The DAV Class 7 Maths Book Solutions Pdf and DAV Class 7 Maths Chapter 3 Worksheet 1 Solutions of Rational Numbers as Decimals offer comprehensive answers to textbook questions.
DAV Class 7 Maths Ch 3 WS 1 Solutions
Question 1.
Express the following rational numbers as decimals:
(i) \(\frac{9}{8}\)
Answer:
\(\frac{9}{8}=\frac{9 \times 125}{8 \times 125}\)
= \(\frac{1125}{1000}\)
= 1.125
(ii) \(\frac{615}{125}\)
Answer:
\(\frac{615}{125}=\frac{123}{25}=\frac{123 \times 4}{25 \times 4}\)
= \(\frac{492}{100}\)
= 4.92
(iii) \(\frac{1}{16}\)
Answer:
\(\frac{1}{16}=\frac{1 \times 625}{16 \times 625}\)
= \(\frac{-75}{100}\)
= 0.0625
(iv) \(\frac{-3}{4}\)
Answer:
\(\frac{-3}{4}=\frac{-3 \times 25}{4 \times 25}\)
= \(\frac{295}{1000}\)
= -0.75
(v) \(\frac{59}{200}\)
Answer:
\(\frac{59}{200}=\frac{59 \times 5}{200 \times 5}\)
= \(\frac{295}{1000}\)
= 0.295
(vi) \(\frac{-24}{25}\)
Answer:
\(\frac{-24}{25}=\frac{-24 \times 4}{25 \times 4}\)
= \(\frac{-96}{100}\)
= -0.96
(vii) \(\frac{-53}{250}\)
Answer:
\(\frac{-53}{250}=\frac{-53 \times 4}{250 \times 4}\)
= \(\frac{-212}{1000}\)
=-0.212
(viii) \(\frac{47}{400}\)
Answer:
\(\frac{47}{400}=\frac{47 \times 25}{400 \times 25}\)
= \(\frac{1175}{10000}\)
= 0.1175
(ix) \(\frac{27}{800}\)
Answer:
\(\frac{27}{800}=\frac{27 \times 125}{800 \times 125}\)
= \(\frac{3375}{100000}\)
= 0.03375
(x) \(\frac{139}{625}\)
Answer:
\(\frac{139}{625}=\frac{139 \times 16}{625 \times 16}\)
= \(\frac{2224}{10000}\)
=0.2224
(xi) \(\frac{3186}{1250}\)
Answer:
\(\frac{3186}{1250}=\frac{3186 \times 8}{1250 \times 8}\)
= \(\frac{25488}{10000}\)
= 2.5488
(xii) \(\frac{133}{25}\)
Answer:
\(\frac{133}{25}=\frac{133 \times 4}{25 \times 4}\)
= \(\frac{532}{100}\)
= 5.32
DAV Class 8 Maths Chapter 3 Worksheet 1 Notes
Conversion of a rational number into decimal form whose denominator is not 10 or a power of 10.
e.g. \(\frac{3}{5}=\frac{3 \times 2}{5 \times 2}\)
\(\frac{6}{10}\) = 0.6
Rational numbers whose denominators can not be converted into 10 or a power of 10 are represented in the form of decimal by using long division method. Such representations may be either terminating or non-terminating but repeating.
Terminating Decimals:
The rational numbers whose denominators are 2 or 5 as their prime factors are represented in the form of terminating decimal system.
e.g. \(\frac{13}{125}, \frac{26}{100}, \frac{37}{80}\) etc.
Non-terminating Decimals:
The rational numbers whose denominators are not 2 or 5 as their prime factors, are represented in the form of non-terminating decimal system using Long division method.
e.g. \(\frac{25}{36}, \frac{7}{3}, \frac{2}{7}\)
Non-terminating repeating decimal numbers:
Decimal numbers having an infinite number of decimal places and a set of digits in the decimal places that repeat are known as non- terminating repeating decimal numbers.
For example, 0.286715………… = \(0 . \overline{286715}\) is non-terminating repeating decimal number. After 5, the same digits, i.e., 2, 8, 6, 7, 1, 5 will keep on repeating again arid again.
To convert a terminating decimal into rational number perform the following steps:
- Count the number of decimal places in the given number.
- Write the given number without the decimal point.
- The denominator is one followed by as many zeroes as is the number of decimal places in the given number.
Example 1:
Convert \(\frac{3}{5}\) in decimal form.
Answer:
Here, the denominator is 5
∴ \(\frac{3}{5}=\frac{3 \times 2}{5 \times 2}\)
= \(\frac{6}{10}\) = 0.6
Example 2:
Represent the following rational numbers as decimals using division method.
(i) \(\frac{3}{8}\)
Answer:
∴ \(\frac{3}{8}\) = 0.375
(ii) \(\frac{17}{25}\)
Answer:
∴ \(\frac{17}{25}\) = 0.68
(iii) \(\frac{124}{40}\)
Answer:
∴ \(\frac{124}{40}\) = 3.1
Example 3:
Convert the following rational numbers in decimal form.
(i) \(\frac{3}{7}\)
Answer:
∴ \(\frac{3}{7}\) = 0.428571428571
= \(0 . \overline{428571}\) (Non-terminating and repeating decimal)
(ii) \(\frac{125}{3}\)
Answer:
∴ \(\frac{125}{3}\) = 41.666…………
= \(41 . \overline{6}\) (Non-terminating and repeating decimal)
(iii) \(\frac{1025}{24}\)
Answer:
∴ \(\frac{1025}{24}\) = 42.7083333….
= \(42.708 \overline{3}\) (Non-terminating and repeating decimal)
Example 4:
Without actual division, convert the following rational numbers into terminating decimals.
(i) \(\frac{45}{24}\)
Answer:
24 = 2 × 2 × 2 × 3
Prime factors of 24 are not 2 and 5 but is not in its lowest form.
\(\frac{45}{24}=\frac{15 \times 3}{8 \times 3}=\frac{15}{8}\)
The prime factors of 8 are 2 × 2 × 2
∴ \(\frac{45}{24}\) = \(\frac{15}{8}\) = 1.875
(ii) \(\frac{31}{64}\)
Answer:
Here 64 = 2 × 2 × 2 × 2 × 2 × 2
Therefore, it is a terminating decimal form
∴ \(\frac{31}{64}\) = 0.484375 (Terminating decimal)