reading decimals say what you see before the decimal say “and” for the decimal say what you see...
TRANSCRIPT
Reading Decimals
Say what you see before the decimal
Say “and” for the decimal
Say what you see after the decimal
Say the place value of the final digit
To write in words, you write what you say
five hundred eighty
and
5 8 0 . 3 2 4
three hundred twenty-four thousandths
Ten thousands
tenths
hundredthsone
s
hundreds
thousands
tensthousandt
hs
tenthousandt
hs
Hundred thousandt
hs
One and
forty-six hundredths
sixty seven and
four thousand eighteen ten thousandths
Twelve thousand three hundred four
and two thousandths
three and forty seven hundredths
Three and forty seven thousandths
three and forty seven
tenths
Three and forty seven
hundred
seventeen thousand eighty two
seventeenand
eighty-two hundredths
seventeenand
eighty-two tenths
seventeenand
eighty-two thousandths
three thousand
two
three thousand two ten
thousandths
Zero and three
thousand two
three thousand
two thousandths
Sixty-four thousand
twenty one
Six hundred forty
thousand twenty one millionths
Sixty four hundredths twenty one
Six hundred forty
thousand twenty one thousandths
Base Ten Blocks
One and
four tenths
One and four tenths
Representsone whole
bar
Represents one tenthof a bar
(meaning youneed ten to make a bar)
Represents one hundredth
of a bar(meaning you
need one hundred to make a bar)
Represents one thousandth
of a bar (meaning you
need one thousand to make a bar)
One and
seven hundredths
One and seven hundredths
Fifty-threehundredths
Fifty-threehundredths or
0.53
One and two hundred forty-five
thousandths
One and two hundred forty-
five thousandths or 1.245
Six thousandths
Six thousandths or 0.006
One and thirteen thousandths
One and thirteen thousandths or
1.013
Two and one hundred
seventy-three thousandths or
2.173
four hundred twenty-five
thousandths or 0.425
One and two hundred eighty-
three thousandths or
1.283
Which is the larger value?
0.129 or 0.31
Prove your choice!
0.129 is less than
0.31, so 0.31 is the largest value
0.129
0.31
Which is the larger value?
0.2 or 0.05
Prove your choice!
0.2 is greater than
0.05
0.2
0.05
Understanding Decimal Values
45.076 45.0076
1098.41098.44
673.09 673.1
1. Understanding Decimal Values
67.7600 67.76
15.9815.099
0.515 0.551
nine out of ten
0.9
910
nine tenths
four out of ten
0.4four tenths
410
2.7
two and seven tenths
two wholes and seven out
of ten
2 7 10
thirty-two hundredths
0.32
Thirty-two out of one hundred
32100
eighty out of one
hundred
0.80
eighty hundredths
80100
six out of one
hundred
0.06
six hundredths
6100
Three and two
hundredths
Three and two
hundredths
3 2 100
3 2 100
3.023.02
Three wholes and
two parts out of a hundred
Three wholes and
two parts out of a hundred
Two and fourteen
hundredths
Two and fourteen
hundredths
2.142.14
Two wholes and fourteen out of one hundred
Two wholes and fourteen out of one hundred
2 14 100
2 14 100
Decimals in Expanded Form
Writing decimals in expanded form is an extension of whole numbers in expanded form.To do this you represent each individual place value
EXAMPLE 4.305 is 4 + 0.3 + 0.0054 x 1 + 3 x 0.1 + 5 x 0.0014 x 100 + 3 x 10-1 + 5 x 10-3
Decimals in Expanded Form34.308
30 + 4 + 0.3 + 0.008
3 x 10 + 4 x 1 + 3 x 0.1 + 8 x 0.001
3 x 101 + 4 x 100 + 3 x 10-1 + 8 x 10 -3
5.28
5 + 0.2 + 0.08
5 x 1 + 2 x 0.1 + 8 x .01
5 x 100 + 2 x 10-1 + 8 x 10-2
Decimals in Expanded Form3 + 0.4 + 0.09 =
9 x 101 + 3 x 10-1 + 5 x 10-2 =
40 + 0.8 + 0.003 =
0.7 + 0.03 + 0.0002 =
0.06 + 0.4 + 3 + 20 + 0.001 =
800 + 3 + 60 000 + 0.02 + 0.007 =
3.493.49
40.80340.803
23.46123.461
60 803.o27
60 803.o27
0.73020.7302
90.3590.35
Decimals in Expanded Form4 x 1000 + 5 x 0.1 + 3 x 0.01 =
7 x 100 + 2 x 0.1 + 5 x 1 + 8 x 0.001 =
4 x 0.0001 + 3 x 0.1 + 2 x 0.01 =
0.006 + 0.01 + 700 + 20 + 0.0004 =
3 x 1 + 4 x 0.01 =
8 x 100 + 5 x 10-2 + 3 x 10-3 =
4000.534000.53
705.208705.208
720.0164720.0164
3.043.04
0.32040.3204
8.0538.053
Rounding DecimalsWhen rounding decimals it is first necessary to identify the place value you are rounding to. The digit that follows will tell you whether you should round up or leave the digit the same.If the digit is: 5 or higher – round up by one
If the digit is: 4 or lower – leave the same
Digits past the rounded digit are not recorded in the rounded number.
When rounding it is helpful if you . . .
Circle the place value you are rounding to. Underline the digit that follows; it is this digit that tells you to round up or leave the same.
Example
34.561 rounded to the nearest tenth
is . . .
3 4 . 5 6 1
34.6
Example
4.6341 rounded to the nearest hundredth is . . .
4 . 6 3 4 1
4.63
Example
67.1125 rounded to the nearest thousandths is
6 7 . 1 1 2 5
67.113
Example
.6971 rounded to the nearest hundredth is . . .
0 . 6 9 7 1
.70
Example
5.96 rounded to the nearest tenth is . . .
5 . 9 6
6
Example
587.469 rounded to the nearest whole number is . . .
5 8 7 . 4 6 9
587
Example
7535.9 rounded to the nearest whole number is . . .
7 5 3 5 . 9
7536
Example
619.844 rounded to the nearest whole number is . . .
6 1 9 . 8 4 4
620
Example
6198 rounded to the nearest hundred is . . .
6 1 9 8
6200
Example
463 228 rounded to the nearest hundred thousand is . . .
463 228
500 000
8 x 0.3 =
Eight groups with three tenths in each group
2.4
2 x 1.6 =
Two groups with one and six tenths in each group
3.2
4 x 0.9 =
Four groups with nine tenths in each group
3.6
9 x 0.5 =
Nine groups with five tenths in each group
4.5
2 x 1.2 =
Two groups with one and two tenths in each group
2.4
Question # 9 Example
To share 1.7 of a bar I would need two bars. I would give away one whole bar and break the second bar into ten equal pieces and give away seven pieces of the ten or one and seven tenths.
One and seven tenth as a fraction is 1 7
10