Exercise 1.6

Exercise 1.6

Miscellaneous Practice Problems

1. Try to open my locked suitcase which has the biggest 5 digit odd number as the password comprising the digits 7, 5, 4, 3 and 8. Find the password.

Answer: Password = 87543

2. As per the census of 2001, the population of four states are given below. Arrange the states in ascending and descending order of their population.

● Tamil Nadu      72147030

● Rajasthan           68548437

● Madhya Pradesh 72626809

● West Bengal        91276115

Solution:

Ascending:

68548437 ; 72147030 ; 72626809 ; 91276115

Descending:

91276115 ; 72626809 ; 72147030 ; 68548437

3. Study the following table and answer the questions.

(i) How many tigers were there in 2011?

Answer: 1706

(ii) How many tigers were less in 2008 than in 1990?

Answer: 3500 − 1400 = 2100

(iii) Did the number of tigers increase or decrease between 2011 and 2014? If yes, by how much?

Answer: Yes, the number of tigers increased by 520 tigers.

Soution:

2226

1706

520 

4. Mullaikodi has 25 bags of apples. In each bag there are 9 apples. She shares them equally amongst her 6 friends. How many apples do each get? Are there any apples left over?

Solution:

No. of apple bags = 25

Each bag contains = 9 apples

Total No. of apples = 25 × 9

= 225 apples.

Total apples shared = 6

They eaach get = 225 / 6

225 / 6 = 37 ; Remainder = 3

among 6 friends; each of them they get 37 apples and 3 apples left over.

5. A poultry has produced 15472 eggs and fits 30 eggs in a tray. How many trays do they need? 

Solution:

No. of eggs produced = 15472

In one tray = 30

No. of trays need = 15472 / 30

For 23 eggs one tray + 515 trays

Totally = 515 + 1 = 516 trays need.

Challenging Problems

6. Read the table and answer the following questions.

(i) Write the Canopus star’s diameter in words, in the Indian and the International System.

(ii) Write the sum of the place values of 5 in Sirius star’s diameter in the Indian System.

(iii) Eight hundred sixty four million seven hundred thirty. Write this in standard form of Indian System.

(iv) Write the diameter in words of Arcturus star in the International System.

(v) Write the difference of the diameters of Canopus and Arcturus stars in the Indian and the International Systems.

Solution:

(i) Conopus star’s diameter = 25941900

Indian System : 2,59,41,900

Two crore fifty nine lakh forty one thousand nine hundred.

International System : 25,941,900

Twenty five million nine hundred forty one thousand nine hundred.

(ii) Sirius = 15,56,500

Sum of the place value of 5

1556500 = 5 × 100000 + 5 × 10000 + 5 × 100

= 500000 + 50000 + 500

= 5,50,500

(iii) 8,64,000,730 = 86,40,00,730

Eighty six crore forty lakh seven hundred thirty

(iv) Acrturus : 19888800

International System : 19,888,800

Nineteen million eight hundred eighty eight thousand eight hundred

(v) Difference :

Canopus =25941900

Arcturus = 19888800

                  6053100

Difference is 6053100

Indian System = 60,53,100

Sixty lakh fifty three thousand hundred

International System = 6,053,100

Six million fifty three thousand hundred

7. Anbu asks Anjali to guess a five digit odd number. He gives the following hints.

● The digit in the 1000s place is less than 5

● The digit in the 100s place is greater than 6

● The digit in the 10s place is 8

What is Anjali’s answer? Does she give more than one answer?

Solution:

It is five digit odd number

1000th place <5

100th place >6

10th place = 8

TTh   Th     H      T        O

x     <  5  >  6       8       1/3/5/7/9

One of the answer is 64781

Many answers are possible.

8. A Music concert is taking place in a stadium. A total of 7,689 chairs are to be put in rows of 90. (i) How many rows will there be? (ii) Will there be any chairs left over?

Solution:

Total number of chairs = 7,689

In one row = 90 chairs

Total number of rows = 7689 / 90

(i) 85 rows will be there

(ii) There will be 39 chairs left over.

9. Round off the seven digit number 29,75,842 to the nearest lakhs and ten lakhs. Are they the same?

Solution:

Seven digit number = 29,75,842

To the nearest lakh = 30,00,000

To the nearest ten lakh = 30,00,000

Yes, both are same.

10. Find the 5 or 6 or 7 digit numbers from a newspaper or a magazine to get a rounded number to the nearest ten thousand.

Solution:

5 digit numbers nearest to ten thousand

56,789 = 6 > 5 => 60,000

95,463 = 5 = 5 => 1,00,000

73,210 = 3 < 5 => 70,000

6 digit no. nearest to ten thousand

1,76,543 = 6 > 5 => 1,80,000

7 digit no. nearest to ten thousand

83,42,693 = 2 < 5 => 83,40,000

Exercise 1.6

1) 87543

2) Ascending Order : 6,85,48,437 < 7,21,47,030 < 7,26,26,809 < 9,12,76,115

Descending Order: 9,12,76,115 > 7,26,26,809 > 7,21,47,030 > 6,85,48,437

3) (i) 1706 tigers in 2011 (ii) 2100 (iii) 520 tigers increased from 2011 to 2014

4) among 6 friends, each of them get 37 apples. 3 apples left over

5) 515 + 1 = 516 trays required

6) (i) Indian System:Two crore fifty nine lakh forty one thousand nine hundred

International System: Twenty five million nine  hundred forty one thousand nine hundred

(ii) 5,50,500

(iii) Eighty six crore forty lakh seven hundred thirty

(iv) Ninteen million eight hundred eighty eight thousand eight hundred

(v) Indian System : 60,53,100 − Sixty lakh fifty three thousand one hundred

International System : 6,053,100 − Six million fifty three thousand one hundred

7) One of the answers is 43781. Many answers are possible

8) (i) 85 rows are required to fill 7650 chairs (ii) The remaining chairs are 39

9) Yes, both are same (30,00,000)

10) Relevant answers are yours

How will you read the large number given below?

731,687,303,715,884,105,727

This is read as 731 quintillion, 687 quadrillion, 303 trillion, 715 billion, 884 million, 105 thousand, 727.