Name: Chapter 2 Rational Numbers - Commack Schools

[Pages:11]31b CN Terminating and Repeating Decimals.notebook

Name: Chapter 2 Rational Numbers

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31b CN 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.

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31b CN 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

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31b CN 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

Notice the repeating bar is over both the 2 and the 7 because both numbers consistently repeat.

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.

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31b CN 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

Example 4

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 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.

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31b CN 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

.3

tenths

The 3 must be in the tenths place value position.

Example 2

You say: twenty seven hundredths

.27

tenths hundredths

The 7 must be in the hundredths place value position.

Example 3

You say: nine hundredths

.09

tenths hundredths

The 9 must be in the hundredths place value position.

Example 4

You say: One hundred three thousandths

.103 tenths thousandths hundredths

The 3 must be in the thousandths place value position.

Example 5

You say: Fifty seven thousandths

.057

tenths thousandths hundredths

The 7 must be in the thousandths place value position.

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

Example 6

You say: thirty five hundredths

.35

tenths hundredths

The 5 must be in the hundredths place value position.

Example 7

You say: eight tenths

.8

tenths

The 8 must be in the tenths place value position.

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31b CN 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 tenths place value position

Example 2:

3.16

Think: 6 is in the hundredths place value position

Example 3:

7.125

Think: 5 is in the thousandths place value position

Example 4:

.055

Think: the last 5 on the right is in the thousandths place value position

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31b CN 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

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