Delgado Adult Education
Decimals Unit
• What happens between the whole numbers
on this number line? Smaller units, called
decimals!
Decimals: what do they mean?
• Like fractions and percents, decimals represent a part of a
whole.
• Think of it this way: in our money system, if we didn’t have
coins, we would have to pay for everything in whole dollar
amounts!
• Money is a good example of decimals in action.
• In our system, the penny is the smallest unit, and it represents
1/100 of a dollar. We write it as .01.
• The nickel is the next largest unit, and it represents 5/100 of a
dollar. We write it as .05.
• The dime represents 10/100 (or 1/10) of a dollar, and is
written as .10.
• and the quarter represents 25/100 of a dollar, and is written
as .25.
Spend a moment looking at these diagrams of the value of each unit place on both
sides of the decimal point. Make notes about any patterns you see.
Place value in decimals
•
Our whole number system operates according to a system of 10’s, and so do our
decimals. That is, when we move to the left, each unit is raised by a power of ten
(x 10), and when we move to the right, each unit is reduced by a power of ten (÷
10). Put plainly, numbers get bigger as we move to the left, and smaller as we
move to the right. Notice that all the decimal place names end in –ths. They
represent parts of a unit, or fractions.
Place value exercises:
• Write each of the numbers below, and circle the
digit in the tenths place in each:
0.3
2.986 12.7 4.1509 428.63
• Write each of the numbers below, and circle the
digit in the hundredths place in each:
0.27 0.018 4.26 3.8597 13.485
• Write the following as decimals:
Four tenths, six and three tenths, nine thousandths,
eight and twenty-nine ten-thousandths
Answers
• 3, 9, 7, 1, 6
• 7, 1, 6, 5, 8
• .4, 6.3, .009 (see how 0 is used as a placeholder
here?), 8.0029
• If you got all these, great—move on to the next
page! If you’d like a little more instruction and
practice, click here (as with all Math is Fun pages,
the exercises are at the bottom):
• http://www.mathsisfun.com/decimals.html
Adding and Subtracting Decimals
• Adding and subtracting decimals is much like adding and
subtracting whole numbers.
• RULE: To add decimals, line up the decimal points with decimal
point under decimal point. Remember that a whole number is
understood to have a decimal point at the right (4 = 4.0).
Example: 3.8 + 49 + .06
3.80
49.00
+ .06
___________
52.86
You will find a list of videos on adding and subtracting decimals,
along with some exercises, by clicking here:
https://www.khanacademy.org/math/arithmetic/decimals/adding_dec
imals/v/adding-decimals-example-1
Multiplying Decimals
•
•
RULE: To multiply decimals, you do not have to line up the numbers by their
decimal points. Put the number with more digits on the top, and multiply it
as you would multiply whole numbers. When you have finished multiplying,
count how many digits fall to the right of the decimal point in the numbers
you multiplied, then make sure your answer has the same number of digits
to the right of the decimal points.
Example:
Reviewing multiplication of whole
numbers
• Here are some links to videos and lessons on multiplying:
• https://www.khanacademy.org/math/cc-fourth-grademath/cc-4th-mult-div-topic/cc-4thmultiplication/v/multiplying-2-digit-numbers
• If you have not memorized the times tables up to 12 X 12,
make this the session in which you do! You could raise
your TABE score by multiple grades just by mastering
multiplication. Please ask me for blank times tables and
practice sheets.
• http://www.mathsisfun.com/tables.html
• http://www.mathsisfun.com/worksheets/multiplication.ph
p
Reviewing multiplication of decimals
• Here are some links to videos and lessons on
multiplying:
• https://www.khanacademy.org/math/arithme
tic/decimals/multiplying_decimals/v/intro-tomultiplying-decimals
• http://www.mathsisfun.com/multiplyingdecimals.html
Dividing decimals by whole numbers
• RULE: To divide a decimal by a whole number, bring the
decimal point up in the quotient (answer) directly above its
position in the dividend (number being divided). Then,
divide as you would with whole numbers.
• https://www.khanacademy.org/math/cc-fifth-grade-math/cc5th-arith-operations/cc-5th-dividing-decimals/v/dividing-adecimal-by-a-whole-number
Dividing decimals by decimals
• RULE: To divide a decimal by a decimal, make the divisor a
whole number. Move the decimal point in the divisor to the
right as far as it will go. Also move the point in the dividend
the same number of places that you moved the point in the
divisor. Then divide.
Videos and exercises on dividing decimals
• https://www.khanacademy.org/math/cc-sixthgrade-math/cc-6th-arithmetic-operations/cc6th-div-decimals/v/dividing-decimals
• http://www.mathsisfun.com/numbers/decima
ls-dividing-animation.html
• http://www.coolmath.com/prealgebra/02decimals/10-decimals-dividing-by-decimal01.htm
Complete enough exercises to demonstrate to yourself that you
have grasped the concept of decimals, and performing all the
basic operations with them.
• http://www.mathdrills.com/decimal/decimals_multiplication_0
302_whole_tenths_006.html
• http://www.mathdrills.com/decimal/decimals_division_ones_te
nths_006.html
• http://www.mathdrills.com/decimal/decimals_division_ones_h
undredths_all.html
To reiterate a point made earlier…
• If you find yourself adding 5 + 5 + 5 + 5 when you are
asked to calculate the answer to 4 x 5, it is time for you
to learn to multiply quickly and accurately. This will
bring long multiplication, long division, and fractions,
as well as all of the other math we’ll be doing all
session, within your grasp. Honestly, you cannot pass
the HiSET without first having fully grasped the
fundamentals of arithmetic. Ask your instructor and
study hall tutors for multiplication practice sheets!
Congratulations on finishing this unit! You are now ready to take on the
wonderful world of fractions.