Rational Numbers and Decimals

Warm Up

Write each rational number as a decimal.

1. 2. 3.

4. 5. 6.

Rational Numbers and Decimals

• A rational number is a number that can be written in the form when a and b are integers and b ≠ 0.

• Every rational number can be written as a terminating decimal or a repeating decimal.

• To convert a fraction to a decimal, the numerator is the dividend and the denominator is the divisor.

Shawna wrote the mixed number as the decimal 5.23. Shawna made a mistake. What did she do wrong? What should she do to correct it?

Converting Fractions to Decimals• When converting fractions to decimals, use long

division to divide the numerator by the denominator.

• Remember, a fraction bar is just another way to write a division problem.

• Even if the denominator is larger than the numerator, the numerator is always the dividend and the denominator is always the divisor.

quotient denominator numerator

−17401124

Using Long Division to Prove to Fractions are Equivalent

14416Does a fraction have to be in

simplest form to convert it into a decimal?

Improper Fractions

The value of an improper fraction is always greater than 1.

Therefore the equivalent fraction for an improper fraction is also greater than 1.

How much money do you have if you have of a dollar?

Converting Mixed Numbers into Decimals

When converting mixed numbers into decimals, keep the whole number and use long division to find the decimal.

The decimal and the mixed number it is converted from will always have the same whole number.

Killian bought pounds of cashews. Express his purchase as a decimal.

Checking to See if an Answer is Reasonable by Comparing the Numerator to the Denominator

• If the numerator is less than half the denominator, the decimal should be less than 0.5. If the numerator is more than half the denominator, the decimal should be more than 0.5.

• If the numerator is greater than the denominator, the decimal should be greater than 1. If the numerator is less than the denominator, the decimal should be less than 1.

The change in the water level at the lake was inches for the month.

a. Write this as an improper fraction.

b. Write this as a decimal.

Marcus is feet tall. Ben is feet tall. Which of the

two boys is taller? Justify your answer.

If one store is selling of a bushel of apples for $9, and another store is selling of a bushel of apples for $9,

which store has the better deal? Explain your answer.

Julie got 21 of the 23 questionson her math test correct. She got 29

of the 32 questions on her sciencetest correct. On which test did she

get a higher score? Can you compare

the fractions and by comparing 29 and 21? Explain. How can Julie

compare her scores?

Exit TicketBob, Tina, and Hadley went running. Bob ran for hour, Tina ran for hours, and Hadley ran for hours.

1. Which running times can be written as improper fractions?

2. Write the number of hours each person spent running as a decimal.

3. Which decimals are repeating decimals?4. Which decimals are terminating decimals?