2-1 rational numbers. 2-1 rational numbers learn to write rational numbers in equivalent forms
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2-1 Rational Numbers
2-1 Rational Numbers
Learn to write rational numbers in equivalent forms.
2-1 Rational Numbers
A rational number is any number that can be written as a fraction , where n
and d are integers and d 0.
nd
2-1 Rational Numbers
The goal of simplifying fractions is to make the numerator and the denominator relatively prime. Relatively prime numbers have no common factors other than 1.
2-1 Rational Numbers
Additional Example 1A: Simplifying Fractions
16
80
Simplify.
2-1 Rational Numbers
–18 29
Simplify.
Additional Example 1B: Simplifying Fractions
2-1 Rational Numbers
18
27
Check It Out: Example 1A
Simplify.
2-1 Rational Numbers
17 –35
Check It Out: Example 1B
Simplify.
2-1 Rational Numbers
Decimals that terminate or repeat are rational numbers.
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
5.37
A. 5.37
7 is in the hundredths place.37 100
= 5
Additional Example 2: Writing Decimals as Fractions
Write each decimal as a fraction in simplest form.
0.622
B. 0.6222 is in the thousandths place.
622 1000
=
= 311 500
Simplify by dividing by the common factor 2.
2-1 Rational Numbers
8.75
A. 8.75
5 is in the hundredths place.75
100= 8
= 8 3 4
Simplify by dividing by the common factor 25.
Write each decimal as a fraction in simplest form.Check It Out: Example 2
0.2625
B. 0.26255 is in the ten-thousandths place.
2625 10,000
=
= 21 80
Simplify by dividing by the common factor 125.
2-1 Rational Numbers
9 11 The pattern repeats.
1
–9
.2
2
0
.0
2
11 9
–1 8
Additional Example 3A: Writing Fractions as Decimals
Write the fraction as a decimal.
The fraction is equivalent to the decimal 1.2.11 9
A repeating decimal can be written with a bar over the digits that repeat. So 1.2222… = 1.2.
Writing Math
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2-1 Rational Numbers
This is a terminating decimal.20 7
.30 5
The remainder is 0.
7 20
–07
1 0
0
0
0
.0
0–6 0
–1 0 0
Additional Example 3B: Writing Fractions as Decimals
Write the fraction as a decimal.
The fraction is equivalent to the decimal 0.35.7 20
2-1 Rational Numbers
9 15 The pattern repeats, so draw a bar over the 6 to indicate that this is a repeating decimal.
1
–9
.6
6
0
.0
6
15 9
–5 4
Write the fraction as a decimal.
Check It Out: Example 3A
The fraction is equivalent to the decimal 1.6.15 9