1.  Write the following numbers in expanded notation.

a. 10,73,487          b. 1,43,069
 

The place value chart is 
 
             a. 10,73,487 = 10,00,000 + 0 + 70,000 + 3000 + 400 + 30 + 7
             b. 1,43,069 = 1,00,00 + 40,000 + 3000 + 0 + 60 + 9.

2.  Write the following numbers in standard form?
          a.  3,00,000 + 60,000 + 4000 + 300 + 80 + 2.
          b.  6,00,000 + 80,000 + 2000 + 60 + 3.
 

a. 3,00,000 + 60,000 + 4000 + 300 + 80 + 2 = 3,64,382
b.  6,00,000 + 80,000 + 2000 + 60 + 3 = 6,82,063.

3. State the place value of 3 in 3, 62, 894.

L TTh Th  H  T  O
3   6    2   8  9  4

              3 is in the one lakh position.
              Position value of 3 = 3 x 1,00,000 = 3,00,000.

4.  State the place value of 7 in 1,78,43,580.

C  TL   L  TTh   Th   H   T   O
 1   7   8    4     3     5   8   0

7 is in the ten lakh position

 place value of 7 = 7 x 10,00,000 = 70, 00, 000.

5.  Write the following numbers in words.
      a.  2, 34, 816                 b.  1, 78, 43, 580.

The place value chart is 

      
a.  Two lakh thrity four thousand eight hundred sixteen
b. One crore seventy eight lakh forty three thousand five hundred eighty.
 
6. Write the following numbers as figures.

a. Two lakh sixty thousand four hundred thirty.
b. Ten lakh fortyone thousand six hundred forty nine.

TL  L  TTH   TH   H   T   O
      2    6      0    4     3   0
 1   0    4      1    6     4   9

a.  2, 60, 430
b.  10, 41, 649

7.  Arrange the following numbers in ascending order 6, 27, 432; 60, 14, 899; 6,10,27,342.

 The place value chart is :

      
 6,27,432; 60,14, 899;   6,10, 27,342.

8. Arrange the following numbers in descending order, 1,12,345; 1,21,345; 1,32, 145; 1,13, 234.

    
From the chart, 1,32, 145; 1,21,345; 1,13, 234; 1,12,345.

9.  State which is greater ?

a.  7 cm or 2mm b, 5 km or 30,000 cm.

7cm = 7 x 10 mm = 70 mm.
70 mm > 2mm  7cm > 2 mm

b.  5km = 5 x 1000m
 = 5 x 1000 x 100 cm = 5,00,000 cm.
 5,00,000 > 30,000
i. e., 5km > 30,000 cm.

10. Add and give the approximate value in thousands

a. 8794 – 2368 b, 2314 + 71 25

8794 is nearer to 900 than 8000.
2368 is nearer to 2000 than 3000.
 8794 – 2368  ≈  9000 – 2000 ≈ 7000.

b.  2314 is nearer to 2000 than 3000. 7125 is nearer to 7000 than 8000
 2314 + 7124  ≈    2000 + 7000   ≈  9000.

11.  Multiply and give the approximate answer.
a.  292 x 312                    b. 491 x 421

a.  292 x 312   
292 is nearer to 300 than 200 and 312 is nearer to 300 than 400.
292 x 312 ≈ 300 x 300 ≈ 90000

b. 491 is nearer to 500 than 400.
421 is nearer to 400 than 500.
 491 x 42 ≈ 500 x 400 ≈ 200000.

12.  Biju bought two motor cycles, each costing Rs. 37,842. He sold one for Rs. 39,246 and the other for Rs. 36,842. Did he lose or gain ?

Cost price of motor cycles
            = 2 x 37, 842 = 75, 684
Selling price = 39,246 + 36, 842  = 76,088.
Selling price > cost price
Gain = ≤ p – cp = 76,088 – 75,684 = Rs. 404.

13. The AKG auditorium had a show on Saturday with full capacity. The total collection of the ticket sale was Rs. 73,500. Each ticket costed Rs.50. As 30 people were admitted as special invitees, they did not have to buy the tickets. Find out the seating capacity of the auditorium .

Total collection = 73,500.
Cost of one ticket = Rs.50
Number of ticket sold = ^73,500/₅₀ = 1470
Total Number of seats = 1470 + 30 = 1500.

14.  A truck carries 65 boxes. Each of these boxes contains 80 smaller packages. Each of these smaller packages contains 15 toy soldiers. How many toy soldiers are being carried in the truck ?

Number of boxes in a truck = 65
Number of packages in each box = 80
Number of toy soldiers in each package = 15
 Total toy soldiers = 65 x 80 x 15 = 78000

15.  The capacity of a water tank in a housing colony is 64 kiloliters. This is sufficient for 30 families in the colony for 4 days. What is the average quantity of water used by 30 households ?

The capacity of a water tank = 64 kilolitres = 64 x 1000 liters = 64000 liters.
The quantity of water for 30 families per day = ⁶⁴⁰⁰⁰/₄ = 16000.

16. In swaroop sweets shop, of a cookie needs 8 gm of ingredients, how many cookies can made with their stock of 44. 4kgm of ingredients ?

Amount of ingredients needed for a cookie = 8 gm.
Number of cookies made form 44.4 kgm of ingredients
 

17.  What are the rules to form Roman Numerals ?

1. If a symbol is repeated one after the other, its value is added as many times as it occurs.
2. The symbol I, x, C and M can be repeated up to a maximum of three times,
3. The symbols V, L and D can never be repeated in a roman numeral.
4. If a symbol with a smaller value is written on the right of a symbol with a greater value, then its value is added to the value of the greater symbol.
5. If a symbol with a larger value, then its value is subtracted from the value of the greater symbol.

18. Simplify 58 + (105 + 220).

First calculate 105 + 220 = 325
Then 58 + ( 105 + 220 ) = 58 + 325 = 383.

19.  Write the equivalent Roman numeral for  a. 15    b. 21   c. 38

a. 15 = 10 + 5 = XV
b. 21 = 10 + 10 + 1 = X X I
c. 38 = 10 + 10 + 10 + 5 + 3 = X X X VIII

20. Write the equivalent Roman numeral for  
a. 395               b. 265              c. 900

395 = 100 + 100 + 100 + ( 100 - 10 ) + 5 = C C C X C V
265 = 100 + 100 + 50 + 10 + 5 = C C L X V
900 = (1000 - 100 ) = CM.

21.  write the Hindu Arabic numerals of ?
a) XXIII     b) XXXI     c) XL

a.  XXIII = 10 + 10 + 1 + 1 + 1 = 23.
b. XXXI = 10 + 10 + 10 + 1 = 31.
c.  XL = 50 - 10 = 40. 

22. Write the Hindu Arabic numerals for 
a) LXXV    b) CCX     c) CD

a. LXXV = 50 + 10 + 10 +  5 = 75
b. CCX = 100 + 100 + 10 = 210
c. CD = 500 - 100 = 400. 

23. Write the approximate value by estimating:- 3228 + 572

3228 is nearer to 3200 than 3300
572 is nearer to 600 than 500
 3228 + 572   ≈ 3200 + 600 ≈ 3800.

24. Insert commas in 500  81200 35  according to international system.

In the Internation system of numeration, all the periods have three place values each.
 5008120035 = 5,008,120,035.