Download Comparing Fractions and Decimals

Converting, Comparing and
Ordering Fractions and
Decimals : Day 2
Foundations of Algebra
Rational Numbers: Fractions and
Decimals
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What is a rational number?
• Definition: Any number that can be made by
dividing one integer by another. The word
comes from "ratio”.
• Examples:
1/2 is a rational number (1 divided by 2)
0.75 is a rational number (3/4)
2 is a rational number (2/1)
2.12 is a rational number (212/100)
-6.6 is a rational number (-66/10)
What is NOT a rational number?
• If a number is not rational, then it is
irrational.
• An irrational number CANNOT be written
as a fraction - the decimal goes on forever
without repeating.
• Examples: π = 3.141592654…..
Comparing
Fractions and Decimals
You cannot compare fractions and
decimals. In order to compare fractions
and decimals, you have to use all of the
skills you have learned to convert them
all to decimals.
Converting Fractions to Decimals
Think about how you say the fraction.
6
= .6
10
8
= .08
100
How many TENTHS are
there? The 6 goes in the
TENTHS place.
How many HUNDREDTHS
are there? The 8 goes in the
HUNDREDTHS place.
Converting Decimals to Fractions
• Converting decimals to fractions is the
opposite of converting fractions to decimals.
• Once again, read the fraction.
• What do you hear? Tenths or hundredths?
Converting Decimals to Fractions
Think about how you say the decimal.
6
.6 =
10
8
.08 =
100
Read the decimal. The 6 is
in the TENTHS place, so the
denominator is 10.
What place is the 8 in? The
HUNDREDTHS place. The
denominator is 100.
Converting Decimals to fractions
.60
6
60
= 10 or 100
16
.16 =
100
40
4
.40 = 100 or 10
Comparing Decimals
• When comparing decimals, you have to look
at the whole numbers.
• If the whole numbers are the same, then look
at the decimal in the tenths place.
• Keep looking at the digits until you can
identify which is the greatest or least.
Comparing Fractions and Decimals
Not all fractions are over 10 or 100, some may
have different denominators. In order to change
them to decimals, we will have to use our
calculators.
Example #1 ~ Compare these fractions.
4
÷
5
=
3
Next, compare the decimals.
÷
7
=
Comparing Decimals
Step 1. Line up the decimal points. Use zeros to
make an equal number of decimal places.
0.800
0.428
Step 2. Start by comparing the greatest place.
Find the first place where the digits are
different.
0.800
0.428
Comparing Decimals
Step 3. Compare the values of the digits.
0.8 is greater than 0.4
So,
0.8 > 0.428