Significant FiguresAnd Figures

Significant FiguresandRounding

Module :MA0001NPFoundation

MathematicsLecture Week 2

Significant FiguresandRounding

Figures

Significant FiguresandRounding

Fractions, Decimals ,Percentage and Ratios

Fractions• Any number in the form p/q (q!=0) is called

fractions. For example : 2/3,1/4…….• Here p is called numerator and q is called

denominator.• If p is less than q then p/q is called proper

fraction .• If p is greater than or equal to q then p/q is

called improper fraction.

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Fractions…Equivalent fractions:Given a fraction we may be able to express it in a

different form .For example:• 3/8 and 9/24 are equivalent factors.• 3/6 = 18/36 = 27/54A fraction is in simplest form when there are no

factors common to both numerator and denominator . For example: 5/12

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Fractions….Q1. Express the following factors in simplest form 24/36 , 58/92 , 25/450 , 169/1300 , 24/228

Q2.Express the following fractions to an equivalent fractions having a denominator 30.

3/4 ,7/6 ,24/21, 8/9 , 10/20

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Fractions….• Addition and Subtraction of fractions In order to add or subtract fractions we first

rewrite each fraction so that they all have the same denominator called common denominator.

For example: 3/5 + 7/2 =3/5*2/2 +7/2*5/5 =6/10 +35/10 =41/10

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Fractions….Mixed Fraction: The numbers like 3 ¾ is called

mixed fraction because it contains a whole number part 3 and a fractional part ¾.

Q. Find 1.1/4 + 2/32.1¾ + 5 ¼3.4½ + 1/34.1/11- 1/2

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Fractions….Multiplication and Division of Fractions Q. Evaluate each of the followings giving your

answer in simplest form 1.4/9 *3/82.3/4 * 1 ¾ * 3½3.6¼ ÷2½ +54.3¼ ÷1¾5.99/100÷1¼

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Ten thousa

ndsThousa

ndsHundre

ds

Tens

Units

100101102103104

The decimal number systemThe decimal number system allows us to use the digits 0 to 9 and the place value system to represent numbers of any size.

To represent whole numbers we label columns using increasing powers of 10:

60475

×10×10×10×10

For example,

Thousa

ndths

10-3Tenth

s

Hundredth

s

10-210-1

Tens

Units

100101

The decimal number systemTo represent fractions of whole numbers in our place value system we extend the column headings in the other direction by dividing by 10.Starting with the tens column we have:

53084

÷10÷10÷10÷10

For example,

The decimal point

Hundreds

102

The decimal number system

The decimal point separates the whole number part from the fractional part.

Thousa

ndths

10-3

Tenths

Hundredth

s

10-210-1

Tens

Units

100101

DECIMAL PARTWHOLE NUMBER PART

We can think of the number in this example as:

200 + 40 + 3 + 510

41000+ 7

100 +243.574 =

475342

The decimal number system Q1. Express the following Decimal numbers as

proper fractions in their simplest form 0.4 , 0.75 , 0.68 , 0.984 , 0.2505

Q2.Express the following as a decimal number 3/10 +7/100 , 8/10 + 3/10000 , 17/1000 + 5/10

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RatioA ratio compares the sizes of parts or quantities to each other.

For example,

What is the ratio of red counters to blue counters?

red : blue

= 9 : 3

= 3 : 1For every three red counters there is one blue counter.

What is the ratio of red counters to yellow counters to blue counters?

Ratio

red : yellow : blue

= 12 : 4 : 8

= 3 : 1 : 2

For every three red counters there is one yellow counter and two blue counters.

Simplifying ratios

Ratios can be simplified like fractions by dividing each part by the highest common factor.

For example,21 : 35

= 3 : 5÷ 7 ÷ 7

For a three-part ratio all three parts must be divided by the same number.

For example,

6 : 12 : 9

= 2 : 4 : 3÷ 3 ÷ 3

When a ratio is expressed in different units, we must write the ratio in the same units before simplifying.

Simplify the ratio 90p : £3

First, write the ratio using the same units.

90p : 300p

When the units are the same we don’t need to write them in the ratio.

90 : 300÷ 30 ÷ 30

= 3 : 10

Simplifying ratios with units

QuestionsQ 1.Simplify the following ratios

• 60 cm :70 m : 40mm

• 150 gm : 2kg :300gm

• 10p :$20

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QuestionsQ.2 Divide $1250 between A and B in the ratio of

7:3 .

Q3. Divide 250 m in the ratio 3:4:2.

Q4. Divide the mass of 560 kg in the ratio 3/4 :1/5

Q5.Simplify the ratio 1700m:5100m:17km

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QuestionsQ6.The ratio of boys to girls in year 10 of a

particular school is 6 : 7. If there are 72 boys, how many girls are there?

Q7. A citrus twist cocktail contains orange juice, lemon juice and lime juice in the ratio 6 : 3 : 1.

How much of each type of juice is contained in 750 ml of the cocktail?

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Percentage

• A percentage is a fraction whose denominator is 100.

For example: 53/100 = 53%The phrase ’ Per cent ’ means out of 100.• To convert a fraction to a percentage divide the

numerator by the denominator ,multiply by 100 and then label the result as a percentage .

For example :5/8 in to percentage = 5/8 * 100 = 62.5%

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Percentage….• To convert a decimal fraction in to a percentage

, multiply by 100 and label the result as a percentage.

For example: 0.145 to percentage = 0.145 *100=15.5 %• To convert a percentage to its equivalent

decimal fraction form divide it by 100.For example: 17.5% in to fraction = 17.5/100 = 0.175

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QuestionsQ1. Calculate 27 % of 120.

Q2. A deposit of $1250 increases by 15%. Calculate the resulting deposit.

Q3. A bicycle is advertised at $355. The retailer offers 15% festival discount. How much do

you pay for the bicycle.

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Questions….Q4. The price of a Television increases from

$ 13000 to $ 17000 .Calculate the percentage increases.(hint: Change percentage=(change/original value) *100

Q5. There are 850 students in a college . Out of them 350 were boys . Calculate the percentage of boys and girls in that college.

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Questions….Q6. The population of certain town increases from

2 millions to 3 millions during 10 yrs .Calculate the percentage increase in the population of that town during 10 years .

Q7. Calculate 29 % of 5800.

Q8. A number X is increased by 20 % to form a new number Y. Y is then decreased by 20 % to form a third number Z . Express Z in terms of X.

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