GMAT Official Guide Quantitative Review 2019_ Book

GMAT® Official Guide 2019 Quantitative Review

3. Decimals
   In the decimal system, the position of the period or decimal point determines the place value of the
   digits. For example, the digits in the number 7,654.321 have the following place values:
   . .μ (JJ ..,
   (JJ (JJ i::
   '"'d i:: '"'d ;::i
   c,l I-< <J.l I-< 0
   (JJ ;::i '"'d (JJ
   0 i:: ;::i (JJ c <J.l c
   F :r: ~^0
   7 6 5 4

Some examples of decimals follow.

0.321 = .1_+ _1_+-^1 - = _ill_

10 100 1,000 1,000

0.0321=.Q+_l__+-^2 -+^1

..c: (JJ

'"'d .....

(JJ <J.l I-<

• .c:: .μ "d c
  c ;::i
  ~ :r:
  3 2

321

10 100 1,000 10,000 10,000

1.56=1+2-+_2_= 156

10 100 100

(JJ

..c: .μ

'"'d i::

c,l (JJ

;::i 0

F

1

Sometimes decimals are expressed as the product of a number with only one digit to the left of the

decimal point and a power of 10. This is called scientifi,c notation. For example, 231 can be written as

2.31 x 10^2 and 0.0231 can be written as 2.31 x 10-^2. When a number is expressed in scientific notation,

the exponent of the 10 indicates the number of places that the decimal point is to be moved in the

number that is to be multiplied by a power of 10 in order to obtain the product. The decimal point is

moved to the right if the exponent is positive and to the left if the exponent is negative. For example,

2.013 x 10^4 is equal to 20,130 and 1.91 x 10-^4 is equal to 0.000191.

Addition and subtraction of decimals.

To add or subtract two decimals, the decimal points of both numbers should be lined up. If one of the

numbers has fewer digits to the right of the decimal point than the other, zeros may be inserted to the

right of the last digit. For example, to add 17 .6512 and 653.27, set up the numbers in a column and add:

Likewise for 653.27 minus 17 .6512:

17.6512

+ 653.2700

670.9212

653.2700

• 17.6512
  635.6188