Transcript 2-1 - TeacherWeb

2-1 Rational Numbers
California
Evaluating Algebraic Expressions
Standards
NS1.5 Know that every rational
number is either a terminating or a repeating
decimal and be able to convert terminating
decimals into reduced fractions.
NS1.3 Convert fractions to decimals.
2-1 Rational Numbers
Put in your notes
A rational number is any number that can
Evaluating AlgebraicnExpressions
be written as a fraction
, where n
d
and d are integers and d  0.
Any fraction can be written as a decimal
by dividing the numerator by the
denominator. A terminating decimal
must end. A repeating decimal , a
decimal with a pattern that never ends,
can be written with a bar over the digits
that repeat. So 0.13333… = 0.13.
2-1 Rational Numbers
Additional Example 1A: Writing Fractions as
Decimals (Put in your Notes)
Evaluating Algebraic Expressions
Write the fraction as a decimal.
11
9
1 .2
9 11 .0
–9
20
–1 8
2
The fraction
The pattern repeats.
11
is equivalent to the decimal 1.2.
9
2-1 Rational Numbers
Additional Example 1B: Writing Fractions as
Decimals (Put in your Notes)
Evaluating Algebraic Expressions
Write the fraction as a decimal.
7
20
0.3 5 This is a terminating decimal.
20 7.0 0
–0
70
–6 0
1 00
–1 0 0
0 The remainder is 0.
7
The fraction
is equivalent to the decimal 0.35.
20
2-1 Rational Numbers
Check It Out! Example 1A (Rally Coach) A is Coach
Write
the fraction
as a decimal.
Evaluating
Algebraic
Expressions
15
9
1 .6
9 15 .0
–9
60
–5 4
6
The pattern repeats, so
draw a bar over the 6 to
indicate that this is a
repeating decimal.
15
The fraction
is equivalent to the decimal 1.6.
9
2-1 Rational Numbers
Check It Out! Example 1B (Rally Coach – B is Coach)
Write the fraction as a decimal.
Evaluating Algebraic Expressions
9
40
0.2 2 5 This is a terminating
40 9.0 0 0 decimal.
–0
90
–8 0
1 00
– 80
200
– 2 00
0 The remainder is 0.
9
The fraction
is equivalent to the decimal 0.225.
40
2-1 Rational Numbers
Evaluating Algebraic Expressions
To write a terminating decimal as a
fraction, identify the place value of the
digit farthest to the right. Then write all of
the digits after the decimal point as the
numerator with the place value as the
denominator.
2-1 Rational Numbers
Additional Example 2: Writing Terminating
Decimals as Fractions
WriteEvaluating
each decimal Algebraic
as a fraction Expressions
in simplest form.
A. 5.37
37
5.37 = 5
100
B. 0.622
622
0.622 =
1000
311
=
500
7 is in the hundredths place,
so write hundredths as the
denominator.
2 is in the thousandths
place, so write thousandths
as the denominator.
Simplify by dividing by the
greatest common divisor.
2-1 Rational Numbers
Put in your Notes
Evaluating Algebraic Expressions
Remember!
A fraction is in reduced, or simplest, form when
the numerator and the denominator have no
common divisor other than 1.
2-1 Rational Numbers
Check It Out! Example 2
Write each decimal as a fraction in simplest form.
Evaluating Algebraic Expressions
A. 8.75
5 is in the hundredths place,
75 so write hundredths as the
8.75 = 8
100 denominator.
3
Simplify by dividing by the
= 8
4
greatest common divisor.
B. 0.2625
5 is in the
2625
0.2625 =
10,000 ten-thousandths place.
Simplify by dividing by the
21
=
greatest common divisor.
80
2-1 Rational Numbers
Shortcut for Example 3 (Notes)
•
•
•
•
•
Evaluating Algebraic Expressions
Write 0.36 as a fraction in simplest form.
Find the place value of the farthest right
place value (Hundredths)
Write it as a number and subtract one
from the number (100 – 1 = 99) This
becomes your denominator.
Write the number of the repeating
fraction as the numerator (36).
Simplify
2-1 Rational Numbers
Check it out Example 3
Evaluating Algebraic Expressions
• 345
• 345
• 999 (1000-1)