Chapter 4 DECIMALS

4.1 Decimals and Fractions1. A decimal is a fraction with a

denominator of 10 or a power of 10.2. To convert a fraction into a decimal,

divide the numerator by the denominator.

3. To change a decimal into a fraction. Divide it by the power of 10 such as 10, 100, 1 000,..

Example:

i)

0.4 is read as zero point four

ii)

3.08 is read as three point zero eight

4.2 Place Value and Digit Value1.

Tens units Decimal point

tenths hundredths

1 2 . 4 5

12.45 = 10 + 2 + 0.4 +0.05

= 10 + 2 +

2. The decimal places are the places occupied by the digit after the decimal point.

Example: i) 7.9

1 digit to the right of the decimal pointTherefore, 7.9 has 1 decimal point.

ii) 7.942 digits to the right of the decimal pointTherefore, 7.94 has 2 decimal points.

iii) 7.9483 digits to the right of the decimal pointTherefore, 7.948 has 3 decimal points.

4.3 Addition and Subtraction of Decimals

To add or subtract decimals, arrange the digits of the same place value in the samevertical column.Example:27.064 +1.3 + 0.91 = 29.274

27 . 064 1. 3

+ 0 . 91 29 . 274

4.4 Multiplication and Division of Decimals

To multiply decimals(a) Multiply the decimals in the same way as

whole numbers.(b) The number of decimal places in the

answer is equal to the sum of decimal places in the individual decimals.

Example :i) 3.45 x 1.7 = 5.865

3.45 ( 2 d.p.) x 1.7 ( 1 d.p.)

2415 345 5.865 ( 3 d.p.)

ii) 6.9 ÷ 0.03 =

= 230

4.5 Combined OperationsIn performing the combined operations of

decimals, we follow the same rule as those for whole nuir

(a) Work out the expressions in brackets.(b) Do multiplication and division from left

to right.(c) Do addition and subtraction from left to

right.Example:6x ( 4.1 – 2.12 ) ÷ 0.8= 6 x 1.98 ÷ 0.8= 11.88 / 0.8 = 14.85

Chapter 5 PERCENTAGES (%)

5.1 Percentages

1. Percentage is a fraction out of 100.2. Change a fraction into a percentage,

multiply it by 100%.

Example: x 100% = 75%

3. To change a decimal into a percentage,multiply by 100%.

Example: 0.29 x 100% = 29%

4. To change a percentage into fraction,divide by 100% and reduce to its lowest terms.

Example:1.30% =

=

5. To change a percentage into a decimal,divide by 100%.

Example: 16% =

= 0.16

5.2 Perform computations

1. To find the percentage of a quantity, change into fraction and multiply by the quantity.

Example: 30% of 400

= x 400

= 120

2. To find the percentage one number is of another, change both quantities to the same unit, form a fraction and multiply by 100%

Example: 3 of 10

= x 100%

= 30%

3. To find a number given the percentage, first find the value of1 % then find the value of 100% of the

number.

Example:Given 10% of a number = 50

1% of a number 50 =

The number = x 100

= 500

4. To find the percentage increase or decrease

5. Increase may be dividend, commission, simple interest or profit.

Example :300 is increased by 20 %

Value of increase =

= 60

Final value = 300 +60= 360

6. Decrease may be discount or loss.

Percentage change =

change in value x 100%original value

Increase = % increase x original value

Final value = Original value + increase

Decrease = % decrease x original value

Final value = Original value - decrease

Example:Selling price = RM 500Discount = 30%

Decrease =

= RM 150Selling price = 500 – 150

=RM 350