Download Decimals Place Value smaller More than 1 Less than 1 The decimal

Decimals
Millions
,
Hundred thousands
Ten thousands
Thousands
,
hundreds
tens
ones
.
tenths
hundredths
thousandths
ten thousandths
hundred thousandths
Place Value
BIGGER
← − − .−→
More than 1
smaller
Less than 1
The decimal point is the word “and”
Standard Form – the way we normally write numbers. example 378.25
Expanded Form – the number written as the sum of the place values.
300 + 70 + 8 + .2 + .05
*The easier way to write expanded form:
627.317
600
70
2
.3
.01
.007
>
notice the 0’s
you need them to show the place value.
Word Form – the number written in words.
Three hundred seventy-eight and twenty-five hundredths
Note: numbers twenty-one through ninety-nine are hyphenated
The comma goes in the same place in words as in the number.
Comparing Decimals
3.03
3.4
3.27
3.03
4 3.40 (add a zero here to even them out) This one is largest.
1 3.15
3 2 3.15
↗
3.27
↑ line up the decimals
Start with row and move through the place values
Adding and Subtracting Decimals
LINE UP THE DECIMALS!! (Line up the decimal points.)
2.610 ⟵add a zero
+ .003
2.613
9.041
-7.264
1.777
BRING THE DECIMAL STRAIGHT DOWN
When you have a whole number, the decimal goes after it.
5 + 3.25 è 5.000 fill in the blanks with zeros; add a decimal and fill in
+.325
5.325
Multiplying Decimals
You DO NOT line up the decimals.
1.
2.
3.
4.
Line up the digits. Put the largest number on the top.
Multiply as usual.
Count the number of digits AFTER the decimals in the problem.
Place the decimal to the left the number of places you counted in step 3
2.614 x .37
2.614 ⟵line up numbers from the right
x .37
18298
+78420
.96718
.05 x .05
.05 count all the places right of the decimal in both
x .05 numbers; there are 4 decimal places
25
+000
.0025
↗ count 4 decimal places. Fill in the gaps with zeros.
22 x 1.2
22
x1.2
44
+220
26.4
Dividing Decimals
You DO NOT line up the decimals.
Quotient bring your decimal up then divide as usual
16.4 ÷ 2
divided by this | first number in the house
(divisor)
(dividend)
dividend ÷ divisor = quotient
08.2
2|16.4
-16↓
Dumb
Monkeys
÷ divide
x multiply
04
Swing
subtract
-4
Backwards ê bring down
0
The decimal goes straight up.
13.70 ÷ 5
02.74
5|13.70
-10↓
37
-35 ↓
20
-20
0
16.4 ÷ .2
_____
.2|16.4
ñ
↪ move it the same number of places in the problem
you have
(as the divisor.)
to move
the decimal
out of the way
082
2|164
-16↓
04
-4
0
16.4 ÷ .02
_____
.02|16.4
↪ ↪ move 2 places; fill in the gap with a zero
Move 2 places
0820
2|1640
-16↓
04
-4
0
= 820 is quotient
Repeating Decimal
What if the decimal repeats?
1
3
Part
Whole
1
3
çthe line means divide
1÷3
Put the top number in the “house”; it is the dividend
1
÷ 3
= answer
Dividend ÷ divisor = quotient
_.3333
3√1.0000
-9 ê| |
10 | |
-9ê|
10
- 9ê
10
-9
1
You write it with a line over the digits that repeat.
1 = _
3 .33
This is called a repeating decimal.
Terminating Decimal
3
5
_.6
5√3.0
-30
0
3 = .6
5
This decimal stops. It is called a terminating decimal.