**10th class maths real numbers exercise 1.3**

- Positive or negative, Large or small, whole numbers or decimal numbers are all
**Real Numbers.**

They are called “**Real Numbers**” because they are not Imaginary Numbers.

## **10th class maths real numbers exercise 1.3**

## **EXERCISE – 1.**3

**2Q. without performing division, state whether the following rational numbers will have a terminating decimal form of a non–terminating, repeating decimal form.**

**Note : We check whether the denominator is of the form 2**^{n}** . 5**^{m}** or not ? If yes, the rational number can be expressed as a terminating decimal.**

** If not, it can’t be expressed as a terminating decimal.**

**3125 = 5 X 5 X 5 X 5 X 5**

**3125 = 5**^{5}

** 1600 = 2 X 2 X 2 X 2 X 2 X 2 X 5 X 5**

** 1600 = 2**^{6}** X 5**^{2}

** 343 = 7 X 7 X 7 **

**343 = 7**^{3}** ( Not of the form 2**^{n}** . 5**^{m}** ) **

**The denominator is of the form 2 ^{n} . 5^{m}**

**Denominator is not of the form 2 ^{m} X 5^{n}**

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#### **10th class maths real numbers exercise 1.3**

**Definition of Real Number : **

- Positive or negative, Large or small, whole numbers or decimal numbers are all
**Real Number**. - They are called “ Real Numbers ” because they are not Imaginary Numbers.
- The type of numbers we normally use , such as 1, 15.82, -0.1, ¾, etc…

**Definition of Imaginary Numbers :**

- A number that when squared gives a negative result.
- When we square a Real Number ( multiply it by itself ) we always get a positive, or zero, result. For example 2 X 2 = 4, and ( -2 ) X (-2 ) = 4 as well.

In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.. The real numbers include all the rational numbers, such as the integer -5 and the fraction 4/3, and all the irrational numbers, such as the square root of 2, an irrational algebraic.

**JOHN NAPIER ( 1550 – 1617 ) :**

JOHN NAPIER is best known as the discoverer of logarithms. He also invented the so – called “ **Napier’s bones** “ and made common the use of the decimal point in arithmetic and mathematics.