Numbers written in decimal notation

Decimal numbers (Decimal)

Used to denote a part of a whole.

Decimal Notation

Name the first 5 place values right of the decimal.

TenTHS

HundredTHS

ThousandTHS

Ten ThousandTHS

Hundred ThousandTHS

Each decimal place value is ____of the place value to its left.

1/10

1/10

1/100

1/1000

1/10,000

What is the value of the 5 in 17.758

5 hundredths

or

5/100

How to write or read decimals

- 758

1) The whole number the standard way “Seventeen”

2) “and” for the decimal point. “And”

3) The Decimal number the standard way as if it were a whole number followed by the place value of the last digit.

“Seventeen and Seven Hundred Fifty Eight Thousandths.”

For any decimal writing ____’s after the last digit to the right of the decimal does not change the numbers value.

0

To compare negative decimals first compare their ______ _____

Add the inequality symbol

then ______it.

Absolute value/ Reverse

To round decimals right of the decimal point.

1) Locate the digit to the right of the given place value 2)Use greater than 5 rule. drop all digits to the right of the given place value if less If more add one the place value and drop all to the right.

When changing decimals from words to standard form be sure to add ___ to make sure the last digit has the correct ____ _____.

Zeros/ Place Value

To change decimals from decimal notation to fractional notation, you must…

1) Write the numbersto the right of the decimal in the numerator.

2) determine the place value of last non-zero digit and make the place value the denominator (minus the -ths)

809 892 . 809-\> — .08920-\> — 1000 10,000

When comparing negative decimals start from the ____. Move to each decimal place to find the digit with more Absolute value, to determine the smaller decimals

Right

- 2.2049 < .-1.2049
- 1..2049 <-0..2049
- 0.2049 < -.2039
- .2039 >-2139

When comparing postive decimals start from the ____. Move to each decimal place to find the digit with less value, to determine the larger decimals.

- 2049> .1.2049
- .2049>0..2049
- .2049> .2039

.2039<2139

In decimal notation writing ___ after the last digit to the right does not _____ ____ ____ of the decimal

Zeros/ change the value.

When adding and subtracting decimals the decimals must be set up so that the sum/diffrence and addends/minuend,subtrahend all _____ _____ ____

Line Up Vertically.

How to multiply Decimals

1) Multiply the decimals as if they were whole numbers.

2) Place the sum of decimal places from both factors in the product.

To multiply decimals by the power of TEN move the decimal to the ____ the same number of places as there are ZEROS.

Right

To multiply decimals by the power of TENTHS move the decimal to the ____ the same number of places as there are DECIMAL PLACES.

Left

Formula for Circumfrence

C=2πr

C=πd

How to divide decimals

1) Move the decimal point in the divisor to the right until the divisor is a whole number

2) Move the decimal point in the dividend to the right the SAME NUMBER of placesthe as the decimal point was moved in the divisor.

3) Divide

4) Place the decimal point in the quotient directly over the moved (step 2) decimal in the dividend.

To divide decimals by the power of TEN move the decimal to the ____ the same number of places as there are ZEROS.

Left

To DIVIDE decimals by the power of TENTHS move the decimal to the ____ the same number of places as there are DECIMAL PLACES.

Right

The Numerical value of a variable

Replacement Value

To write a fraction as a decimal you must

Divde the numerator by the demoninator

When converting a fraction to a decimal via division you should consider he numerator the ____ and the denominator the _____

Dividend/ Divisor

How to compare the value of FRACTIONS & DECIMALS.

1) Write the fraction as a decimal via division

2) Compare the decimals as normal

The _____ of a number is a number time itself

Square

The inverse operation of a square root.

Squaring

This (√ ̅ or √) is called a…

Radical sign

The formula for the square root of a number.

The Square root (√ ̅ /√) of a positive number a is the positive number b whose square is a.

√ ̅ a=b if b^{2 }=a

Important:

The radical sign (√ ̅) is used to indicate the positive square root of a ______ number.

Non-negative

Every positive number has _______square roots

Two

√ ̅ 25 = (5x5)

√ ̅ 25= (-5 x-5)

When you multiply a number by itself using

a base number

and

an exponent of 2 and ONLY 2

Squaring

A number that has a rational number as its square root

Perfect Square

A radical with a number that does not have two WHOLE NUMBERS to produce the number inside of the radical.

An imperfect square

When you have an imperfect square Use a _____ or an ______ to find the square root

Calculator/Appendix

√32≈5.657

The sum of the squares of the lengths of the sides of a right triangle is equal to the square of the length of the _______.

Hypotenuse

Pythagorean Theorem

The Pythagorean Theorem

a^{2 }+ b^{2}= c^{2}

or

(Leg 1)^{2}+(Leg 2)^{2}=(Hypotenuse)^{2}

A bar over the farthest digit to the right signiifys that it _____

–

2/3=0.666

Repeats

The bar over recurring decimals.

Vinculum bar

≈

The appoximately equal sign.