**Chapter 1 Knowing Our Numbers**

Very Short Answer Type

Question 1.

Write the smallest three digit number whose value does not change on reversing its digits.

Solution:

The required number is 101.

Question 2.

Write the greatest three digit number which does not change on reversing its digits.

Solution:

The required number is 999.

Question 3.

What must be added to 203 to get a number whose digits are reversed of the given number?

Solution:

The number obtained by reversing the digits of 203 = 302.

∴ Difference = 302 – 203 = 99

Hence, the required number is 99.

Question 4.

Write the following in Roman numerals:

(a) 72

(b) 38

Solution:

(a) 72 = LXXII

(b) 38 – XXXVIII

Question 5.

Write 438 in its expanded form.

Solution:

438 = 4 x 100 + 3 x 10 + 8.

Question 6.

Write the greatest five-digit number using the digits 4, 2 and 0.

Solution:

The greatest five-digit number using the digits 4, 2 and 0 is 44420.

Question 7.

The capacity of a water tank is 300 litres. Express its capacity in millilitres.

Solution:

We know that

1 litre = 1000 mL

∴ 300 litres = 300 x 1000 mL = 3,00,000 mL

Hence, the capacity of water tank = 3 lakh millilitres.

Question 8.

What is the successor of greatest 6-digit number?

Solution:

Greatest 6-digit number = 999999

Successor of it = 999999 + 1 = 1000000

i. e., smallest 7-digit number.

Hence, the required successor = 10,00,000.

Question 9.

What is the place value of 7 in 1743?

Solution:

Let us write 1743 in its expanded form

1743 = 1000 + 700 + 40 +3

Place value of 7 = 700

Hence, the place value of 7 = 700.

Short Answer Type

Question 10.

Of 7,12,540 and 71,25,400 which number is greater and by how much?

Solution:

Since 71,25,400 is a seven-digit number and 7,12,540 is a six-digit number.

So 71,25,400 is greater than 7,12,540.

Hence 71,25,400 is greater than 7,12,540 by 64,12,860.

Question 11.

Write the smallest and the greatest 5-digit numbers using the digits 0,2,4,6,8 (Repetition of digits is not allowed).

Solution:

Given digits are 0, 2, 4, 6, 8

5 – digit greatest number = 86420;

5 – digit smallest number = 20468.

Question 12.

Write the following numbers in ascending order. How many of them are even numbers?

63,854, 63,584, 65,348, 68,543, 64,835

Solution:

The given numbers are 63,854, 63,584, 65,348, 68,543 and 64,835.

Ascending order is 63,584 ; 63,854 ; 64,835 ; 65,348 ; 68,543

Even numbers are 63,584, 63,854 and 65,348.

Question 13.

Round the given numbers to the nearest tens.

(a) 48

(b) 59

(c) 64

(d) 215

Solution:

Given number Rounded off to tens

(a) 48 → 50

(6) 59 → 60

(c) 64 → 60

(d) 215 → 220

Question 14.

Estimate the following products:

(а) 86 x 316

(b) 898 x 786

Solution:

(a) 86 x 316

∵ 86 → 90 [Rounding off to tens] and 316 → 320 [Rounding off to tens]

So, the estimated product is 90 x 320 = 28800

(b) 898 x 786

∵ 898 → 900 [Rounding off to hundreds] and 786 → 800 [Rounding off to hundreds]

So, the estimated product is 900 x 800 = 720000.

Question 15.

Divide 2,63,175 by 275.

Solution:

We have

Hence, quotient = 957 and remainder = 0.

Question 16.

A student multiplied 3759 by 231 instead of multiplying by 213. How much was his product greater than the correct product?

Solution:

First Method:

(3759 x 231)-(3759 x 213) = 868329 – 800667 = 67662

Second Method: 3759 x (231 – 213) = 3759 x 18 = 67662

Hence, the product difference is 67662.

Question 17.

Estimate: 25,148 + 7394 + 9343 + 752

Solution:

Estimated values are

25,148 → 25100

7394 → 7400

9343 → 9300

752 → 800

So, the estimated sum is 25100 + 7400 + 9300 + 800 = 42600

Hence, the estimated sum is 42600.

Question 18.

Write all the even numbers between 90 and 100 in Roman Numerals.

Solution:

Even numbers between 90 and 100, we have 92, 94, 96, 98.

∴ 92 = XCII,

94 = XCIV,

96 = XCVI,

98 = XCVIII

Long Answer Type

Question 19.

Write the missing digits in the following sums:

Solution:

Question 20.

