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# Rational Numbers

A look into the different forms of Rational numbers and conversions between the different forms.

by

Tweet## Caitlin Purser

on 21 September 2012#### Transcript of Rational Numbers

Converting Fractions into Decimals

and Decimals into Fractions Rational Numbers Whole numbers

Integers

Fractions

Decimals (includes repeating decimals)

Percents Rational Numbers are... "Any number that can be written as a fraction n/d

where n and d are integers and d is not 0." If you can turn a number into a fraction,

then it is a rational number! -32 -2987 245 0.33333333333333333333333333333... Numbers that cannot be written in fraction form. Rational Numbers Are Not... Real Numbers that are not

rational are called: Irrational Numbers Fractions (mixed number, improper, simplified)

Decimals (repeating)

Percents Rational Numbers can have

many different forms In a simplified fraction the numerator and denominator are relatively prime (the GCF is 1). Simplifying Fractions In other words their only common factor is one. To simplify a fraction, think of common

factors of the denominator and numerator,

then divide the numerator and denominator

by that common factor. Keep doing this

until the only common factor left is 1. Here's an example: 18 and 81 have a common factor of 3, so 3 is divided into both 18 and 81. Now what is left are 6 and 27, they have a common factor of 3. 3 is again divided into 6 and 27 and we are left with 2 and 9. 2 and 9 are relatively prime (only common factor is 1). So 2/9 is our simplified fraction. 1.) -3/7 Your Turn: -21 _____ 49 1.) 2.) 64 _____ 104 3.) 39 _____ 312 2.) 8/13 3.) 1/8 Decimals into fractions Conversions Think of your place values! Decimals into Fractions 0.26 = 26 _____ 100 26 is the numerator and 100 (the place value of 26 is the denominaor) But can't 26/100 be simplified? Always simplify when you can! 0.26 = 13 ___ 50 3.) 8.92 You Try: 1.) 0.45 2.) -2.5 1.) 9/50 2.) -2 5/9 3.) 8 23/25 Fractions into Decimals To find the decimal form for a fraction, we can use division! Fractions into Decimals

(by division) Divide the numerator by the denominator

(top in bottom out) Example: Do not do this for "easy" fractions such as 1/2, 1/4, 1/8, 1/3, etc. This is used for fractions that are not used every day for example, 23/24. Also if your denominator is a factor of 10, 100, 1000, etc., then make an equivalent fraction with a denominator that is a power of 10. Keep dividing until your

remainder is 0.

Remember if you have a

repeating decimal, then there

will be a pattern when

dividing. 5 You Try: _______ 4 1.) 2.) -7 _____ 12 3.) 23 _____ 25 1.) 1.25

(convert to a

mixed number) 2.) -0.583

(divide;

recognize

the pattern) _ Decimals into Percents 3.) 0.92

( find equivalent fraction:

92/100) Decimals into Percents Percents into Decimals Fractions into Percents Percents into Fractions Move the decimal point over two

places to the right and

add a percent sign. DP Example: 0.358 = 35.8% 1.) 1.03 Your Turn 2.) -0.789 3.) 0.001 1.) 103% 2.) -78.9% 3.) 0.1% Percents into Decimals Move the decimal point over two places to the left and drop the percent sign. DP Example: 23.67% = 0.2367 1.) 26% Now You Try... 2.) -3.46% 3.) 125.7% 1.) 0.26 2.) 1.257 3.) -0.0346 Change the fraction into a decimal then move the decimal point over two places to the right. Fractions into Percents OR Make an equivalent fraction that's denominator is a power of 10. 3/5 = 0.6 = 60% 3/5 = 6/10 = 60/100 = 60% 1.) 4/5 Your Turn 2.) 2/3 3.) 5/8 1.) 80% 2.) 66.6% _ 3.) 62.5% The percent is the numerator and the

denominator is always 100.

(if there is a decimal in the

percent it might be easier to change

it to a decimal and then convert to a percent) Percents to Fractions Don't forget to simplify!!! Example: 36% = 36/100 = 9/25 1.) 30% Try These: 12.4% = 0.124 = 124/1000 = 31/ 250 2.) 45% 3.) 32.4% 1.) 3/10 2.) 9/20 3.) 81/250 1.) Tommy had 13 hits in 40 at bats for his baseball team. What is his batting average? (Batting average is the number of hits divided by the number of at bats, expressed as a decimal) What is his batting average percentage? In Action: 0.245 Negative Fractions! -2 3 _____ = 2 _____ -3 = 2 _____ 3 - Repeating Decimals Examples: 0.3 = 3/9 = 1/3 0.69 __ = 69/99 = 23/33 _ Same number of 9's

as the amount

of digits repeating. 0.325, 32.5% 2.) A pie chart is divided into 8 slices. If 3 of the slices are shaded, what percent of the pie chart is shaded? 37.5% 3.) Over the past year, the sales at

Adams bakery increased by 100%.

Which of the following is equivalent

to the increase in sales?

A.) 0.001

B.) 0.01

C.) 0.1

D.) 1 D.) 1 _ Overall... Rational numbers are numbers

that can be made into a fraction. A simplified fraction means that the numerator and denominator are relatively prime. Conversions...

