Section 7.1 - Decimals

• Recall that is expanded form

• We have seen the exponents of 10 go from the ones place (10⁰) to the thousands place (10³) and even
further. Now we will extend this idea to negative powers of 10

•· What does 10^-1 really mean ? It is 1/10 So if we have

• Now we can include fractional values !

Form of the Decimal:

• Recall that the decimal point is used for any values that are less than 1, it is our way of separating the
powers of 10 from the positive (0, 1, 2, 3 etc) to the negative ( –1, –2, –3, etc)

• Example
1

• In the above example, the 5 is in the tenths place, the 6 is in the hundredths place, and the 7 is in the
thousandths place

Converting:

•Converting fractions to decimals uses our knowledge of fractions as division
•

• In fact, if 10 is the divisor (the denominator) then all we have to do is move the decimal place to the
left the same number of times as we have 0s

•5/10 has 1 zero on the bottom , so we move the decimal place (5.0) to the left one time (0.5)

• Example. Convert 6/100 to decimal form.
Move the decimal point 2 places to the left
0.06

•Converting decimals to fractions is the reverse process, where you write the entire decimal value
divided by a power of 10
What power of 10 (how many zeros do you need)? The same as how many places you have to move
the decimal to get a whole number

• Example. Convert 0.45 into a fraction
(NOTE: you have to move the decimal 2 places to the right, so you need 2 zeros)

Exercises:
• Example, page 273 number 1c. Writein decimal form

•Example, page 273 number 2b. Write 34.007 as a fraction and in expanded form

•Example, page 273 number 3b. Write seven hundred forty six thousand and seven hundred for six
millionths as a decimal numeral

746 millionths = 746/10⁶
746,000.000746

• Example, page 273 number 4b. Write 7,589.12345 in words
seven thousand five hundred eighty nine and
twelve thousand three hundred forty five hundred thousandths
NOTE: hundred thousandths because it is 12345/10⁵

Terminating Decimals :

• A fraction in simplest form is a terminating decimal if and only if the denominator has only 2s and
5s in its prime factorization

• If the prime factorization has any values other than 2s and 5s in it's prime factorization, it is a
nonterminating or repeating decimal

•Example
1/3 is a repeating decimal
• Example, page 273 number 5b. Isa terminating decimal?

. No, it has a 7 in the denominator

• Example, page 273 number 6. Decide which fractions terminate, and if they do, in how many places
1/11 No

Yes. Terminates in 4 places, because that is the highest power

Yes. Terminates in 9 places, because it is the highest power

Yes. Terminates in 23 places, because it is the highest power
 

• Example, page 273 number 7b. Order the fractions by changing to decimals