TOPIC 1: WHOLE NUMBERS - STANDARD THREE MATHEMATICS NOTES

TOPIC 1: WHOLE NUMBERS – STANDARD THREE MATHEMATICS NOTES

What are whole numbers?

Whole numbers are a set of numbers starting at zero and increasing by one each time.

Whole numbers do not include fractions, decimals, or negative numbers. They are positive integers.

0,1,2,3,4,5,6,7,8,9,10….

All whole numbers are integers, but not all integers are whole numbers since integers also include negative numbers. Both whole numbers and integers are rational numbers.

PLACE VALUE IN WHOLE NUMBERS

The place value of digit in a number can be read from right to left as follows:

The first position from left represents ones
The second position from left represents tens
The third position from left represents hundreds
The fourth position from left represents thousands
The fifth position from left represents ten thousands
The sixth position from left represents hundred thousands
The seven position from left represents millions

Example 1

Write the place value of each digit in 1364

Example 2

Write the place value of each digit in 6948

Example 3

A number has seven in the thousands place, 0 in the tens place and 4 in the oes place. What is the number?

Answer

The number is 7304

Example 4

1. Fill in the blanks with the place value of each digit in the given number

(a) 5463 has _____ thousands ____ hundreds ____ tens and ____ ones

Answer

5463 has 5 thousands 4 hundreds 6 tens and 3 ones

(b) 6010 has _____ thousands ____ hundreds ____ tens and ____ ones

Answer

6010 has 6 thousands 0 hundreds 1 tens and 0 ones

Exercise

Identify the plaace value of each digit in the following whole numbers

(a) 4628 (b) 3456 (c) 7304 (d) 9000

Answer

Exercise 1

1. Write he place value of each digit in 9825

_________ is in tens place

_________ is in ones place

_________ is in the thousands place

_________ is in the hundreds place

2. Write a number with the following place values

3. Fill in the following table the place value of each digit in the given numbers

(a) which digit is in the hundreds place in 7029?

(b) which digit is in the thousands place in 8173?

(d) a number has 0 in the ones [lace, 6 in the tens place and 7 in the hundreds place. What is the number?

2. (a) How many hundreds are there in 3287?

(b) There are 9674 apples in the basket. How many thousands apples are there?

3. (a) Identify the place value of each digit in the following whole numbers? +

4. Write the place value of underlined digit in the following whole numbers

5. Fill in the blanks with the place values of the given digits

a) In 2968

2 is in ___________, 9 is in ________________

6 is in ___________, and 8 is in _____________

b) In 9801

9 is in ___________, 8 is in ________________,

0 is in ___________, and 1 is in _____________

c) In 7236

7 is in ___________, 2 is in ________________

3 is in ___________, and 6 is in _____________

d) In 5649

5 is in ___________, 6 is in ________________

4 is in ___________, and 9 is in _____________

6. Write the number represented by the following values in the following table

7. Fill in the blanks with the correct place values of the following whole numbers

8. Write the digit in the thousands place value in each of the following whole numbers

(a) 7682 (b) 9501 (c) 8306 (d) 6412

9. Write the place value of 3 in each of the following whole numbers

(a) 436 (b) 3900 (c) 2843 (d) 2301

10. Underline the digit in the hundreds place in each of the following numbers

(a) 269 (b) 7901 (c) 3749 (d) 9568

11. (a) I am a two – digit number with 3 in the ones place. The digit in the tens exceeds that in the ones by 4. What number do I represent?

(b) I am a two-digit number with 9 in the tens place. The digit in the ones is less than the digit in the tens by 3. What number am i?

WRITING THE PLACE VALUE OF A DIGIT IN A NUMBER USING ABACUS

Example 1

Write the place value of each digit in the following abacus

Answer

The abacus represents 4263.

