NCERT Solutions Class 9 Maths Chapter 3 The World of Numbers on Padhaiwise

NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 3 The World of Numbers Exercise Set 3.1

Mon, 01 Jan 0001 00:00:00 +0000

NCERT Solutions for Class 9 Maths Chapter 3 — Exercise Set 3.1#

Natural numbers $\mathbb{N} = \{1, 2, 3, \ldots\}$ are the counting numbers. This exercise uses them for exchange, patterns and counting, and checks whether they are closed under an operation (whether the answer is always a natural number again).

1. A merchant in the port city of Lothal is exchanging bags of spices for copper ingots. He receives 15 ingots for every 2 bags of spices. If he brings 12 bags of spices to the market, how many copper ingots will he leave with? #

Solution

Every 2 bags give 15 ingots, so we count how many groups of 2 bags he has:

NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 3 The World of Numbers Exercise Set 3.2

Mon, 01 Jan 0001 00:00:00 +0000

NCERT Solutions for Class 9 Maths Chapter 3 — Exercise Set 3.2#

Integers $\mathbb{Z} = \{\ldots, -3, -2, -1, 0, 1, 2, 3, \ldots\}$ add zero and the negative numbers to the natural numbers. Brahmagupta described positive numbers as fortunes (dhana) and negative numbers as debts (ṛiṇa), and gave the rules for working with them:

Operation	Rule
Fortune × fortune, or debt × debt	fortune (positive)
Fortune × debt, or debt × fortune	debt (negative)
Subtracting a debt	the same as adding a fortune

1. The temperature in the high-altitude desert of Ladakh is recorded as 4 °C at noon. By midnight, it drops by 15 °C. What is the midnight temperature? #

Solution

A drop of 15 °C means we subtract 15 from the noon temperature:

NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 3 The World of Numbers Exercise Set 3.3

Mon, 01 Jan 0001 00:00:00 +0000

NCERT Solutions for Class 9 Maths Chapter 3 — Exercise Set 3.3#

A rational number is a number of the form $\dfrac{p}{q}$, where $p$ and $q$ are integers and $q \neq 0$. To add or subtract rational numbers, first make the denominators equal using the LCM. To multiply, multiply the numerators and the denominators. To divide, multiply by the reciprocal.

Two rational numbers $\dfrac{a}{b}$ and $\dfrac{c}{d}$ are equal when $ad = bc$ (cross-multiplication).

NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 3 The World of Numbers Exercise Set 3.4

Mon, 01 Jan 0001 00:00:00 +0000

NCERT Solutions for Class 9 Maths Chapter 3 — Exercise Set 3.4#

To place $\dfrac{p}{q}$ on the number line, divide each unit into $q$ equal parts and move $p$ parts from 0 — to the right if the number is positive, to the left if it is negative. Between any two rational numbers there are infinitely many rational numbers; one of them is their average $\dfrac{a + b}{2}$.

1. Represent the rational numbers $\dfrac{2}{3}$, $-\dfrac{5}{4}$ and $1\dfrac{1}{2}$ on a single number line. #

Solution

We first write each number as a fraction and see between which integers it lies:

NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 3 The World of Numbers Exercise Set 3.5

Mon, 01 Jan 0001 00:00:00 +0000

NCERT Solutions for Class 9 Maths Chapter 3 — Exercise Set 3.5#

The decimal expansion of a rational number either terminates or repeats. The decimal expansion of an irrational number never ends and never repeats.

Let $\dfrac{p}{q}$ be in its lowest terms. Its decimal terminates exactly when the prime factors of $q$ are only 2s and/or 5s. Otherwise the decimal repeats.

1. Without performing long division, determine which of the following rational numbers will have terminating decimals and which will be repeating: $\dfrac{7}{20}$, $\dfrac{4}{15}$ and $\dfrac{13}{250}$. Then check your answers by explicitly performing the long divisions and expressing these rational numbers as decimals. #

Prediction (without division)

Each fraction is already in its lowest terms. We factorise each denominator:

NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 3 The World of Numbers End-of-Chapter Exercises

Mon, 01 Jan 0001 00:00:00 +0000

NCERT Solutions for Class 9 Maths Chapter 3 — End-of-Chapter Exercises#

1. Convert the following rational numbers in the form of a terminating decimal or non-terminating and repeating decimal, whichever the case may be, by the process of long division: #

(i) $\dfrac{3}{50}$

Bring down	÷ 50	Remainder
30	0	30
300	6	0

The remainder becomes 0, so the decimal stops:

$$\dfrac{3}{50} = 0.06$$

This is a terminating decimal.