**Ex 1.4
Question $1 .$**

Fill in the blanks.

(i) The nearest 100 of 843 is

(ii) The nearest 1000 of 756 is

(iii) The nearest 10,000 of 85654 is

Solution:

(i) 800 .

The digit in tens place is $4<5$

(ii) 1000 .

The digit in hundred places is $7 \geq 5$

(iii) 90,000 .

The digit in a thousand places is $5 \geq 5$

**Question $2 .$**

Say True or False.

(i) 8567 is rounded off as 8600 to the nearest 10 .

(ii) 139 is rounded off as 100 to the nearest 100 .

(iii) $1,70,51,972$ is rounded off as $1,70,00,000$ to the nearest lakh.

Solution:

(i) False

(ii) True

(iii) False

**Question $3 .$**

Round off the following to the given nearest place.

(i) 4065 ; hundred

(ii) 44,555 ; thousand

(iii) 86943 ; ten thousand

(iv) $50,81,739$; lakh

(v) $33,75,98,482$; Ten crore

Solution:

(i) We have to round off 4065 to hundreds

The place value is a hundred

The digit in hundreds place is 0

The digit to the right is $6>5$

Adding 1 to $0 \Rightarrow 0+1=1$

Changing the digits to the right of 41 to zeros

$4065 \simeq 4100 \Rightarrow 4100$

(ii) To round off 44555 to thousands

The digit in the thousands place is 4

digit to the right is $5=5$.

Adding 1 to the thousand place value digit $4 \Rightarrow 4+1=5$

Changing the digits to the right of 45 to zeros we get 45000

$44555 \simeq 45000$

(iii) To round off 86,943 to ten thousand

The digit in ten thousand places is 8

The digit to the right is $6>5$

Adding 1 to $8 \Rightarrow 8+1=9$.

Changing the digits to the right of 9 to zeroes we get 90,000

$86943 \simeq 90,000$

(iv) To round off 5081739 to lakhs

The digit in the lakhs place is 0

The digit to the right is $8>5$

Adding 1 to $0 \Rightarrow 1+0=1$

Changing the digits right off 51 to zeros

We get $51,00,000$

$5081739 \simeq 51,00,000$

(v) To round off 337598482 to ten crore

The digit in the ten crores place is 3

The digit to the right is $3<0$

The digit in ten crore place remains the same 3 .

Changing the digit to the right of 3 zeros we get $30,00,00,000$

$33,75,98,482 \simeq 30,00,00,000$

**Question $4 .$**

Estimate the sum of 157826 and 32469 rounded off to the nearest ten thousand. Solution:

$\begin{array}{rlr}

157,826 & \Rightarrow & 1,60,000 \\

\frac{32,469}{1,90,295} & \Rightarrow & \frac{30,000}{1,90,000} \\

\hline

\end{array}$

**Question $5 .$**

Estimate by rounding off each number to the nearest hundred.

(i) $8074+4178$

(ii) $1768977+130589$

Solution:

(i) $8074+4178$

$8074 \Rightarrow 8100$ $4178 \Rightarrow \frac{4200}{12,300}$ $1768977+130589$

(ii)

$\begin{aligned}

17,68,977 & \Rightarrow 1769000 \\

1,30,589 & \Rightarrow \frac{130600}{18,99,600} \\

\hline

\end{aligned}$

**Question $6 .$**

The population of a city was $43,43,645$ in the year 2001 and $46,81,087$ in the year 2011 . Estimate the increase in population by rounding off to the nearest thousand.

Solution:

Population in $2001=43,43,645$

Population in $2011=46,81,087$

Increase in population $=46,81,087-43,43,645=3,37,442$

When rounded off to the nearest thousand $=3,37,000$

**Objective Type Questions**

**Question $7 .$**

The number which on rounding off to nearest thousands given 11000 is

(a) 10345

(b) 10855

(c) 11799

(d) 10056

Solution:

(b) 10855

In 10855 , the digit in a hundred places is $8 \geq 5$. So 11000

**Question 8 .**

The estimation to the nearest hundred of 76812 is

(a) 77000

(b) 76000

(c) 76800

(d) 76900

Solution:

(c) 76800

**Question $9 .$**

The number 9785764 is rounded off to nearest lakh as

(a) 9800000

(b) 9786000

(c) 9795600

(d) 9795000

Solution:

(a) 9800000

In ten thousand places, the digit is 85 . So 9800000

**Question $10 .$**

The estimated difference of 167826 and 2765 rounded off to the nearest thousand is

(a) 180000

(b) 165000

(c) 140000

(d) 155000

Solution:

(b) 165000