There are 4 thousands, 3 hundreds, 6 tens and 3 ones

Example 2

Write the place value of each digit in the following abacus

Answer

The abacus represents 6004. There are 6 thousands, 0 hundreds, 0 tens and 4 ones

Exercise 3

Carefully study the abacus 1- 6, then write the number represented by each

7. Represent the following numbers on an abacus

(a) 4279 (b) 5802 (c) 6247 (d) 5108

TOTAL VALUE OF A DIGIT IN A WHOLE NUMBER

The total value of digit in a number increases from right to left.

Example 1.

Write the total value of each digit in 9672

Answer

Example 2

Write the total value of each underlined digit in 8794

Answer

The total value of 9 is 90

The total value of 8 is 8000

Example 3

Count the number 7985, write the following

the place value of each digit
the total value of each digit

Example 4

Write the place value of 6 and the total value of 4 in 4612

Answer

The place value of 6 in 4612 in hundreds

The total value of 4 in 4612 is 4000

Exercise 3

1. Write the total value of each underlined digit in the following numbers

2. Write the total value of each digit in the following numbers

(a) 2345 (b) 1246 (c) 8769 (d) 9876

3. Write the total value of 5 in the following numbers

(a) 5672 (b) 3564 (c) 9851 (d) 1695

4. Given the number 9864, write the following:

The place value of each digit
The total value of each digit

EXPRESSING NUMBERS IN EXPANDED FORM

Example 1

Write each of the following numbers in expanded form

(a) 9732

(b) 5080

(d) 3334

Answer

(a) 9732 = 9000 + 700 + 30 + 2.

(b) 5080 = 5000 + 0 + 80 + 0.

(d) 3334 = 3000 + 300 + 30 + 4.

Example 2

Write each of the following in short form

(a) 4000 + 500 + 30 + 1 =

(b) 4000 + 800 + 40 + 2 =

(d) 5000 + 0 + 0 + 1 =

Answer

(a) 4000 + 500 + 30 + 1 = 4531.

(b) 4000 + 800 + 40 + 2 = 4842.

(d) 5000 + 0 + 0 + 1 = 5001.

Exercise 4

1. Write each of the following numbers in short form

9000 + 800 + 70 + 2 =
8000 + 800 + 80 + 0 =
1000 + 0 + 0 + 6 =
5000 + 600 + 50 + 8 =
9000 + 700 + 0 + 2 =

2. Complete the following table. Take the first row as an example

3. In thediagram A – F, one circle has four branches of circles. The of numbers in each branches gives the answer in short form. Taking 3(a) as an example, write down the missing numbers

4. Write each of the following numbers in expanded form

(a) 7889

(b) 2043

(d) 9690

(e) 3245

(f) 9770

(g) 3891

(h) 1654

READ AND WRITE WHOLE NUMBERS

A. Reading whole numbers

Example 1

Read the following numbers

(a) 1001

(b) 1086

Answer

Exercise 5

Read the following numbers

Example 2 Read each of the following numbers

(a) 1350 (b) 1572 (c) 9700 (d) 9540 (e) 9998

Answer

Exercise 6

Read the numbers in the following table

Exercise 7

1. Read the following numbers horizontally and vertically

2. Read numbers in the following chart

3. Read the following numbers

(a) 6546

(b) 7865

(e) 4006

(f) 8009

(g) 7016

(h) 9468

WRITING WHOLE NUMBERS

Example 1

Write the following numbers in words

(a) 1000 (b) 1001 (c) 1002 (d) 1003 (e) 1004

(f) 1005 (g) 1006 (h) 1007 (i) 1008 (j) 1009 (k) 1010

Answer

Example 2

Write the following numbers in words

(a) 1018

(b) 4216

Answer

(a) 1018 = One thousand and eighteen

(b) 4216 = Four thousand, two hundred and sixteen

Example 3

Write each of the following numbers in numerals

Thirteen thousand, one hundred and fifty-five
Three hundred six hundred and eight
Nine thousand four hundred and twelve

Answer

Thirteen thousand, one hundred and fifty-five =13155
Three hundred six hundred and eight =3608
Nine thousand four hundred and twelve = 9412

