Chapter 3 Notes
hundredths
thousandths
Ten
thousandths
Hundred
thousandths
0
.
0
0
4
2
0
1
.
.
.
0
4
3
0
3
0
0
0
0
2
1
millionths
tenths
1
Decimal
point
1
ones
tens
hundreds
Decimal Place Values
4
How to read decimals
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First, read the number before the decimal point.
Second, read the decimal point as the word “and”
Third, read the number after the decimal point as if there were no decimal point
Finally, read the place value of the number furthest to the right
Examples
0.004= zero and four thousandths
2.000004= two and four millionths
0.43= forty-three hundredths
111.3021= one-hundred, eleven and three thousand, twenty-one ten thousandths
Rounding Decimals
How to round a decimal to a given place
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
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Find the place you are rounding to
Look at the number to its right. If the number is less than 5, keep the place number the same. If
the digit is 5 or more, round up one place.
Drop all the digits to the right of the place you are rounding to.
If it says round to the nearest nonzero place, round the number to the place value furthest to
the left that is not a zero
Examples
1. Round 1.2349 to the nearest thousandth.
a. Since the number to the right of the thousandths place is 9, round up= 1.235
2. Round 1.2291 to the nearest tenth.
a. 1.2291 Since the number to the right of the tenths place is 2, keep the tenths place the
same = 1.2
3. Round 0.87 to the greatest nonzero place.
a. The greatest nonzero place is the tenths place so round the 8. Since the number to the
right of the tenths is 7, , round up=0 .9
Compare and Order Decimals
How to compare decimals
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
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Start at the left and compare digits in the same places.
Start with the greatest place, then the next greatest place, and so on.
Any empty place values are equal to zero.
Examples
0.834 ____0.732
Start with the tenths place. Since 8 is greater than 7 in the tenths place, 0.834 > 0.732.
12.580 _____12.58
Start with the tens place and keep comparing. Write a zero so that the decimals have the same
number of places. 12.580 = 12.58
How to order decimals
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
Line up the decimal points.
Compare the digits in each place, starting with the greatest place. Fill in empty place values with
zero.
Examples
0.1285
1.6993
0.0668
0.0914
Starting with the ones place, 1.6993 is the greatest. Then,
comparing the tenths place, 0.1285 is the next greatest. Next,
looking at the hundredths place0.0914 is the next greatest. This
leaves 0.0668 as the least. In order from greatest to least, the
decimals are: 1.6993, 0.1285, 0.09`4, 0.0668. From least to
greatest, the decimals are: 0.0668, 0.0914, 0.1285, 1.6993.
Adding Decimals
How to add decimals
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Line up the decimal points in the numbers—one underneath the other--before you add.
In a whole number, the decimal point is understood to be “on the right of the whole number”.
So 4 = 4.000. You may add as many zeros as needed.
Fill in any empty place values with a zero.
Add normally. Don’t forget to bring down the decimal point.
Examples
3
3.00
7.8
7.80
+4.23 = +4.23
+2.91= +2.91
7.23
10.71
Subtracting Decimals
How to subtract decimals
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

Line up the decimal points.
Place zeros in any empty place value.
Subtract and regroup if necessary. Don’t forget to bring down the decimal point.
Examples
9 – 5.25=
0.8 – 0.314=
9.00
0.800
-5.25
-0.314
3.75
0.486