Full transcriptand Decimals into Fractions Rational Numbers Whole numbers

Integers

Fractions

Decimals (includes repeating decimals)

Percents Rational Numbers are... "Any number that can be written as a fraction n/d

where n and d are integers and d is not 0." If you can turn a number into a fraction,

then it is a rational number! -32 -2987 245 0.33333333333333333333333333333... Numbers that cannot be written in fraction form. Rational Numbers Are Not... Real Numbers that are not

rational are called: Irrational Numbers Fractions (mixed number, improper, simplified)

Decimals (repeating)

Percents Rational Numbers can have

many different forms In a simplified fraction the numerator and denominator are relatively prime (the GCF is 1). Simplifying Fractions In other words their only common factor is one. To simplify a fraction, think of common

factors of the denominator and numerator,

then divide the numerator and denominator

by that common factor. Keep doing this

until the only common factor left is 1. Here's an example: 18 and 81 have a common factor of 3, so 3 is divided into both 18 and 81. Now what is left are 6 and 27, they have a common factor of 3. 3 is again divided into 6 and 27 and we are left with 2 and 9. 2 and 9 are relatively prime (only common factor is 1). So 2/9 is our simplified fraction. 1.) -3/7 Your Turn: -21 _____ 49 1.) 2.) 64 _____ 104 3.) 39 _____ 312 2.) 8/13 3.) 1/8 Decimals into fractions Conversions Think of your place values! Decimals into Fractions 0.26 = 26 _____ 100 26 is the numerator and 100 (the place value of 26 is the denominaor) But can't 26/100 be simplified? Always simplify when you can! 0.26 = 13 ___ 50 3.) 8.92 You Try: 1.) 0.45 2.) -2.5 1.) 9/50 2.) -2 5/9 3.) 8 23/25 Fractions into Decimals To find the decimal form for a fraction, we can use division! Fractions into Decimals

(by division) Divide the numerator by the denominator

(top in bottom out) Example: Do not do this for "easy" fractions such as 1/2, 1/4, 1/8, 1/3, etc. This is used for fractions that are not used every day for example, 23/24. Also if your denominator is a factor of 10, 100, 1000, etc., then make an equivalent fraction with a denominator that is a power of 10. Keep dividing until your

remainder is 0.

Remember if you have a

repeating decimal, then there

will be a pattern when

dividing. 5 You Try: _______ 4 1.) 2.) -7 _____ 12 3.) 23 _____ 25 1.) 1.25

(convert to a

mixed number) 2.) -0.583

(divide;

recognize

the pattern) _ Decimals into Percents 3.) 0.92

( find equivalent fraction:

92/100) Decimals into Percents Percents into Decimals Fractions into Percents Percents into Fractions Move the decimal point over two

places to the right and

add a percent sign. DP Example: 0.358 = 35.8% 1.) 1.03 Your Turn 2.) -0.789 3.) 0.001 1.) 103% 2.) -78.9% 3.) 0.1% Percents into Decimals Move the decimal point over two places to the left and drop the percent sign. DP Example: 23.67% = 0.2367 1.) 26% Now You Try... 2.) -3.46% 3.) 125.7% 1.) 0.26 2.) 1.257 3.) -0.0346 Change the fraction into a decimal then move the decimal point over two places to the right. Fractions into Percents OR Make an equivalent fraction that's denominator is a power of 10. 3/5 = 0.6 = 60% 3/5 = 6/10 = 60/100 = 60% 1.) 4/5 Your Turn 2.) 2/3 3.) 5/8 1.) 80% 2.) 66.6% _ 3.) 62.5% The percent is the numerator and the

denominator is always 100.

(if there is a decimal in the

percent it might be easier to change

it to a decimal and then convert to a percent) Percents to Fractions Don't forget to simplify!!! Example: 36% = 36/100 = 9/25 1.) 30% Try These: 12.4% = 0.124 = 124/1000 = 31/ 250 2.) 45% 3.) 32.4% 1.) 3/10 2.) 9/20 3.) 81/250 1.) Tommy had 13 hits in 40 at bats for his baseball team. What is his batting average? (Batting average is the number of hits divided by the number of at bats, expressed as a decimal) What is his batting average percentage? In Action: 0.245 Negative Fractions! -2 3 _____ = 2 _____ -3 = 2 _____ 3 - Repeating Decimals Examples: 0.3 = 3/9 = 1/3 0.69 __ = 69/99 = 23/33 _ Same number of 9's

as the amount

of digits repeating. 0.325, 32.5% 2.) A pie chart is divided into 8 slices. If 3 of the slices are shaded, what percent of the pie chart is shaded? 37.5% 3.) Over the past year, the sales at

Adams bakery increased by 100%.

Which of the following is equivalent

to the increase in sales?

A.) 0.001

B.) 0.01

C.) 0.1

D.) 1 D.) 1 _ Overall... Rational numbers are numbers

that can be made into a fraction. A simplified fraction means that the numerator and denominator are relatively prime. Conversions...