Basic Math Skills Review
0011 0010 1010 1101 0001 0100 1011
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2
Decimals
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Introduction to Decimals
0011 0010 1010 1101 0001 0100 1011
• Numbers to the right of a decimal point are less than one.
• The decimal place is the number of digits to the right of the
decimal point.
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2
• As the number of decimal places increases, the value of the
number gets smaller.
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• Whole numbers can be written with a decimal point to the
right of the ones place followed by zeros.
• Zeros are place holders between non-zero numbers.
• Decimals can be converted to exponents or fractions.
Place Value
0011 0010 1010 1101 0001 0100 1011
Place Name Decimal Fraction
1
Tenths 0.1 10
1
2
1
Hundredths 0.01 100
4
1
Thousandths 0.001
1000
Ten- 1
0.0001
Thousandths 10000
The suffix “–ths” indicates that the digits are to the right of the decimal point.
The decimal point replaces the ones place.
Converting Fractions to Decimals
0011 0010 1010 1101 0001 0100 1011
In order to write a fraction as a decimal, you must
have a power of ten in the denominator.
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2
The number of zeros in the denominator is equal to
the number of decimal places.
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If the denominator is not a power of ten you must
either:
1) Find an equivalent fraction or
2) Divide and write the quotient in decimal form.
Powers of Ten
0011 0010 1010 1101 0001 0100 1011
103 102 101 100 10-1 10-2
1000 100 10 1 1 1
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2
10 100
Brief review of exponents:
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2=100 10 2=10•10=100
10
base power
exponent
Example: Equivalent Fractions
0011 0010 1010 1101 0001 0100 1011
There are some fractions which can be easily
converted to decimals. An example of this
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2
are ones with factors of 100 in the
denominator.
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Look for:
2, 4, 5, 10, 20, 25, 50
Example: Equivalent Fractions
0011 0010 1010 1101 0001 0100 1011
1 Since the equivalent fraction
4 has two zeros in the
2
denominator, we can rewrite it
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1 25 25
4 25 100 as a number with two decimal
places.
25
0.25
4
100
45
It even works with 20
improper fractions. 45 5 225
20 5 100
225
2.25
100
Example: Equivalent Fractions
0011 0010 1010 1101 0001 0100 1011
There are some fractions which can be easily converted to
decimals. Another example of this are ones with factors of 10
in the denominator.
2
Look for: 2 or 5
Since the denominator
is a 10, there is only one 3 1
4
3
decimal place.
5 2
3 5 15
3 2
6
5 2 10 2 5 10
15
6
0 .6 1 .5
10 10
Addition
0011 0010 1010 1101 0001 0100 1011
1) Line up the decimal points.
2) Write zeros at the right end of the numbers,
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2
if needed.
3) Find the sum (just like with whole
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numbers).
4) Bring down the decimal point.
Example: Addition
0011 0010 1010 1101 0001 0100 1011
Note: Decimal points are written to the right
of the ones place in whole numbers.
56 32.85
56.00
Re-write before solving
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2
4
Line up decimal points and add
32.85
88.85
Subtraction
0011 0010 1010 1101 0001 0100 1011
1) Line up the decimal points.
2) Write zeros at the right end of the numbers,
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2
if needed.
3) Find the difference (just like with whole
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numbers).
4) Bring down the decimal point.
Example: Subtraction
0011 0010 1010 1101 0001 0100 1011
38 25.34
38.00 Line up the decimal points.
2
Write zeros at the right end of the numbers, if needed.
25.34
387.09 010 1
4
Find the difference
25.34
12.66 Bring down the decimal point
Multiplication
0011 0010 1010 1101 0001 0100 1011
1) Find the product (just like whole numbers).
2) Count the number of decimal places in the
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2
factors.
3) Start at the ones place in the product.
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Count the digits (from right to left) the
number of places from step 2. Place the
decimal point to the left of the digit you
stopped on.
Example: Multiplication
0011 0010 1010 1101 0001 0100 1011
2.16
Find the product
6.3
Count the number of decimal places in the factors.
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2
648
In this example, there are three decimal places.
12960
13608 Move the decimal three place to the left.
The final answer is 13.608
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Division
0011 0010 1010 1101 0001 0100 1011
Only use these rules if there is a decimal in the divisor.
If not, move the decimal directly up to the top of the division
symbol and divide.
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2
1) Move the decimal point as many places to the right as
needed to make the divisor a whole number.
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2) Move the decimal of the dividend the same number of
places. Annex zeros, if needed.
3) Move the decimal point to the top of the long division
symbol ( ). .
4) Find the quotient. 42 .36 982 .335
Example: Division
0011 0010 1010 1101 0001 0100 1011
Find the quotient of 4.8 by 2.4. Set up the problem: 2.4 4.8
Move the decimal point to make the divisor a whole number.
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2
1 decimal place 24 4.8
Move the decimal of the dividend the same number of places.
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1 decimal place 24 48
Move the decimal point to the top of the division symbol.
.
24 48 .0
2
Find the quotient. 24 48
NOVA Math Placement Test
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•The Math Placement test is given in the Testing Center.
•There is a review book for the placement exam in the
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Annandale Library. (CG 3rd Floor)
•It’s called Chart Your Success on the Compass Exam.
•Brush-up on current skills, go through what you know.
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•Don’t try to teach yourself anything that you do not know.
•Use the list of suggested websites to help you review.
•Neither the Math Center nor the Tutoring Center will help
you study for the exam.