Exercise 8

1. Carefully study the following table and fill in the blanks. The first row is provided as an example

2. Write each of the following numbers in words

3. Write each of the following numbers in numer

4. Fill in the blanks in the following table

5. (a) Put a tick if a statement is correct, and cross if it is incorrect. the first row is provided as an example

(b) Write correctly all the incorrect numbers in words from question 1 (a)

6. Study figure 1 and 2, read their captions and then answer the questions that follow:

Figure 1. The old fort in Zanzibar was built in the year one thousand six hundred and ninety-nine

Figure 2. Kilimanjaro mountain is five thousand eight hundred and ninety-five metres high

Write in numerals the numbers you have read from each caption
Write the place value of each digit you have read from each caption

READING AND WRITING NUMBERS EXCEEDING 10000

Example 1.

Write the place value of each digit in 61270, then write the number in words Answer

The place values of the digits in 61270 are as follows:

Therefore, 61270 is read as sixty-one thousand two hundred and seventy.

Example 2

Write the place value of each digit in 876543, then write the number in words Solution

Therefore 876543 is read as eight hundred, seventy-six thousand five hundred and forty-three

Example 3

Write the place value of each digit in 9261514, then write the number in words Solution

Therefore 9261514, is read as nine million two hundred sixty-one thousand five hundred and fourteen

Example 4

Wrutethe following numbers in expanded from

(a) 24765

(b) 273453

Answer

Example 5.

Write the following whole numbers in numerals

Ten thousand three hundred and fifty – five
One million nine hundred eighty thousand three hundred and ninety-five

Answer

(a) 10355

(b) 1980395

Example 6

Write the total value of each digit in 9876543

Exercise 9

1. Write each of the following numbers in words

2. Write each of the following numbers in numerals

3. Write the numbers represented by each abaci,

4. Write the place value of 6 in each of the following whole numbers

(a) 645218 (b) 446128 (c) 21610 (d) 699222 (e) 364974 (f) 239364

5. Write the total value of the underlined digits in each if the following numbers

(a) 49002 (b) 6249356 (c) 541341 (d) 4755964 (e) 7 215549 (f) 36314

6. Write each of the following numbers in expanded form

(a) 79684 (b) 645218 (c) 8321483 (d) 9432370

7. Write each of the following numbers in short form (a) 60000 + 5000 + 400 + 30 + 2

(a) 800000 + 70000 + 6000 + 0 + 20 + 9

(b) 7000000 + 600000 + 40000 + 5000 + 400 + 30 + 7

8. Write the place value of the underlined digits in each if the following numbers

COMPARING WHOLE NUMBERS

Whole numbers can be compared when they are equal, greater than or less than another

Basic symbols for comparing numbers

Example

Use the symbols <, = or > to compare the following numbers

(a) 8900 __ 8090 (b) 3220 ___ 3220 (c) 3240 __ 3420 (d) 715 __ 517 Answer

(a) 8900 > 8090 (b) 3220 = 3220 (c) 3240 < 3420 (d) 715 > 517

Exercise

1. Use the symbols <, = or >to compare the numbers in the following table. (a) is provided as an example

2. Use the symbols <, = or > to compare the given numbers

3. The following chart shows different fruits and their quantities

4. Baraka has a card written nine thousand five hundred and forty. Furaha has a card written 9450. Between the two, who has the card with smaller number?

5. Halima has a card numbered 2010 and Yusufu has a card numbered 1577. Between the two, who has a card with a larger number?

6. Carefully study the following pictures and compare the number of the objects

(a) How many pencils are in box A?

(b) How many pencils are in box B?

(d) Use the symbols <, = or > to compare the number of pencils

SEQUENCE OF WHOLE NUMBERS

Example 1

Write the missing number in the following sequence

1, 4, 7, 10, 13, 16, 19, ___, ___ Solution

In this sequence the numbers are increasing by 3 in each step, thus

Therefore, the answer is 1, 4, 7, 10, 13, 16, 19, 22, 25.

