Understanding decimals and fractions is an integral part of building a strong foundation in mathematics. You need to have a proper understanding of what decimals and fractions are and how to convert them easily to start your mathematical journey in the higher classes. Class 7 Maths NCERT Chapter 3, 'A Peek beyond the Point', provides the students with a clear idea about the tenths, hundredths, and thousandths of a number, as well as the need for smaller units, their application in our everyday life, and how to compare them. Therefore, it is essential to understand this chapter with a proper understanding and clarity, and this is where the NCERT Solutions for Class 7 Maths come into play.
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These NCERT Solutions provide detailed and step-by-step explanations for the students. With the help of these Class 7 Maths Chapter 3 Solutions, they can practice the problems, verify their answer and strengthen their weak areas that need improvement. This will also clear their doubts and give them a proper idea about the concepts of the chapter. Students can refer to the NCERT Solutions for Class 7 to access the subject-wise solutions of Class 7.
Page number: 58 Number of Questions: 1 |
Figure it Out
Question: Find the sums and differences:
(a) $\frac{3}{10}+3 \frac{4}{100}$
(b) $9 \frac{5}{10} \frac{7}{100}+2 \frac{1}{10} \frac{3}{100}$
(c) $15 \frac{6}{10} \frac{4}{100}+14 \frac{3}{10} \frac{6}{100}$
(d) $7 \frac{7}{100}-4 \frac{4}{100}$
(e) $8 \frac{6}{100}-5 \frac{3}{100}$
(f) $12 \frac{6}{100} \frac{2}{100}-\frac{9}{10} \frac{9}{100}$
Solution:
(a) $\frac{3}{10}+3 \frac{4}{100}$
$=\frac{30}{100}+3+\frac{4}{100}$
$=3+\left(\frac{30}{100}+\frac{4}{100}\right)$
$=3+\frac{34}{100}=3 \frac{34}{100}$
(b) $9 \frac{5}{10} \frac{7}{100}+2 \frac{1}{10} \frac{3}{100}$
$=(9+2)+\left(\frac{5}{10}+\frac{1}{10}\right)+\left(\frac{7}{100}+\frac{3}{100}\right)$
$=11+\left(\frac{5+1}{10}\right)+\left(\frac{7+3}{100}\right)$
$=11+\frac{6}{10}+\frac{10}{100}$
$=11+\frac{6}{10}+\frac{1}{10}=11+\frac{7}{10}=11 \frac{7}{10}$
(c) $15 \frac{6}{10} \frac{4}{100}+14 \frac{3}{10} \frac{6}{100}$
$=(15+14)+\left(\frac{6}{10}+\frac{3}{10}\right)+\left(\frac{4}{100}+\frac{6}{100}\right)$
$=29+\left(\frac{6+3}{10}\right)+\left(\frac{4+6}{100}\right)$
$=29+\frac{9}{10}+\frac{10}{100}$
$=29+\frac{9}{10}+\frac{1}{10}$
$=29+\frac{10}{10}=29+1=30$
(d) $7 \frac{7}{100}-4 \frac{4}{100}$
$=(7-4)+\left(\frac{7}{100}-\frac{4}{100}\right)$
$=3+\frac{3}{100}=3 \frac{3}{100}$
(e) $8 \frac{6}{100}-5 \frac{3}{100}$
$=(8-5)+\left(\frac{6}{100}-\frac{3}{100}\right)$
$=3+\frac{3}{100}=3 \frac{3}{100}$
(f) $12 \frac{6}{10} \frac{2}{100}-\frac{9}{10} \frac{9}{100}$
$=12 \frac{62}{100}-\frac{99}{100}$
$=11+1+\frac{62}{100}-\left(\frac{99}{100}\right)$
$=11+\frac{100}{100}+\frac{62}{100}-\left(\frac{99}{100}\right)$
$=11+\frac{162}{100}-\left(\frac{99}{100}\right)$
$=11+\left(\frac{162}{100}-\frac{99}{100}\right)$
$=11+\frac{63}{100}=11 \frac{63}{100}$
Page number: 75 Number of Questions: 2 |
Figure it Out
Question 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
Solution:
(a) 5.3 + 2.6 = 7.9
(b) 18 + 8.8 = 26.8
(c) 2.15 + 5.26 = 7.41
(d) 9.01 + 9.10 = 18.11
(e) 29.19 + 9.91 = 39.10
(f) 0.934 + 0.6 = 1.534
(g) 0.75 + 0.03 = 0.78
(h) 6.236 + 0.487 = 6.723
Question 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
Solution:
(a) 5.6 – 2.3 = 3.3
(b) 18 – 8.8 = 9.2
(c) 10.4 – 4.5 = 5.9
