Place Value Tenths

Period Hundredths

Powers of Ten Thousandths

Decimal Ten Thousandths

Decimal Point Millionths

Fraction Ten Thousandths

Percent

• Standard Form • Written Form• Expanded Form• Pictures• Fractions• Percent

In our place value system, the value of a digit depends on its place, or position, in the number.

Each place has a value of 10 times the place to its right.

A number in standard form is separated into groups of three digits using spaces (USA uses commas). Each of these groups is called a period.

Not every number is a whole number. Our decimal system lets us write numbers of all types and sizes, using a symbol called the decimal point.

Numbers Get Numbers Get

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As you move right from the decimal point, each place

value is divided by 10.

hundreds tens ones tenths hundredths thousandths

125 . 578

Example: Read 38.7425

Solution:

Step 1: Values to the left of the decimal point are greater than one.38 means 3 tens and 8 ones.

Step 2: The word name of the decimal is determined by the place value of the digit in the last place on the right.

The last digit (5) is in the ten-thousandth place.

38.7425 is read as thirty-eight and seven thousand four hundred twenty-five ten thousandths

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• 4 5 1

1 5 0 • 1 21. Read the entire number first, then add the last right digit’s place value to the end

E.g “four hundred fifty one” thousandths

2. When there is a whole number too, read the whole number first then add “AND” the decimal number as above

e.g. “ one hundred fifty AND twelve hundredths

*** Notice Decimal Number Names end in “–ths” ***

The value of a digit is determined by its place value.

When the decimal point of a number is not shown (for example, in whole numbers), then it is assumed to be at the end of the number on the right hand side

Example : 321 = 321. 4 = 4.

Number Place Value (of underlined

digit)

Value of the digit (as a decimal)

Value of the digit (as a fraction)

3 .145 Ones 3 3

3. 145 Tenths 0.1 110

3.1 45 Hundredths 0.04 4100

3.14 5 Thousandths 0.005 51000

A decimal number is a number that has digits before and after a decimal point. The decimal point is placed after the ones digit.

Example : 3.145

Each digit in a decimal number has a place value depending on its position.

Tens Ones Decimal point

Tenths

Hundredths

Thousandths

3 . 1 4 5

• Read the whole number before the decimal without the use of “and.”

• Write that number down.• At the decimal point use the word “and” • Read the entire number after the decimal as if it

were a whole number.• Add the name of the place value of the last digit

on the right hand side (after the decimal of course)

Example: Write the following decimal in words 8 243.67

Eight thousand, two hundred forty-three AND sixty-seven hundredths

Example: Write the following decimal number in standard form:

two hundred six and fifty-four ten-thousandths

206 .The word “ten-thousandths” indicates that we need four decimal places.

__ __ __ __5 40 0

When we clean it up, the answer is 206.0054

Fifty eight hundredths0.58

12.5

23.6

1.777

0.0005

0.351

100.10

Eight hundred fifty four thousandths

Twelve and five tenths

One and seven hundred seventy seven thousandths Five ten thousandths

Three hundred fifty one thousandths

One hundred and ten hundredths seven thousand

0.854

Twenty three and six tenths

Five hundredths 0.05

0.023

39.6

30.0001

0.7

9 000.01

80.541

0.0021

Eighty and five hundred four one thousandths

Twenty one ten thousandths

Thirty nine and six tenths

nine thousand and one hundredth

Thirty and one ten thousandths

Seven tenths

Twenty three thousandths

• Similar to writing whole numbers in expanded form.

• Write the number that appears before the decimal point in expanded form.

• For decimals, place a zero in the ones place.

• Also, substitute zeroes for all spaces after the decimal point that come before the digit that you are working with.

For Example: Write the following decimal 13.361 in expanded form.

1. Use the decimals 13.361 = 10 + 3 + 0.3 + 0.06 + 0.001

There are two ways to write 13.361 in expanded form.

2. Use the fractions 13.361 = 10 + 3 + 3 + 6 + 1 10 100 1000

Decimal numbers can also be represented by pictures using the base 10 blocks

Rod = 10 Flat = 100 Cube = 1000

Unit = 1

Using the following pictures write a fraction and decimal for the grey area.

There are 100 units in this flat

50 are grey

So the fraction is 50 100

and the decimal is 0.5

Using the following pictures write a fraction and decimal for the coloured area.

There are 100 units in this flat

50 are coloured

So the fraction is 75 100

and the decimal is 0.75

Using the following pictures write a fraction and decimal for the coloured area.

There are 100 units in this flat

6 are coloured

So the fraction is 6 100

and the decimal is 0.06

Equivalent Decimals

Examples:

0.5 = 0.50 = 0.500 = 0.5000002.4 = 02.40 = 2.400 = 0002.4000.

034 is the same as 34. The number still has no hundredths, 3 tens and 4 ones.

1.5 is the same as 1.50. The number still has 1 one, 5 tenths, and no hundredths.  000032.456000 = 032.456 = 32.456 = 32.4560000 These all have 3 tens,, 2 ones, 4 tenths, 5 hundredths and 6 thousandths.

Basic Rules:1. Add as many zeros LEFT of digits that are BEFORE a decimal.2. Add as many zeros as you want RIGHT of the digits AFTER the decimal.