Example 2

Fill in the missing numbers in the following sequence

1, 3, 5, 7, 9, ___, ___

Solution

In this sequence the numbers are increasing by 2 in each step, thus

Therefore, the answer is 1, 3, 5, 7, 9, 11, 13

Example 3

Fill in the missing numbers in the following sequence

25, 23, 21, ___, ___

Solution

This sequence shows that numbers are decreasing by 2 in each step Thus

25 – 2 = 23 23 – 2 = 21 21 – 2 = 19 19 – 2 = 17 Therefore, the answer is 25, 23, 21, 19, 17.

Example 4

Fill in the missing numbers in the following sequence

750, 600, 450, 300, 150, ___

Solution

This sequence shows that numbers are decreasing by 150 in each step

Thus

Therefore, the answer is 750, 600, 450, 300, 150, 0

Example 4

Fill in the missing numbers in the following sequence: 45, 41, 37, 33, ___

Solution

This sequence shows that numbers are decreasing by 4 in each step

Thus

45 – 4 = 41 41 – 4 = 37 37 – 4 = 33 33 – 4 = 29

Therefore, the answer is 45, 41, 37, 33, 29.

Exercise 11

1. Arrange number given in the following table in ascending order

7, _____, _____, _____, _____, _____, _____, _____, _____, _____

2. Arrange number given in the following table in ascending order

44, ___, ___, ___, ___, ___, ___, ___, ___, ___

3. Write the missing numbers in each of the following sequences

(i) 0, 2, 4, 6, ___, ___, ___

(ii) 11, 22, 33, 44, ___, ___, ___

(iv) 2, 6, 10, 14, 18, ___, ___, ___

(v) 3, 8, 13, 18, 23, 28, 33, ___, ___, ___

(vi) 465, 466, 467, ___, ___, ___

(vii) 210, 220, 230, 240, 250, 260, ___, ___, ___

4. Write the next number in each of the following sequences

(a) 14, 12, 10, 8, ___, ___, ___

(b) 23, 20, 17, 14, 11

5. Write the place value of each digit in 9825

(a) _________ is in tens place

(b) _________ is in ones place

(d) _________ is in the hundreds place

6. Write the missing numbers in each of the following sequences

(a) 500, 600, ____, ____, 900, ____

(b) 433, 430, ____, 424, ____, 418, 415, ____

(e) 4, 10, ____, 22, ____, 34, 40, 46, ____, 58

(f) 415, 418, ____, 424, ____, 430, 433, ____

(g) 1011, 1014, ____, 1020, 1023, ____, 1029

(h) 56, 54, 52, ___, ___, ___

(i) 69, 60, 51, 42, 33, ___, ___, ___

(j) 95, 85, 75, 65, 55, 45, ___, ___, ___

(k) 260, 250, 240, 230, 220, 210, ___, ___, ___

7. Carefully study the following sequences, then for each sequence state the operation used. Take (a) as an example

8. The height of 4 mountains were rrrecordered as follows: shira is 3, 626 metres, Oldeani 3, 188 metres, Meru 4, 566 metres and Klute 3, 952 high. Arrange the height of the mountains from the lowest to the highest mountain.

9. Majura sold 15 cups of milk on the first day. He sold 8 more cups on each subsequent day. How many cups of milk did he sell on the fourth day?

10. The factory printed 50 books on the first day. It printed 20 more books in each subsequent day. How many books were printed on the third day?

11. Pamela bought 3 mangoes on the first day. She bought two more mangoes on the sequent day. How many mangoes did she buy on the fourth day?

12. Mkeya has 5 chuldren. The difference in ages between two successive children is 4 years. If the first born is 39 years old, how old is the last born?

