1. 1 Lesson 1.3.1 Decimals

2. 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: You’ll learn more about the place values of decimals. Key words: decimal point tenth hundredth thousandth

3. 3 Lesson 1.3.1 Decimals You’ve seen decimals in earlier grades — but now you’re going to deal with different place values and negative decimals too. – 10 1 – 0.5 0.5

4. 4 Decimals Are Numbers Between Integers Lesson 1.3.1 Decimals 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. 0.81.4

5. 5 685. 625. 628. 285. 6285. The number plus 2 thousandths.plus 8 hundredthsplus 5 tenths6 ones Example 1 Solution follows… Lesson 1.3.1 Decimals 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.

6. 6 Example 2 Solution follows… Lesson 1.3.1 Decimals 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.

7. 7 Guided Practice Solution follows… Lesson 1.3.1 Decimals 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 = 5 Thousandths = 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 Hundredths = 6 Thousandths = 3 Hundredths = 0 Thousandths = 2 Hundredths = 3 Thousandths = 4

8. 8 Decimals Can Be Shown on the Number Line Lesson 1.3.1 Decimals 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 ones6 tenths 2.68 8 hundredths

9. 9 Example 3 Solution follows… Lesson 1.3.1 Decimals 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 one4 tenths 1.43 3 hundredths and then 3 hundredths. Solution

10. 10 Lesson 1.3.1 Decimals You can plot negative decimals in the same way. But this time you move in the negative direction — that’s to the left.

11. 11 Example 4 Solution follows… Lesson 1.3.1 Decimals 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 hundredths2 tenths –1.27 is 1 along the number line in the negative direction… and then 2 tenths in the same direction…

12. 12 Guided Practice Solution follows… Lesson 1.3.1 Decimals 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 –2.86.3–0.5

13. 13 Draw Zoomed-in Number Lines to Be More Accurate Lesson 1.3.1 Decimals 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

14. 14 Example 5 Solution follows… Lesson 1.3.1 Decimals Put –0.183 on the number line. and then 8 hundredths in the same direction, Solution 1 tenth –0.183 3 thousandths 8 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…

15. 15 Guided Practice Solution follows… Lesson 1.3.1 Decimals 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

16. 16 Guided Practice Solution follows… Lesson 1.3.1 Decimals 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 0.580.59 0.60 0.597

17. 17 Independent Practice Solution follows… Lesson 1.3.1 Decimals 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

18. 18 Independent Practice Solution follows… Lesson 1.3.1 Decimals 3.–2.28 4.–19.23 5.3.246 Place the numbers in Exercises 3–5 onto a number line. 3.23 3.243.253.26 –21 –20–19–18 –2.4 –2.3–2.2–2.1 3.246 –19.23 –2.28

19. 19 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 you’ll see how that helps you put decimals in order.