(d) 17 – 16.198 = 0.802
(e) 17 – 0.05 = 16.95
(f) 34.505 – 18.1 = 16.405
(g) 9.9 – 9.09 = 0.81
(h) 6.236 – 0.487 = 5.749
Page number: 78 Number of Questions: 16 |
Figure it Out
Question 1: Convert the following fractions into decimals:
(a) $\frac{5}{100}$ (b) $\frac{16}{1000}$ (c) $\frac{12}{10}$ (d) $\frac{254}{1000}$
Solution:
(a) $\frac{5}{100}$ = 0.05
(b) $\frac{16}{1000}$ = 0.016
(c) $\frac{12}{10}$ = 1.2
(d) $\frac{254}{1000}$ = 0.254
Question 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
Solution:
(a) $0.34=\left(3 \times \frac{1}{10}\right)+\left(4 \times \frac{1}{100}\right)=\frac{3}{10}+\frac{4}{100}$
(b) $1.02=(1 \times 1)+\left(2 \times \frac{1}{100}\right)=1+\frac{2}{100}$
(c) $0.8=\left(8 \times \frac{1}{10}\right)=\frac{8}{10}$
(d) $0.362=\left(3 \times \frac{1}{10}\right)+\left(6 \times \frac{1}{100}\right)+\left(2 \times \frac{1}{1000}\right)=\frac{3}{10}+\frac{6}{100}+\frac{2}{1000}$
Question 3: What decimal number does each letter represent in the number line below?
Solution:
Total divisions between 6.4 and 6.6 = 8
Each division = $\frac{6.6-6.4}{8}$ = $\frac{0.2}{8}$ = $\frac{2}{80}$ = 0.025
Therefore,
$a=6.4+(2 \times 0.025)=6.4+0.050=6.425$
$c=6.4+(5 \times 0.025)=6.4+0.125=6.525$
$b=6.4+(6 \times 0.025)=6.4+0.150=6.550$
Question 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
Solution:
(a) $11.10>11.01>1.101>11.011>1.01$
(b) $2.768>2.698>2.675>2.567>2.499$
(c) $4.678 \mathrm{~g}>4.666 \mathrm{~g}>4.656 \mathrm{~g}>4.600 \mathrm{~g}>4.595 \mathrm{~g}$
(d) $33.331 \mathrm{~m}>33.313 \mathrm{~m}>33.31 \mathrm{~m}>33.133 \mathrm{~m}>33.13 \mathrm{~m}$
Question 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.
Solution:
(a) Possible numbers: 14.860,40.168
30 – 14.860 = 15.14
40.168 – 30 = 10.168
Therefore, 40.168 is the closest number to 30.
(b) The smallest possible decimal number between 100 and 1000 is 104.68.
Question 6: Will a decimal number with more digits be greater than a decimal number with fewer digits?
Solution:
Maybe, but not always. A number with more decimal digits can be smaller.
For Example:
0.12 has 2 decimal digits.
0.111 has 3 decimal digits.
But, 0.12 > 0.111
Question 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 of the items she bought.
Solution:
Total weight = (0.25 + 0.3 + 0.5 + 0.2 + 0.05) kg = 1.3 kg
Question 8: Pinto supplies 3.79 L, 4.2 L, and 4.25 L of milk to a milk dairy in the first three days. In 6 days, he supplies 25 litres of milk. Find the total quantity of milk supplied to the dairy in the last three days.
Solution:
Milk supplied in first 3 days = (3.79 + 4.2 + 4.25) L = 12.24 L
Milk supplied in 6 days = 25 L
Therefore, Milk supplied in the last three days = (25 – 12.24) L = 12.76 L
Question 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?
Solution:
Since 35.75 > 34.50,
Therefore, he has lost weight.
Change in weight = (35.75 – 34.50) kg = 1.25 kg
So, Tinku has lost 1.25 kg.
Question 10: Extend the pattern: 5.5, 6.4, 6.39, 7.29, 7.28, 6.18, 6.17, ____, _____
Solution:
Pattern alternates: +0.9, –0.01, +0.9, –0.01, –1.1, –0.01,
Therefore, the next two terms are: 5.07 (–1.1), 5.06 (–0.01).
Question 11: How many millimetres make 1 kilometre?
Solution:
1 km = 1000 m = (1000 × 1000) mm = 10,00,000 mm.
Question 12: Indian Railways offers optional travel insurance for passengers who book e-tickets. It costs 45 paise per passenger. If 1 lakh people opt for insurance in a day, what is the total insurance fee paid?