Write Hindu-Arabic numerals for:

(a) LXXXVI

(b) LXXV

(c) XCIX

(d) XCI

Solution:

(a) LXXXVI = 50 + 30 + 6 = 86

(b) LXXV = 50 + 20 + 5 = 75

(c) XCIX = (100 – 10) + 9 = 99

(d) XCI = (100 – 10) + 1 = 91

Question 21.

The distance between the school and Reena’s house is 1 km 480 m. Everyday she walks both ways. What distance does she cover in 6 days of a week?

Solution:

Distance covered when she walks one way = 1 km 480 m = 1480 m

Therefore, the distance covered when she walk both ways in a day = 1480 x 2 m = 2960 m

Total distance covered by Reena in 6 days = 2960 x 6 m = 17760 m or 17 km 760 m.

Question 22.

Simplify: 36 ÷ [5 + {4 x 5 ÷ 2}]

Solution:

Given:

36 ÷ [5 + {4 x 5 ÷ 2}]

Using B, O, D, M, A, S

Question 23.

To stitch a pant 1 m 15 cm cloth is needed. Out of 36 m cloth, how many pants can be stitched and how much cloth will remain?

Solution:

Cloth required to stitch 1 pant = 1 m 15 cm

= 100 cm + 15 cm [∵ 1 m = 100 cm]

= 115 cm

Total cloth = 36 m = 36 x 100 cm = 3600 cm

Therefore number of pants stitched =

Hence, 31 pants can be stitched and cloth left over is 35 cm.

Question 24.

Write each of the following numbers in figures:

(a) Eighty-one million four hundred twelve thousand six hundred fifty.

(b) Twenty million three hundred eighty thousand one hundred.

(c) Ninety million nine.

(d) Forty-nine million seven hundred eighty two thousand fifty eight.

(e) Six millions three hundred fifty-two thousand nine hundred forty-six.

(f) Seven crore twenty-three lakh eighty-six thousand, five hundred ninety-four.

(g) Fifty crore forty lakh sixty thousand nine.

(h) Nineteen crore, ninety lakh, fourteen thousand, six hundred eighty.

Solution:

In words In figure

(а) Eighty-one millions four hundred twelve thousand, six hundred fifty. 81,412,650

(b) Twenty million three hundred eighty thousand one hundred 20,380,100

(c) Ninety million nine 90,000,009

(d) Forty-nine million seven hundred eighty-two thousand fifty-eight 49,782,058

(e) Six-millions three hundred fifty-two thousand nine hundred forty-six 6,352,946

(f) Seven crore, twenty-three lakh eighty-six thousand five hundred ninety-four 7,23,86,594

(g) Fifty crore forty lakh sixty thousand nine 50,40,60,009

(h) Nineteen crore ninety lakh fourteen thousand six hundred eighty. 19,90,14,680

Question 25.

Write True/False for the following statements:

(a) Roman symbol X cannot be repeated more than three times

(b) VXXX = 25 …….. .

(c) Estimate value of274 rounding off to nearest hundreds = 200 …….

(d) I and X can repeat at the most three times …….

(e) V, L and D are neither, repeated nor written to the left of greater value symbol ……..

(f) There are six basic symbols in Roman Numeration system ……..

Solution:

(a) True

(b) False

(c) False

(d) True

(e) True

(f) False.

Higher Order Thinking Skills (HOTS)

Question 26.

There are two factories located at place P and the other at place Q. From these factories, a certain commodity is to be delivered to each of the depots situated at A, B and C. Weekly production of commodity by P and Q are 120 kg and 150 kg respectively. Weekly requirement of commodity by A, B and C are 80 kg, 90 kg and 100 kg respectively. P delivers 60 kg to A, 40 kg to B and 20 kg to C. How much amount of the commodity should Q deliver to A, B and C to meet their requirement? If the rate of the commodity is ? 20 per kg, find the total amount to be paid to P and Q.

Solution:

Amount of commodity delivered by P to A = 60 kg

Amount of commodity delivered by Q to A = 80 – 60 = 20 kg

Amount of commodity delivered by P to B = 40 kg

Amount of commodity delivered by Q to B – 90 – 40 = 50 kg

Amount of commodity delivered by P to C = 20

Amount of commodity delivered by Q to C = 100 – 20 = 80 kg.

Now Amount of money to be paid to P by A, B and C = ₹( 60 x 20 + 40 x 20 + 20 x 20)

= ₹ (1200 + 800 + 400)

= ₹ 2400

and amount of money to be paid to Q by A, B and C

= ₹ (20 x 20 + 50 x 20 + 80 x 20)

= ₹ (400 + 1000 + 1600) = ₹ 3000

Hence, the total amount

= ₹ 2400 + ₹ 3000 = ₹ 5400.