Decimals

1
Decimals
Lesson 1.3.1
2
Lesson 1.3.1
Decimals
California Standard Number Sense 1.1 Compare and
order positive and negative fractions, decimals,
and mixed numbers and place them on a number line.
What it means for you Youll learn more about
the place values of decimals.

• Key words
• decimal point
• tenth
• hundredth
• thousandth

3
Lesson 1.3.1
Decimals
Youve seen decimals in earlier grades but now
youre going to deal with different place values
and negative decimals too.
1
0
0.5
0.5
1
4
Lesson 1.3.1
Decimals
Decimals Are Numbers Between Integers
Decimals are used to represent numbers between
integers. Digits after the decimal point
represent part of an integer.
Each one on the number line is divided into 10
tenths.
0.8 means 0 plus 8 tenths,
and 1.4 means 1 plus 4 tenths.
Each tenth is then divided into 10 hundredths.
In other words, each one is divided into 100
hundredths.
Similarly, each one on the number line is divided
into 1000 thousandths.
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Lesson 1.3.1
Decimals
Example 1
Explain the meaning of each of the digits in the
number 6.582. Between which two integers does the
number 6.582 lie?
Solution
The number
means
plus 2 thousandths.
plus 8 hundredths
plus 5 tenths
6 ones
6.582 is 6 ones plus numbers after a decimal
point.
So the number 6.582 lies between 6 and 7.
Solution follows
6
Lesson 1.3.1
Decimals
Example 2
David spent 1 hour and 30 minutes playing
basketball. Express this number of hours as a
decimal.
Solution
30 minutes is 0.5 of an hour, so David played
basketball for 1 whole hour plus an extra 0.5
hours.
Putting those together, David played basketball
for 1.5 hours.
Solution follows
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Lesson 1.3.1
Decimals
Guided Practice
In Exercises 14, first say which digit is in the
hundredths place, then which digit is in the
thousandths place.
Hundredths 5 Thousandths 1
Hundredths 3 Thousandths 4
1. 34.251 3. 0.163
2. 128.734 4. 3514.902
Hundredths 6 Thousandths 3
Hundredths 0 Thousandths 2
5. A runner completed a marathon in 4 hours and
15 minutes. Express this number as a decimal.
4.25 hours
Solution follows
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Lesson 1.3.1
Decimals
Decimals Can Be Shown on the Number Line
To put a decimal on the number line, read it as
an instruction.
For example, with the number 2.68

• first move 2 ones along the number line,

• then move 6 tenths in the same direction,

• then move 8 hundredths in the same direction.

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Lesson 1.3.1
Decimals
Example 3
Put 1.43 on the number line.
Solution
1.43 is 1 along the number line,
then 4 tenths
1.43 is 1 along the number line
then 4 tenths,
and then 3 hundredths.
Solution follows
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Lesson 1.3.1
Decimals
You can plot negative decimals in the same
way. But this time you move in the negative
direction thats to the left.
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Lesson 1.3.1
Decimals
Example 4
Put 1.27 on the number line.
Solution
1.27 is 1 along the number line in the negative
direction,
1.27 is 1 along the number line in the negative
direction
and then 2 tenths in the same direction
and then 2 tenths in the same direction,
and then 7 hundredths in the same direction.
Solution follows
12
Lesson 1.3.1
Decimals
Guided Practice
Place the numbers in Exercises 69 onto a number
line.
6. 1.4 7. 2.8 8. 6.3 9. 0.5
Solution follows
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Lesson 1.3.1
Decimals
Draw Zoomed-in Number Lines to Be More Accurate
It is hard to show thousandths on a normal number
line accurately. Instead, you can draw a zoomed
in number line.
This one has a scale marked in tenths rather than
integers, with divisions for hundredths.
14
Lesson 1.3.1
Decimals
Example 5
Put 0.183 on the number line.
Solution
0.183 is 1 tenth along the number line in the
negative direction,
0.183 is 1 tenth along the number line in the
negative direction
and then 8 hundredths in the same direction,
and then 8 hundredths in the same direction
and then 3 thousandths in the same direction.
Solution follows
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Lesson 1.3.1
Decimals
Guided Practice
Place the numbers in Exercises 1011 onto the
number line.
10. 1.73 11. 5.78
1.9
1.8
1.7
1.6
5.9
5.8
5.7
5.6
Solution follows
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Lesson 1.3.1
Decimals
Guided Practice
Place the numbers in Exercises 1213 onto the
number line.
12. 5.624 13. 0.597
5.64
5.63
5.62
5.61
0.58
0.59
0.60
Solution follows
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Lesson 1.3.1
Decimals
Independent Practice
1. The temperature in Celsius of a substance
during a science experiment is twelve and
twenty-three hundredths below zero. Represent
this temperature using a decimal.
12.23 C
2. Place the number 23.5 onto the number line.
Solution follows
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Lesson 1.3.1
Decimals
Independent Practice
Place the numbers in Exercises 35 onto a number
line.
3. 2.28 4. 19.23 5. 3.246
2.4
2.3
2.2
2.1
21
20
19
18
3.23
3.24
3.25
3.26
Solution follows
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Lesson 1.3.1
Decimals
Round Up
Decimals look complicated, but they can be
broken up into tenths, hundredths, and
thousandths, and put on the number line.
In the next Lesson youll see how that helps you
put decimals in order.