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)