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JSS2: MATHEMATICS - 1ST TERM

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  1. Properties of Whole Numbers I | Week 1
    4 Topics
    |
    1 Quiz
  2. Properties of Whole Numbers II | Week 2
    4 Topics
    |
    1 Quiz
  3. Properties of Whole Numbers III | Week 3
    5 Topics
    |
    1 Quiz
  4. Indices | Week 4
    2 Topics
    |
    1 Quiz
  5. Laws of Indices | Week 5
    5 Topics
    |
    1 Quiz
  6. Whole Numbers & Decimal Numbers | Week 6
    4 Topics
    |
    1 Quiz
  7. Standard Form | Week 7
    3 Topics
    |
    1 Quiz
  8. Significant Figures (S.F) | Week 8
    4 Topics
    |
    1 Quiz
  9. Fractions, Ratios, Proportions & Percentages I | Week 9
    6 Topics
    |
    1 Quiz
  10. Fractions, Ratios, Proportions & Percentages II | Week 10
    4 Topics
    |
    1 Quiz
  11. Fractions, Ratios, Proportions & Percentages III | Week 11
    3 Topics
    |
    1 Quiz
  12. Approximation & Estimation | Week 12
    1 Topic
    |
    1 Quiz



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To round off numbers simply means making a number simpler but keeping its value close to what it was. Rounding numbers means adjusting the digits (up or down) to make rough calculations easier.

The result will be an estimated answer, not a precise one.

For example, if the population of a country is 8, 214, 426 in a certain year, this number is hard to remember but if we say the population of that country is 8 million, it is a good estimate, because it does not make any real difference what the exact number is. For example, 73 is rounded off to 70 because 73 is closer to 70 than 80.

Rules:

1. Round down digits  0, 1, 2,3,4,   (i.e. add 0)

2. Round up digits  5, 6, 7, 8, 9   (i.e add 1)

To find the number of decimal places, simply count the number of figures after the decimal point.

Decimal places (d.p)

decimal place4 e1606123505338

Example 1

Write:

a. 17.6536
b. 25.2999 

to 

i. 1 d.p
ii. 2 d.p
iii. 3 d.p

Solution a

i. 17.6536 to 1 d.p

1 d.p2 d.p3 d.p4 d.p
17.6536

5  is closest to 6 (the 1st d.p)

5 is a round-up number so we add 1 to 6

= 17.7

ii. 17.6536 to 2 d.p

1d.p2d.p3d.p4d.p
17.6536

3  is closest to 5 (the 2nd d.p)

3 is a round-down number so we add 0

= 17.65

iii. 17.6536 to 3 d.p

1d.p2d.p3d.p4d.p
17.6536

6  is closest to 3 (the 3rd d.p)

6 is a round-up number so we add 1

= 17.654

Solution b

i. 25.299 to 1 d.p

1d.p2d.p3d.p4 d.p
25.2999

9  is closest to 2 (the 1st d.p)

9 is a round-up number so we add 1

= 25.3

ii. 25.299 to 2 d.p

1d.p2d.p3d.p4 d.p
25.2999

9  is closest to 9 (the 2nd d.p)

9 is a round-up number so we add 1

= 25.30

iii. 25.299 to 3 d.p

1d.p2d.p3d.p4 d.p
25.2999

9  is closest to 9 (the 3rd d.p)

9 is a round-up number so we add 1

= 25.300

To round a decimal number to the nearest tenth (t) is the same as rounding to the 1st decimal place etc.

rounding off e1606123975477

Tenth =  1st d.p

Hundredth =  2nd d.p

Thousandth = 3rd d.p

Ten Thousandth = 4th d.p

Hundred Thousandth = 5th d.p

Millionth = 6th d.p

Ten Millionth = 7th d.p

Hundred Millionth = 8th d.p

Billionth =  9th d.p

Example 2

Round of  62. 57498992  to the nearest 

i. tenth   
ii. hundredth 
iii. thousandth
iv. millionth

Solution

i. 62. 57498992  to the nearest tenth

Screen Shot 2020 11 23 at 10.36.05 AM

7  is closest to 5 (the Tenth = 1st d.p)

7 is a round-up number so we add 1

= 62.6 to the nearest tenth

ii. 62. 57498992  to the nearest hundredth

Screen Shot 2020 11 23 at 10.36.48 AM

7  is closest to 4 (Hundredth = 2nd d.p)

4 is a round-down number so we add 0

  = 62.57 to the nearest hundredth

iii. 62. 57498992  to the nearest thousandth

Screen Shot 2020 11 23 at 10.37.45 AM

9  is closest to 4 (Thousandth = 3rd d.p)

9 is a round-up number so we add 1

  = 62. 575 to the nearest thousandth

iv. 62. 57498992  to the nearest millionth

Screen Shot 2020 11 23 at 10.39.51 AM

9  is closest to 9 (Millionth = 6th d.p)

9 is a round-up number so we add 1 which gives 10. In this case, we then add 1 to the column on the left which is 8.

