1 lesson 1.3.1 decimals. 2 lesson 1.3.1 decimals california standard: number sense 1.1 compare and...

$: 1 Lesson 1.3.1 Decimals. 2 Lesson 1.3.1 Decimals California Standard: Number Sense 1.1 Compare and order positive and negative fractions, decimals, and$
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Lesson 1.3.1Lesson 1.3.1

DecimalsDecimals

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Lesson

1.3.1DecimalsDecimals

California Standard:Number Sense 1.1Compare and order positive and negative fractions, decimals, and mixed numbers and place them on a number line.

What it means for you:You’ll learn more about the place values of decimals.

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

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Lesson


You’ve seen decimals in earlier grades — but now you’re going to deal with different place values and negative decimals too.

– 1 0 1– 0.5 0.5

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Decimals Are Numbers Between Integers

Lesson


Decimals are used to represent numbers between integers.

Digits after the decimal point represent part of an integer.

0.8 means “0 plus 8 tenths,”and 1.4 means “1 plus 4 tenths.”

In other words, each one is divided into 100 hundredths.

Each one on the number line is divided into 10 tenths.

Similarly, each one on the number line is divided into 1000 thousandths.

Each tenth is then divided into 10 hundredths.

0.8 1.4

5

6 85.6 25.6 28. 285.6 285.The number

plus 2 thousandths.plus 8 hundredthsplus 5 tenths6 ones

Example 1

Solution follows…

Lesson


Explain the meaning of each of the digits in the number 6.582.

Between which two integers does the number 6.582 lie?

Solution

6.582 is 6 ones plus numbers after a decimal point.

6

Ones

2

Thousandths

8

Hundredths

5

Tenths

means:

So the number 6.582 lies between 6 and 7.

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Example 2

Solution follows…

Lesson


David spent 1 hour and 30 minutes playing basketball.

Express this number of hours as a decimal.

30 minutes is 0.5 of an hour, so David played basketball for 1 whole hour plus an extra 0.5 hours.

Solution

Putting those together, David played basketball for 1.5 hours.

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Guided Practice

Solution follows…

Lesson


1. 34.251

3. 0.163

In Exercises 1–4, first say which digit is in the hundredths place, then which digit is in the thousandths place.

Hundredths = 5Thousandths = 1

5. A runner completed a marathon in 4 hours and 15 minutes. Express this number as a decimal.

2. 128.734

4. 3514.902

4.25 hours




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Decimals Can Be Shown on the Number Line

Lesson


To put a decimal on the number line, read it as an instruction.

For example, with the number 2.68:

• then move 6 tenths in the same direction,

• then move 8 hundredths in the same direction.

• first move 2 ones along the number line,

2 ones 6 tenths

2.68

8 hundredths

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Example 3

Solution follows…

Lesson


Put 1.43 on the number line.

then 4 tenths… 1.43 is 1 along the number line…then 4 tenths, 1.43 is 1 along the number line,

1 one 4 tenths

1.43

3 hundredths

and then 3 hundredths.

Solution

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Lesson


You can plot negative decimals in the same way.

But this time you move in the negative direction — that’s to the left.

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Example 4

Solution follows…

Lesson


Put –1.27 on the number line.

–1.27 is 1 along the number line in the negative direction,and then 2 tenths in the same direction,

Solution

and then 7 hundredths in the same direction.

1 one

–1.27

7 hundredths 2 tenths

–1.27 is 1 along the number line in the negative direction…and then 2 tenths in the same direction…

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Guided Practice

Solution follows…

Lesson


6. 1.4

7. –2.8

8. 6.3

9. –0.5

Place the numbers in Exercises 6–9 onto a number line.

1.4–2.8 6.3–0.5

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Draw Zoomed-in Number Lines to Be More Accurate

Lesson


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.

one tenthone hundredth

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Example 5

Solution follows…

Lesson


Put –0.183 on the number line.

and then 8 hundredths in the same direction,

Solution

1 tenth

–0.183

3 thousandths8 hundredths

and then 3 thousandths in the same direction.

–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…

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Guided Practice

Solution follows…

Lesson


10. –1.73

11. –5.78

Place the numbers in Exercises 10–11 onto the number line.

–1.73

–1.9 –1.8 –1.7 –1.6

–5.9 –5.8 –5.7 –5.6

–5.78

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Guided Practice

Solution follows…

Lesson


12. –5.624

13. 0.597

Place the numbers in Exercises 12–13 onto the number line.

–5.64 –5.63 –5.62 –5.61

–5.624

0.58 0.59 0.60

0.597

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Independent Practice

Solution follows…

Lesson


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.

23.5

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Independent Practice

Solution follows…

Lesson


3. –2.28

4. –19.23

5. 3.246

Place the numbers in Exercises 3–5 onto a number line.

3.23 3.24 3.25 3.26

–21 –20 –19 –18

–2.4 –2.3 –2.2 –2.1

3.246

–19.23

–2.28

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Lesson


Round UpRound 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 you’ll see how that helps you put decimals in order.

1 lesson 1.3.1 decimals. 2 lesson 1.3.1 decimals california standard: number sense 1.1 compare and...

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