** Think of it as PAC –MAN, his mouth is ALWAYS open towards the LARGER number.

Examples: a). Compare 1123 and 1126 1123 < 1126 b). Compare 567 and 497 567 > 497 c). Compare 1 and 0.002 1 > 0.002 d). Compare 0.402 and 0.412, 0.402 < 0.412 e). Compare 120.65 and 34.999 120.65 > 34.999f). Compare 12.345 and 12.097. 12.345 > 12.09.

< (less than) > (greater than) = (equals)≤ (less than or equal to) ≥ (greater than or equal to)

Basic Steps• Compare the whole number parts first.• Start and move LEFT TO RIGHT • Compare the next most significant digit of each number in the same place.• If they are equal, move onto the next place to the right.

BASIC RULES1. If the number to the RIGHT of the Rounding Number is 5 or more (5, 6, 7 8 or 9) then

the LEFT (Rounding Number) number goes UP by ONE place.

2. If the number to the RIGHT of the Rounding Number is 4 or less (4, 3, 2, 1 or 0) then the LEFT (Rounding Number) number remains the SAME.

3. Every number AFTER the Rounding Number becomes 0.

4. Everything BEFORE the Rounding Number remains the same.

5. If the Rounding Number is a 9 and it goes up by one, then a 0 is placed in the Rounding Number Place and 1 is moved to the next place to the LEFT. (same as carrying in adding)

Examples Because ...

3.1416 rounded to hundredths is 3.14 ... the next digit (1) is less than 5

1.2635 rounded to tenths is 1.3 ... the next digit (6) is 5 or more

1.2635 rounded to 3 decimal places is 1.264 ... the next digit (5) is 5 or more

134.9 rounded to tens is 130 ... the next digit (4) is less than 5

12,690 rounded to thousands is 13,000 ... the next digit (6) is 5 or more

1.239 rounded to units is 1 ... the next digit (2) is less than 5

 

Example #1: 76.69 + 51.37

1) Line up the decimal points: 76.69

+51.372). Then add.

76.69 +51.37

128.06

Example #2 : 12.924 + 3.6

1) Line up the decimal points: 12.924 +  3.600

2) Then add. 12.924 +  3.600

16.524

Basic Steps:• First, line up the decimal points • When one number has more decimal places than another, use 0's as place

holders to give them the same number of decimal places. • Add.

Example: 18.2 - 6.008

1) Line up the decimal points. 18.2   

-  6.008

2) Add extra 0's, using the fact that 18.2 = 18.200

18.200 -  6.008

3) Subtract. 18.200- 6.008 12.192

Basic Steps:1). Line up the decimal points on all the numbers2). When one number has more decimal places than another, use 0's as place holders to give them the same number of decimal places3). Subtract.

Example 1: Example 2:

1. Multiply 4.032 × 4 1. Multiply 6.74 × 9.063

2. Line up Numbers 4.032 2. Line up Numbers 6.74 x 4 x 9.063

3. Multiply 4.032 3. Multiply 6.74 x 4 x 9.063 16128 2022

40444. Count the Number of Decimal Places 0000 in both Numbers. +6066 .The decimal moves 3 digits from the right: 6108462

4.032 x 4 4. Count the Number of Decimal Places 16.128 in both Numbers.

The decimal moves 5 digits from the right:

6.74 x 9.063 61.88462

Basic Steps.1. Line up the NUMBERS, not the decimals.2. Multiply the same way as you would with whole numbers.3. After multiplying, add the numbers of digits to the RIGHT of the decimal point in both factors.4. This is how many places the decimal will move to the LEFT of the last right digit.

Basic Steps.

1. When dividing the decimal goes STRAIGHT UP from where it is in the dividend.2. Divide the same way as whole numbers.

Example 1: Example 2:

1. Divide 15.567 ÷ 3 1. Divide 241.8 ÷ 22

2. ______ 2. ______ 3 | 15.567 22 | 241.8

3. Place the decimal straight up 3. Place the decimal straight up from the dividend from the dividend

4. Solve 4. Solve

5.189 10.99 3 | 15.567

22 | 241.800 -15 -22

05 21 - 3 - 0 26 218 -24

-198 27 200 -27 -198 0R 2R

Basic Steps.1. First, it is easier to make the Divisor a whole number.2. Move the decimal in the Divisor as many places to the RIGHT as to create a whole Number. 3. Move the decimal in the Dividend the same number of places to the RIGHT.4. Next, the decimal goes STRAIGHT UP from where it is in the dividend.5. Divide the same way as whole numbers.

Example 1: Example 2:

1. Divide 24.808 ÷ .3 1. Divide 250.85 ÷ 0.25

2. ______ 2. ______ 0.3 | 24.808 0.25 | 250.85

3. Move the Decimal in the Divisor 3. Move the Decimal in the Divisor and the Dividend 1 places to and the Dividend 2 places to the RIGHT to make the Divisor the RIGHT to make the Divisor a Whole Number a Whole Number

4. The decimal goes straight up now 4. The decimal goes straight up now

5. Solve 5. Solve

82.69 1003.4 3 | 248.08 25 | 25085.0

-24 -25 08 00

- 6 - 0 20

08 -18 - 0 28

85 -27 -75 1R

100 -100 0R