DECIMAL

FRACTIONS

By: David Robinson

 The Decimal

Modern methods of writing decimals were invented less

than 500 years ago.

Calculations using decimals are faster and more accurate

than common fractions.

Decimal fraction are not written with a numerator and

denominator, instead it is written with a decimal point.

Decimal fractions are equivalent to common fractions

having denominators that are powers of 10.

Robinson
 Reading Decimal Fractions
The following chart indicates the place value of the parts
of a number with respect to its position from the decimal
point.
Decimal Point
Whole Numbers Decimals Fractions

6 5 4 3 2 1 1 2 3 4 5

Hundred Hundred
Thousands Thousandths
Ten Thousands Ten Thousandths
Thousands Thousandths
Hundreds Hundredths
Tens Tenths
Units Robinson
 Reading Decimal Fractions
To read a decimal, read the number as a whole number
then say the name of the place value of the last digit to
the right.
For example,0.567 is read as:
“Five hundred sixty seven thousandths”
To read a mixed number, a whole number and a decimal,
read the whole number and then say “and” then read the
decimal.

For example,25.567 is read as:

“Twenty five and Five hundred sixty seven thousandths”

Robinson
 Rounding Decimal Fractions
Rounding Rules:

First determine the place value to which the

number is to be rounded.

Look at the digit immediately to the right of the

place value to which the number is to be rounded.

If the digit is less than 5, drop it and all the digits

to the right.

If the digit is 5 or more, add 1 to the place value

which you are rounding, then drop all the digits to
the right.
Robinson
 Rounding Examples

Round 14.763 to the nearest hundredth.

6 is in the hundredths place value.

3 is in the number directly to the right of 6.

Because 3 is less than 5, leave 6 unchanged and drop the 3.

Answer: 14.76

Robinson
 Rounding Examples

Round 0.0065789 to the nearest ten thousandth.

5 is in the ten thousandth place value.

7 is in the number directly to the right of 5.

Because 7 is greater than 5, raise 5 to 6 and drop all the

digits to the right.

Answer: 0.0066

Robinson
 Practice Problems

Round the following decimals to the indicated place value:

0.0078 0.01 10.6666 10.667

0.8376 0.838 22.3789 22.38
0.847 0.8 14.984 15
0.1955 0.196 10.999 11
0.8994 0.90 72.010101 72.01010

Robinson
 Converting Common Fractions
To
Decimal Fractions

Common fractions can be converted into decimal fraction

by dividing the numerator by the denominator.

.625
Express 5/8 as a decimal fraction: 8)5.0 0 0
48
20
16
40
40
0 Robinson
 Practice Problems

Convert the following Common Fraction to Decimals :

1/16 0.0625 5/8 0.625

1/8 0.125 3/4 0.75
1/4 0.25 7/8 0.875
3/8 0.375 11/16 0.6875
1/2 0.50 15/16 0.9375

Robinson
 Converting Decimal Fractions
To
Common Fractions
To convert a decimal fraction into a common fraction,
write the number after the decimal point as the
numerator of a common fraction.

Then write the denominator as 1 followed by as many

zeros as there are digits to the right of the decimal.

Or simply write the denominator of the common fraction

using the place value of the last digit in the decimal.

Robinson
 Example of Converting a Decimal - Fraction

Change 0.015 to a common fraction:

0.015 is read as fifteen thousands.

15 becomes the numerator.

15 3
1,000 becomes the denominator. 1,000 = 200
Reduce to lowest terms.

Robinson
 Practice Problems

Convert the following Decimals to Common Fractions :

.17 17/100 .125 1/8

.625 5/8 .375 3/8
.875 7/8 .475 19/40
.019 19/1,000 .345 69/200
.6 3/5 .485 97/200

Robinson
 Addition & Subtraction of
Decimal Fractions
To add or subtract decimals, arrange the numbers so the
decimal points are aligned directly under each other.

Add or subtract using the rules for whole numbers.

Place the decimal point in the answer directly under the

other decimals.
42.58
42.58 + 21.12 = + 21.12
63.70
Robinson
 Practice Problems
Perform the following operations as indicated:

2.45 + 11.34 13.79 2.45 − 1.34 1.11

.768 + 23.67 24.438 7.58 − 3.67 3.91
.25 + 3.68 3.93 4.25 − 3.68 0.57
.125 + 4.68 4.805 .125 − .068 0.057
32.67 + 15.39 48.06 32.67 − 15.39 17.28

Robinson
 Multiplication of Decimal Fractions
To multiply a decimal fraction, use the same procedure as
with whole numbers.

Count the total number of digits to the right of the

decimal points in both numbers being multiplied.

Starting from the last digit on the right of the product

move the decimal point the same number of spaces
counted to the left.

1 2 34
3.25 X .75 = 24375
.

Robinson
 Practice Problems
Perform the following operations as indicated:

2.4 x 1.3 3.12 2.4 x 1.3 3.12

0.76 x 3.67 2.7892 0.58 x 0. 7 0.406
0.25 x 0.68 0.17 4.25 x 3.68 15.64
0.28 x 0.6 0.168 0.12 x .068 0.00816
2.67 x 0.39 1.0413 2.67 x 5.39 14.3913

Robinson
 Division of Decimal Fractions
To divide a decimal fraction, use the same procedure as
with whole numbers.

Move the decimal point of the divisor to the right as many

places as necessary to make it a whole number.

Move the decimal point of the dividend to the right the

same number of places.

Divide and place the decimal point in the answer

directly above the decimal point in the dividend.

Robinson
 Example of
Dividing Decimals
Divide 1.325 by .18 7.361
Move the decimal 2 places to the 18.) 132.5
.18 1.325
right making .18 a whole number 126
65
Move the decimal 2 places to the 54
right in the numerator. 110
108
Place the decimal straight up in the 20
answer. 18
Divide using the rules for 20
whole numbers.
Robinson
 Practice Problems
Perform the following operations as indicated:

1.2 ÷ 0.3 4 7.8 ÷ 1.3 6

0.72 ÷ 0.04 18 0.64 ÷ 0.008 80
2.25 ÷ 0.05 45 4.25 ÷ 0.75 5.667
6.48 ÷ 0.6 10.8 .412 ÷ 0.002 206
4.70 ÷ 0.25 18.8 8.024 ÷ 1.003 8

Robinson
 Multiplying & Dividing by Powers of 10

When multiplying by powers of 10 move the decimal

point to the right as many places as there are zeros.

When dividing by powers of 10 move the decimal point

to the left as many places as there are zeros.

Decimal Point
Dividing Multiplying

7 7 4 9 8 1 0 3
 Practice Problems
Perform the following operations as indicated:

2.45 x 10 24.5 2.45 ÷ 10 0.245

7.68 x 100 768 7.68 ÷ 100 0.0768
42.5 x 1,000 4,2500 42.5 ÷ 1000 0.0425
.125 x 10,000 1,250 .125 ÷ 10,000 0.0000125
326.7 x 105 32,670,000 326.7 ÷ 10-5 0.003267

Robinson