1. Warm-Up
29 1/ /5
29 1/7 = / /7 = / /7 = 13.

2. Decimals Many decimal numbers are rational numbers: but most are not.
A decimal is a rational number if it can be written as a fraction. So, those are decimals that either terminate (end) or repeat.
Repeating decimals: …; …
Terminating decimals: 4.8; ; 0.75

3. A decimal like … is not rational because although there is a pattern, it does not repeat. It is irrational.
Compare this to … It is rational because 556 repeats.
All fractions can be represented by terminating or repeating decimals!

4. When decimals are equal
3.56 =
But, ≠
To see why, examine the place values.
3.056 = • • • .001
whole tenths hundredths thousandths
3.560 = • • • .001
Think of units, rods, flats, and cubes.

5. Ways to compare decimals
Write them as fractions and compare the fractions as we did in the last section.
Use base-10 blocks.
Write them on a number line.
Line up the place values.

6. Language
Write down (in words) how you would say 0.5
Does 1/3 = 0.33?

7. Connections

8. Exploration 5.16
Do #2, 4, 7, and 8.

9. Rounding 3.784: round this to the nearest hundredth.
Look at the hundredths.
Well, is between 3.78 and On the number line, which one is closer to?
3.785 is half way in between.

10. Practice Rounding Round to the nearest tenth: 5.249
Closer to 5.2 or 5.3?
Round to the nearest hundredth:
Closer to 5.24 or 5.25?
Round to the nearest whole:
Closer to 357 or 358?
Round to the nearest hundred:
Closer to 300 or 400?

11. Practice Rounding Round to the nearest thousandth: 5.0099
Must have the last 0 for the thousandths place!
Round to the nearest hundredth:
64.28
Round to the nearest tenth:
11.0 Must have the last 0 for the tenths place!