Solution:
45 paise = Rs 0.45
1 lakh = 1,00,000
The total insurance fee paid = (1,00,000 × 0.45) = Rs. 45,000
Question 13: Which is greater?
(a) $\frac{10}{1000}$ or $\frac{1}{10}$?
(b) One-hundredth or 90 thousandths?
(c) One-thousandth or 90 hundredths?
Solution:
(a) $\frac{10}{1000}=\frac{1}{100}=0.01$
$\frac{1}{10}=0.1$
Since $0.01<0.1$
Therefore, $\frac{10}{1000}<\frac{1}{10}$
(b) One-hundredth $=\frac{1}{100}=0.01$
90 thousandths $=\frac{90}{1000}=\frac{9}{100}=0.09$
Since $0.01<0.09$
$\therefore$ One-hundredth $<$ 90 thousandths.
(c) One thousandth $=\frac{1}{1000}=0.001$
90 hundredths $=\frac{90}{100}=\frac{9}{10}=0.9$
Since $0.001<0.9$
$\therefore$ One-thousandth < 90 hundredths.
Question 14: Write the decimal forms of the quantities mentioned (an example is given):
(a) 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
Solution:
(a) 87 ones, 5 tenths and 60 hundredths
$=(87 \times 1)+\left(5 \times \frac{1}{10}\right)+\left(60 \times \frac{1}{100}\right)$
$=87+\frac{5}{10}+\frac{6}{10}$
$=87+0.5+0.6=88.10$
(b) 12 tens and 12 tenths
$=(12 \times 10)+\left(12 \times \frac{1}{10}\right)$
$=120+\frac{12}{10}$
$=120+1.2=121.2$
(c) 10 tens, 10 ones, 10 tenths, and 10 hundredths
$\begin{aligned}
& =(10 \times 10)+(10 \times 1)+\left(10 \times \frac{1}{10}\right)+\left(10 \times \frac{1}{100}\right) \\
& =100+10+1+\frac{1}{10} \\
& =100+10+1+0.1 \\
& =111.1
\end{aligned}$
(d) 25 tens, 25 ones, 25 tenths, and 25 hundredths
$\begin{aligned}
& =(25 \times 10)+(25 \times 1)+\left(25 \times \frac{1}{10}\right)+\left(25 \times \frac{1}{100}\right) \\
& =250+25+\frac{25}{10}+\frac{25}{100} \\
& =250+25+2.5+0.25 \\
& =277.75
\end{aligned}$
Question 15: Using each digit 0 – 9 not more than once, fill the boxes below so that the sum is closest to 10.5:
Solution:
Question 16: 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) $\frac{4}{5}$
Solution:
(a) $\frac{1}{2}=\frac{1}{2} \times \frac{10}{10}=\frac{5}{10}=0.5$
(b) $\frac{3}{2} =\frac{3}{2} \times \frac{10}{10}=\frac{15}{10}=1.5$
(c) $\frac{1}{4} =\frac{1}{4} \times \frac{100}{100}=\frac{25}{100}=0.25$
(d) $\frac{3}{4} =\frac{3}{4} \times \frac{100}{100}=\frac{75}{100}=0.75$
(e) $\frac{1}{5} =\frac{1}{5} \times \frac{10}{10}=\frac{2}{10}=0.2$
(f) $\frac{4}{5} =\frac{4}{5} \times \frac{10}{10}=\frac{8}{10}=0.8$
The important topics that are covered in Class 7 Maths NCERT Chapter 3, A Peek Beyond the Point, are:
Given below are the chapter-wise NCERT solutions for class 7 mathematics, provided in one place:
The NCERT Solutions for Class 7, Subject-wise, can be downloaded using the links below.
Students can also check the NCERT Books and the NCERT Syllabus here:
Frequently Asked Questions (FAQs)
Yes, a reliable platform like Careers360 offers free downloadable Class 7 Maths Chapter 3 Solutions in PDF format. These solutions are accurate and easy to understand as they are made by experienced subject matter experts.
The important topics that are covered in Class 7 Maths NCERT Chapter 3, A Peek Beyond the Point, are:
A Peek beyond the Point Class 7 NCERT Solutions offer detailed, step-by-step explanations on identifying tenths, hundredths, and thousandths, and on comparing decimals accurately using number lines.
Class 7 Maths NCERT Chapter 3 includes multiple in-text exercises involving reading decimal lengths on scales, writing decimals in fractional form, and performing addition, subtraction of decimals.
Measurements like the lengths of screws, leaves, or fish illustrate why smaller units like tenths or hundredths are essential, helping learners link mathematics to the nature and objects around them.
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