  = 62.574 990 to the nearest millionth.

Evaluation Questions:

1. Express the following in standard form 

a.    90785
b.    29560578
c.    287.251
d.    20000
e.    55000
f.    107000
g.    770
h.    4

View Answers

2. Change these standard forms to ordinary numbers

a.    6.2 × 10o
b.    4.3 × 105
c.    9.37 × 107
d.    3.02 × 106
e.    1.2 × 103
f.    15.23 × 104

View Answers

3. Express these numbers in standard form:

a.    0.546
b.    0.000307
c.    0.00275
d.    0.000 057
e.    0.000 0001
f.    0.251
g.    0.0251
h.    0.00251
i.    0.000251
j.    0.000 0251

View Answers

4. Express the following as decimal fractions:

a.    4.3 x 10-3
b.    3.2 x 10-5
c.    1.89 x 10-7
d.    1.3 x 10-4
e.    3.08 x 10-2
f.    9 x 10-5
g.    4 x 10-6
h.    5.5 x 10-3

View Answers

5. Round the following to 

i.    1  d.p
ii.    2 d.p
iii.    3 d.p
iv.    4. d.p

a.    0.088055
b.    25.43998
c.    16.27092
d.    0.99905

View Answers

6. Round off the following to the nearest 

i.    tenth
ii.    hundredth
iii.    thousandth
iv.    millionth

a.    5. 248 635 299
b.    3. 998 225 698

View Answers

Responses

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Evaluation Questions 1

Answers:

a. \( \scriptsize 9.0785 \: \times \: 10^4 \)

b. \( \scriptsize 2.9560578 \: \times \: 10^7 \)

c. \( \scriptsize 2.87251 \: \times \: 10^2\)

d. \( \scriptsize 2\: \times \: 10^4 \)

e. \( \scriptsize 5.5 \: \times \: 10^4 \)

f. \( \scriptsize 1.07 \: \times \: 10^5 \)

g. \( \scriptsize 7.7 \: \times \: 10^2 \)

h. \( \scriptsize 4 \: \times \: 10^0 \)

 

Evaluation Questions 2

Answers:

a. 6.2

b. 430 000

c. 93 700 000

d. 3 020 000

e. 1 200

f. 152 300

 

Evaluation Questions 3

Answers:

a. \( \scriptsize 5.46 \: \times \: 10^{1} \)

b. \( \scriptsize 3.07 \: \times \: 10^{-4} \)

c. \( \scriptsize 2.75 \: \times \: 10^{-3} \)

d. \( \scriptsize 5.7 \: \times \: 10^{-5} \)

e. \( \scriptsize 1 \: \times \: 10^{-7} \)

f. \( \scriptsize 2.51 \: \times \: 10^{-1} \)

g. \( \scriptsize 2.51 \: \times \: 10^{-2} \)

h. \( \scriptsize 2.51 \: \times \: 10^{-3} \)

i. \( \scriptsize 2.51 \: \times \: 10^{-4} \)

j. \( \scriptsize 2.51 \: \times \: 10^{-5} \)

Evaluation Questions 4

Answers:

a. 0.0043

b. 0.000032

c. 0.000 000 189

d. 0.000 13

e. 0.0308

f.  0.00009

g. 0.000 004

h. 0.0055

Evaluation Questions 5

Answers:

a.
i. 0.1
ii. 0.09
iii. 0.088
iv. 0.0881

b.
i. 25.4
ii. 25.44
iii. 25.440
iv. 25.4400

c.
i. 16.3
ii. 16.27
iii. 16.271
iv. 16.2709

d.
i. 1.0
ii. 1.00
iii. 0.999
iv. 0.9991

Evaluation Questions 6

Answers:

a.
i. 5. 2
ii. 5.25
iii. 5.249
iv. 5.249635

b.
i. 4.0
ii. 4.00
iii. 3.998
iv. 3.998 226

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