Decimals
A decimal is a number that can be written as a fraction whose
denominator is 1, 10, 100, 1000, and so on. For example: Decimal
Notation = Fraction Notation
In a whole number, the decimal point is located to the right
of the digit in the ones place. For example: (252 = 252 .). The
place value of a digit is determined by where it is in relation
to the decimal point. The digits to the left of the decimal point
are whole numbers; they have place values of 1, 10, 100, 1000,
10,000 and so on. The digits to the right of the decimal point
are fractional parts; they have place values of and so
on. Note: each place is as large as the place to its immediate
left.
In the place value chart, the numbers to the left of the
decimal point end in ‘s’ and represent the whole number
part of the decimal while the numbers to the right of the decimal
point end in ‘ths’ and represent the fractional part of
the decimal.
To write the word name for a Decimal: If
there is no number other than ‘0’ to the left of the
decimal point, omit steps one and two.
 Write the name for the whole number to the left of the
decimal point.
 Write the word ‘and’ for the decimal point.
 Write the name for the number to the right of the decimal
point as if it were a whole number. Then write the name
for the place value of the last digit on the right.
Example: 253.5674 is two hundred fiftythree
and five thousand six hundred seventyfour ten thousandths.
To add or subtract decimals, line up all the
decimal points in a vertical column.
Example 1. add: 10.5 + 3 +.072 + 195.0035
Example 2. Subtract: 123.7450 – 2.00034
To multiply two decimals:
 Multiply the two numbers as if they were whole numbers.
 Locate the decimal point by counting the number of
decimal places (to the right of the decimal point) in
both numbers. The total of these two counts is the number
of decimal places the product must have.
 If necessary, add zeros to the left of the numeral so
that there are enough decimal places.
Examples:
1. 2.7 x 4 = 10.8 Notice that there is
‘1’ decimal place in the product.
2. 3.456 x .5 = 1.7280 In this product, there
are ‘4’ decimal places. 1.7280 can also be written as
1.728.
3. .45 x .12 Notice that 45 x 12 = 540, but
there should be 4 decimal places in the product. Therefore, add a
zero to the left of the ‘5’.
.45 x .12 = .0540 = .054
To divide two decimal numbers:
 If the divisor is not a whole number, move both decimal
points to the right the same number of decimal places
until the divisor is a whole number.
 Place the decimal point in the quotient above the decimal
place in the dividend.
 Divide as if both numbers were whole numbers.
 If the numbers do not divide evenly, round off to the
given place value.
Examples:
Multiplication and Division by powers of Ten: A
power of ten is a number that can be written as a product of
tens; 10, 100, 1000, 10000…..are powers of ten. In
exponential form, these are A power of ten can be recognized by
looking for the number ten written with an exponent or a single
‘1’ followed by zeros.
To multiply a number by a power of ten, move the decimal point
to the right. To divide a number by a power of ten, move the
decimal point to the left. The number of places to move is shown
by the number of zeros in the power of ten. If the exponent of
ten is negative, move the decimal point to the left as in
division.
Examples:
