 + 5/10 = 10 + 5/10 = 10.5

Answer: (a) 2.34 | (b) 10.5

Locating and Comparing Decimals

Name all the divisions between 1 and 1.1 on the number line.

The segment from 1 to 1.1 represents 1 tenth.

If this tenth is divided into 10 equal parts, each part = 1/100.

The division marks between 1 and 1.1 are:

1.01, 1.02, 1.03, 1.04, 1.05, 1.06, 1.07, 1.08, 1.09

Answer: 1.01, 1.02, 1.03, 1.04, 1.05, 1.06, 1.07, 1.08, 1.09

All 47 questions in A Peek Beyond the Point are solved step by step in the Solutions PDF above.

Keep solving

More solutions in Ganita Prakash

01Large Numbers Around Us02Arithmetic Expressions04Expressions using Letter Numbers05Parallel and Intersecting Lines06Number Play07A Tale of Three Intersecting Lines08Working with Fractions09Geometric Twins10Operations with Integers11Finding Common Ground12Another Peek Beyond the Point13Connecting the Dots14Constructions and Tilings15Finding the Unknown
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More NCERT Solutions for Class 7

Read the A Peek Beyond the Point textbook chapter / PDF, or browse all NCERT Class 7 Mathematics solutions.

← PreviousCh 2: Arithmetic ExpressionsNext →Ch 4: Expressions using Letter Numbers

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