Warm-Up 29 1/5 - 16 2/5 29 1/7 = 28 11/7 - 16 4/7 = 16 4/7 12 7/7 = 13.

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Presentation transcript:

Warm-Up 29 1/5 - 16 2/5 29 1/7 = 28 11/7 - 16 4/7 = 16 4/7 12 7/7 = 13.

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: 7.6666…; 0.727272… Terminating decimals: 4.8; 9.00001; 0.75

A decimal like 3.56556555655556555556… is not rational because although there is a pattern, it does not repeat. It is irrational. Compare this to 3.556556556556556556… It is rational because 556 repeats. All fractions can be represented by terminating or repeating decimals!

When decimals are equal 3.56 = 3.56000000 But, 3.056 ≠ 3.560. To see why, examine the place values. 3.056 = 3 + 0 • .1 + 5 • .01 + 6 • .001 whole tenths hundredths thousandths 3.560 = 3 + 5 • .1 + 6 • .01 + 0 • .001 Think of units, rods, flats, and cubes.

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.

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

Connections

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

Rounding 3.784: round this to the nearest hundredth. Look at the hundredths. Well, 3.784 is between 3.78 and 3.79. On the number line, which one is 3.784 closer to? 3.785 is half way in between. 3.78 3.785 3.79

Practice Rounding Round to the nearest tenth: 5.249 Closer to 5.2 or 5.3? Round to the nearest hundredth: 5.249 Closer to 5.24 or 5.25? Round to the nearest whole: 357.82 Closer to 357 or 358? Round to the nearest hundred: 357.82 Closer to 300 or 400?

Practice Rounding Round to the nearest thousandth: 5.0099 5.010 Must have the last 0 for the thousandths place! Round to the nearest hundredth: 64.284 64.28 Round to the nearest tenth: 10.957 11.0 Must have the last 0 for the tenths place!