NCERT Solutions for Class 10 Mathematics Chapter 1 Real Numbers Ex 1.4 are part of NCERT Solutions for Class 10 Maths. Here we have given NCERT Solutions for Class 10 Mathematics Chapter 1 Real Numbers Ex 1.4.

Board | CBSE |

Textbook | NCERT |

Class | Class 10 |

Subject | Maths |

Chapter | Chapter 1 |

Chapter Name | Real Numbers |

Exercise | Ex 1.4 |

Number of Questions Solved | 3 |

Category | NCERT Solutions |

### NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers Ex 1.4

**Ex 1.4 Class 10 Question 1.**

**Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion:**

**Solutions:**

**Ex 1.4 Class 10 NCERT Solutions Question 2.**

**Write down the decimal expansions of those rational numbers in Question 1 above which have terminating decimal expansions.**

**Solutions:**

In Question 1, (i), (ii), (iv), (vi), (viii) and (ix) are having terminating decimal expansion.

**Class 10 Ex 1.4 Question 3.**

**The following real numbers have decimal expansions as given below. In each case, decide whether they are rational or not. If they are rational, and of the form \(\frac { p }{ q }\), what can you say about the prime factors of q?**

**(i) 43.123456789**

**(ii) 0.120120012000120000…**

**(iii) 43. \(\overline { 123456789 }\)**

**Solutions:**

**(i) 43.123456789**

Since the decimal expansion terminates,so the given real number is rational and therefore of the form \(\frac { p }{ q }\)

Here, q = 29 x 59, So prime factorisation of q is of the form 2^{n} x 5^{m}.

**(ii) 0.120120012000120000…**

Since the decimal expansion is neither terminating nor non-terminating repeating, therefore the given real number is not rational.

**(iii) 43. \(\overline { 123456789 }\)**

Since the decimal expansion is non-terminating repeating, therefore the given real number is rational and therefore of the form \(\frac { p }{ q }\)

Let x = 43. \(\overline { 123456789 }\) = 43.123456789123456789… ….(i)

Multiply both sides of (i) by 1000000000, we get

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