In this chapter, we provide RD Sharma Class 10 Ex 1.6 Solutions Chapter 1 Real Numbers for English medium students, Which will very helpful for every student in their exams. Students can download the latest RD Sharma Class 10 Ex 1.6 Solutions Chapter 1 Real Numbers pdf, Now you will get step by step solution to each question.

Textbook | NCERT |

Class | Class 10 |

Subject | Maths |

Chapter | Chapter 1 |

Chapter Name | Real Numbers |

Exercise | 1.6 |

Category | RD Sharma Solutions |

**RD Sharma Solutions for Class 10 Chapter** **1 Real Numbers Ex 1.6 Download PDF**

**Chapter 1: Real Numbers Exercise – 1.6**

**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.

(i) 23/8

(ii) 125/441

(iii) 35/50

(iv) 77/210

**Solution:**

(i) The given number is 23/8

Here, 8 = 2^{3} and 2 is not a factor of 23.

So, the given number is in its simplest form.

Now, 8 = 2^{3} is of the form 2^{m} × 5^{n}, where m = 3 and n = 0.

So, the given number has a terminating decimal expansion.

(ii) The given number is 125/441

Here, 441 = 3^{2} × 7^{2} and none of 3 and 7 is a factor of 125.

So, the given number is in its simplest form.

Now, 441 = 3^{2} × 7^{2} is not of the form 2^{m} × 5^{n}

So, the given number has a non-terminating repeating decimal expansion.

(iii) The given number is 35/50 and HCF (35, 50) = 5.

Here, 7/10 is in its simplest form.

Now, 10 = 2 × 5 is of the form 2^{m} × 5^{n}, where in = 1 and n = 1.

So, the given number has a terminating decimal expansion.

(iv) The given number is 77/210 and HCF (77, 210) = 7.

Here, 11/30 is in its simplest form. 30

Now, 30 = 2 × 3 × 5 is not of the form 2^{m} × 5^{n}.

So, the given number has a non-terminating repeating decimal expansion.

(v) The given number isClearly, none of 2, 5 and 7 is a factor of 129.

So, the given number is in its simplest form.

**Question: 2**

Write down the decimal expansions of the following rational numbers by writing their denominators in the form of 2^{m} × 5^{n}, where m, and n, are the non- negative integers.

(i) 3/8

(ii) 13/125

(iii) 7/80

(iv) 14588/625

**Solution:**

(i) The given number is 3/8

Clearly, 8 = 2^{3} is of the form 2^{m} × 5^{n}, where m = 3 and n = 0.

So, the given number has terminating decimal expansion.

(ii) The given number is 13/125

Clearly, 125 = 5^{3} is of the form 2m × 5″, where m = 0 and n = 3.

*So*, the given number has terminating decimal expansion.

(iii) The given number is 7/80.

Clearly, 80 = 2^{4} × 5 is of the form 2^{m} × 5^{n}, where m = 4 and n = 1.

So, the given number has terminating decimal expansion.

(iv) The given number is 14588/625

Clearly, 625 = 5^{4} is of the form 2^{m} × 5^{n}, where m = 0 and n = 4.

So, the given number has terminating decimal expansion?

(v) The given number is Clearly, 2^{2} × 5^{7} is of the form 2^{m} × 5^{n}, where in = 2 and n = 7.

So, the given number has terminating decimal expansion?

**Question: 3**

What can you say about the prime factorization of the denominators of the following rational?

(i) 43.123456789

(iv) 0.120120012000120000

**Solution:**

(i) Since 43.123456789 has terminating decimal expansion. So, its denominator is of the form 2^{m} × 5^{n}, where m, n are non-negative integers.

(ii) Since has non-terminating decimal expansion. So, its denominator has factors other than 2 or 5.

(iii) Since has non-terminating decimal expansion. So, its denominator has factors other than 2 or 5.

(iv) Since 0.120120012000120000 … has non-terminating decimal expansion. So, its denominator has factors other than 2 or 5.

**All Chapter RD Sharma Solutions For Class10 Maths**

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