CHAPTER 3 RATIONAL NUMBERSName: - Commack Schools

[Pages:111]Name: _________________________

CHAPTER 3 RATIONAL NUMBERS

1

31a Terminating and Repeating Decimals.notebook

Terminating and Repeating Decimals (31)

fraction into decimals

decimals into fractions

Note: When you see a fraction with the denominator of 9, remember that it represents a repeating decimal.

To change a fraction into a decimal, divide the denominator into the numerator.

To change a decimal into a percent, multiply the decimal by 100.

2

31a Terminating and Repeating Decimals.notebook

Please take out your calculator!

To change a fraction into a decimal: Divide the numerator by the denominator

numerator

ex.

means...

denominator

OR

numerator denominator ex. 15 ? 3

means...

denominator

numerator

3

31a Terminating and Repeating Decimals.notebook Sometimes you will get a: Repeating decimal: Reminder: use the bar notation to illustrate a repeating decimal

Example 1

Reminder: the numerator jumps into the box

Example 2

1st method change the mixed number into an improper fraction. Then divide the denominator into the numerator.

=

2nd method place the whole number in your answer box and just work with the fraction. Divide the denominator into the numerator.

= 8.

* Example 3

Method 1 You can recognize that there is a 9 in the denominator. When there is a 9 in the denominator, the decimal equivalent is the numerator expressed as a repeating decimal.

Method 2 divide the denominator into the numerator.

4

31a Terminating and Repeating Decimals.notebook

Sometimes you will get a ...

DON'T FORGET THE NEGATIVE SIGNS IN YOUR ANSWERS.

Terminating decimal: You know it is a terminating decimal because the repeating decimal will be zero. Your division will end because you get zero for a remainder.

Example 1

Example 2

Example 3

1st method change the mixed number into an improper fraction. Then divide the denominator into the numerator.

2nd method place the whole number in your answer box and just work with the fraction. Divide the denominator into the numerator.

Example 4

Example 5

1st method change the mixed number into an improper fraction. Then divide the denominator into the numerator.

2nd method place the whole number in your answer box and just work with the fraction. Divide the denominator into the numerator.

5

31a Terminating and Repeating Decimals.notebook If the denominator of a fraction is a power of ten (10, 100, 1000, etc.) you can: Use the place value to write the fraction as a decimal.

Example 1

You say: three tenths

Example 2

You say: twenty seven hundredths

Example 3

You say: nine hundredths

Example 4

You say: One hundred three thousandths

Example 5

You say: Fifty seven thousandths

If you can make the denominator a power of 10, here is what you can do...

Example 6

You say:

Example 7

You say:

6

31a Terminating and Repeating Decimals.notebook

Every terminating decimal can be written as a fraction:

To write a decimal as a fraction: Use the place value of the last digit on the right as the denominator Always write your answer in simplest form

Example 1:

.4

Think: 4 is in the

place value position

Example 2:

3.16 Think: 6 is in the place value

position

Example 3:

7.125

Think: 5 is in the

place value position

Example 4:

.055

Think: the last 5 on the right is in the

place value position

7

31a Terminating and Repeating Decimals.notebook

Changing a repeating decimal to a fraction:

If one digit repeats, the denominator is 9

If two digits repeat, the denominator is 99

If three digits repeat, the denominator is 999

8

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download