REVISION EXERCISE

1. Write the number obtained from the following place values

a) Seven thousands, six hundreds, two tens and two ones

b) Seven ten thousands, zero thousands, six hundreds, eight tens and three ones

c) Two ten thousands, three thousands, four hundreds, six tens and six ones

d) One millions, seven hundred thousands, four ten thousands, one thousands, one hundreds, two tens and zero ones

e) Three millions, seven hundred thousands, six ten thousands, five thousands, three hundreds, one tens and three ones

2. Write each of the following numbers in short form

(a) 4000 + 200 + 50 + 1 =

(b) 9000 + 800 + 30 + 3 =

(d) 600000 + 40000 + 4000 + 300 + 0 + 2 =

(e) 2000000 + 600000 + 40000 + 0 + 700 + 90 + 9 =

3. Use the following number to fill in the blanks with the place value of each digit

4. Write each of the following numbers in numerals

(a)One thousand and seven

(b)Five thousand five hive hundred and three

(d) One hundred eighty thousand five hundred and forty –one

(e) Two million six hundred ninety- eight thousand six hundred and fifty-two

5. Write each of the following numbers in words

(a) 2022

(b) 4969

(d) 291649

(e) 1889 773

6. Write each of the following numbers in expanded form

(a) 7007

(b) 5712

(d) 64645

(e) 303067

7. Write each of the following numbers in the ascending order

(i) 5, 2, 6, 12, 19, 3, 1, 20,17

(ii) 36, 21, 15, 7, 10, 28, 45, 11

(iii) 789, 63, 32, 981, 252, 172, 426

8. Write each of the following numbers in the descending order

(a) 125, 78, 111, 89, 305, 32, 120, 360, 115, 92, 412, 76,61, 27, 56

(b) 200, 903, 730, 341, 81, 199, 189, 800, 463, 72, 326, 247

9. Write the numbers represented by each abacus:

10 Use the symbols <, = or > to compare the given numbers

(a) 8765 and 8576 (b) 2341 and 2341 (c) 2222 and 222

(d) 180541 and 180514 (e) 1234 and 2134 (f) 23466 and 24366

11. Fill in the missing numbers in each of the following sequence:

(a) 71, 66, 61, 56, 51, 46, _____, _____, 31

(b) 100, 75, _____, 25, _____

(d) 729600, 729590, _____, _____, _____, 729550

(e) 70, 61, 52, 43, 34, _____, _____, _____

12. Write the operation used in each of the following sequence. Question (a) is provided as an example

(i) 1, 2, 3, 4, 5, 6, 7, 8 one is added in each step

(ii) 0, 4, 8, 12, 16, 20, 24, 28 _____

(iii) 68, 60, 52, 44, 36, 28, 20 _____

(iv) 100, 90, 80, 70, 60, 50, 40, 30, 20, 10, 0 _____

(v) 1 444, 2 444, 3 444, 4 444, 5 444 _____

13. Fill in the missing numbers in each of the following sequences

(a) 2398, 2390, 2382, ____, ____, 2358, 2350, ____

(b) 52552, 51552, ____, ____, 48552, 47552, ____, 45552

(d) 2342, 2350, 2358, _____, _____, 2382, 2390, 2398, _____

(e) 45562, 46562, _____, _____, 49562, 50562, _____, 52562

14. A teacher arranged numbers in a sequence as follows: 45, 41, 37, 33, ___, ___. Find the next two numbers

15. The first number in a sequence is 50. If 3 is subtracted in each step, what will be the value of the fifth number?

16. Pupils wrote a sequence starting with 3. If they added 5 in each step, what is the value of the sixth number?

17. Write a sequence of numbers from 0 to 50 with a step of 5.

18. Write a sequence with an interval of 6 in each step from 72 to 0

19. The attendance of standard three pupils increases by three students each week. If there are 123 pupils in the first week, how many pupils attend in the fourth week?

20. Write 895674 by using

The place value of each digit
The total value of each digit

WHOLE NUMBERS GENERAL QUESTIONS

1. Write the place value of each digit in 9825

(a) _________ is in tens place

(b) _________ is in ones place

(e) _________ is in the hundreds place

2. (a) which digit is in the hundreds place in 7029?

(b) which digit is in the thousands place in 8173?

