Prealgebra Review R.3

R.3 DECIMAL NOTATION

a. Convert from decimal notation to fraction notation.

b. Add, subtract, multiply, and divide using decimal notation.

c. Round numbers to a specified decimal place.

Objective a
Convert from decimal notation to fraction notation.

The decimal notation 42.3245 means:
4 tens + 2 ones + 3 tenths + 2 hundredths + 4 thousandths + 5 ten-thousandths
We read this number as
“Forty-two and three thousand two hundred forty-five ten-thousandths.”
The decimal point is read as “and”.

To convert from decimal to fraction notation,

Example A

Example B

To convert from fraction notation to decimal notation when the denominator is 10, 100, 1000 and so on,

Example C

Objective b
Add, subtract, multiply, and divide using decimal notation.

Adding with decimal notation is similar to adding whole numbers.
First we line up the decimal points so that we can add corresponding place-value digits.
Add the digits from the right.
If necessary, we can write extra zeros to the far right of the decimal point.

Example D

Example E

Example F

Multiplication with Decimal Notation

a) Ignore the decimal points, and multiply as whole numbers.
b) Place the decimal point in the result of step (a) by adding the number of decimal places in the original factors.

Example G

Dividing When the Divisor is a Whole Number
a) Place the decimal point in the quotient directly above the decimal point in the dividend.
b) Divide as whole numbers.

Example H

Dividing When the Divisor is not a Whole Number

a) Move the decimal point in the divisor as many places to the right as it takes to make it a whole number. Move the decimal point in the dividend the same number of places to the right and place the decimal point in the quotient.
b) Divide as whole numbers, inserting zeros if necessary.

Example I

Example J

Example K

Example L

Objective c

Round numbers to a specified decimal place.

Rounding Decimal Notation
To round to a certain place:
a) Locate the digit in that place.
b) Consider the digit to its right.
c) If the digit to the right is 5 or higher, round up, if the digit to the right is less than 5, round down.

Example M

Example N

Example O