(d) a number has 0 in the ones [lace, 6 in the tens place and 7 in the hundreds place. What is the number?

3. (a) How many hundreds are there in 3287?

(b) There are 9674 apples in the basket. How many thousands apples are there?

4. (a) Identify the place value of each digit in the following whole numbers?

(a) 6247

(b) 9999

(d) 4444

(e) 3239

(f) 2776

(g) 1111

(h) 8107

(i) 9009

(j) 5108

5. Write the place value of underlined digit in the following whole numbers

6. Fill in the blanks with the place values of the given digits

a) In 2968

2 is in ___________, 9 is in ________________

6 is in ___________, and 8 is in _____________

b) In 9801

9 is in ___________, 8 is in ________________

0 is in ___________, and 1 is in _____________

c) In 7236

7 is in ___________, 2 is in ________________

3 is in ___________, and 6 is in _____________

d) In 5649

5 is in ___________, 6 is in ________________

4 is in ___________, and 9 is in _____________

7. Write each of the following numbers in short form

(A) 5000 + 700 + 50 + 1 =

(B) 8000 + 400 + 50 + 3 =

(d) 600000 + 60000 + 6000 + 600 + 0 + 7 =

(e) 4000000 + 700000 + 30000 + 0 + 100 + 50 + 9 =

(f) 9000 + 800 + 70 + 2

8. Fill in the missing numbers in each of the following sequences

(a) 2398, 2390, 2382, ____, ____, 2358, 2350, ____

(b) 52552, 51552, ____, ____, 48552, 47552, ____, 45552 ____, ____, ____, 840000, ____, 860000, ___

(d) 45562, 46562, _____, _____, 49562, 50562, _____, 52562

(e) 219, _____, 221, 222

9. Write Three tens, zero hundred, two ones and eight thousands as a single digit

10. Amina wrote ‘nine thousand, nine hundred and seventy-three’ in numerals.

Which numerals did she write?

11. Write the number 1350 in words

12. Kituko wrote the number pattern as shown below: 15, 14, 13, ______ , ______ , 10, 9

14. What are the two missing numbers in that pattern?

15. Sudi wanted to write 1908 in words. Help him to write the shown number.

16. Sinyorita had nine thousand and ninety goats. Write the number of goats in numerals.

17. In the number 13567, which digit is in thousands place value?

18. My sister told me to write the next number just after two thousand and ninetynine.

19. What is the correct answer?

Juha had written a certain number on the blackboard. If you write that number in long form, it is seen as

(a) 7000 + 500+00+0 . Which number was that? Write the next number in the sequence below;

(b) 14, 19, 24, ______

20. Joan was finding the total value of the first digit from the left in the number 5697. What was her correct answer?

21. Which of the following application is true? ( a or b )

(a) 3480 > 3840

(b) 2560 > 2056

22. Write the following numbers in words

(a) 520850

(b) 4512365

23. Write the following numbers in numerals

(a) One hundred twenty-seven thousand Eight hundred and seven

(b) Eight million two hundred seventy-seven thousand two hundred and fifty.

(d) Three hundred and four

24. Circle the largest number

(a) 270 46 460 640

(b) 301 310 140 305

25. Underline the smallest number

(a) 730 342 225 205

(b) 616 661 696 678

26. Write the place value of 6 in 46128

27. Write 8321 in expanded form

28. Write 60000+5000 +400 + 30 + 2 in short form

29. Use the symbols < . = or >to compare the numbers

(a) 100 _____ 1000

(b) 8962 _____ 2968

30. Fill in the missing number

21, 23,25,27, ___________

31. Write the operation sign used in

1, 3, 5, 7

32. In which rate are numbers descending in

50, 40, 30, 20, 10

33. Arrange the following numbers in ascending order

252, 172, 426, 789

34. Mary has 8510 cows. Write the number of cows in figure. 56. Write thirty two thousand and sixty five in numerals 57. What is the place value of 8 in 38674?

35. Find the total value of 4 in 38674