3-1 Representing, Comparing, and Ordering Decimals Warm Up Problem of the Day Lesson Presentation Course 1

Warm Up Order the numbers from least to greatest. 1. 242, 156, 224, 165 2. 941, 148, 914, 814, 721 3. 345, 376, 354, 397 156, 165, 224, 242 148, 721, 814, 914, 941 345, 354, 376, 397

Problem of the Day Lupe is taller than Reba and shorter than Miguel. Tory is shorter than Lupe but taller than Reba. List the four brothers and sisters in order from tallest to shortest. Miguel, Lupe, Tory, Reba

Put these decimals in order from largest to smallest Put these decimals in order from largest to smallest. Come up with a rule for ordering. 8.008 8 8.8 8.07 88.1 8.088

Additional Example 1: Reading and Writing Decimals Write each decimal in standard form, expanded form, and words. A. 1.07 B. 0.03 + 0.006 + 0.0009 Expanded form: 1 + 0.07 Word form: one and seven hundredths Standard form: 0.0369 Word form: three hundred sixty-nine ten-thousandths

Additional Example 1: Reading and Writing Decimals Write the decimal in standard form and expanded form. C. fourteen and eight hundredths Standard form: 14.08 Expanded form: 10 + 4 + 0.08

Check It Out: Example 1 Write each decimal in standard form, expanded form, and words. A. 1.12 B. 0.6 + 0.008 + 0.0007 Expanded form: 1 + 0.1 + 0.02 Word form: one and twelve hundredths Standard form: 0.6087 Word form: six thousand eighty-seven ten-thousandths

Check It Out: Example 1 Write each decimal in standard form and expanded form. C. eleven and two hundredths Standard form: 11.02 Expanded form: 10 + 1 + 0.02

Additional Example 2: Earth Science Application The star Wolf 359 has an apparent magnitude of 13.5. Suppose another star has an apparent magnitude of 13.05. Which star has the smaller magnitude? Line up the decimal points. Start from the left and compare the digits. 13.50 Look for the first place where the digits are different. 13.05 0 is less than 5. 13.05 < 13.50 The star that has an apparent magnitude of 13.05 has the smaller magnitude.

Check It Out: Example 2 Tina reported on a star for her science project that has a magnitude of 11.3. Maven reported on another star that has a magnitude of 11.03. Which star has the smaller magnitude? Line up the decimal points. Start from the left and compare the digits. 11.30 Look for the first place where the digits are different. 11.03 0 is less than 3. 11.03 < 11.30 The star that has a magnitude of 11.03 has the smaller magnitude.

Order the decimals from least to greatest. Additional Example 3: Comparing and Ordering Decimals Order the decimals from least to greatest. 16.67, 16.6, 16.07 Compare two of the numbers at a time. Write 16.6 as “16.60.” 16.67 16.60 16.60 < 16.67 16.67 16.07 Start at the left and compare the digits. 16.07 < 16.67 16.60 16.07 Look for the first place where the digits are different. 16.07 < 16.60

Additional Example 3 Continued Graph the numbers on a number line. 16.6 16.67 16.07 16 16.1 16.2 16.3 16.4 16.5 16.6 16.7 16.8 16.9 17 The numbers are ordered when you read the number line from left to right. The numbers in order from least to greatest are 16.07, 16.6, and 16.67.

Order the decimals from least to greatest. Check It Out: Example 3 Order the decimals from least to greatest. 12.42, 12.4, 12.02 Compare two of the numbers at a time. Write 12.4 as “12.40.” 12.42 12.40 12.40 < 12.42 12.42 12.02 Start at the left and compare the digits. 12.02 < 12.42 12.40 12.02 Look for the first place where the digits are different. 12.02 < 12.40

Check It Out: Example 3 Continued Graph the numbers on a number line. 12.42 12.4 12.02 12 12.1 12.2 12.3 12.4 12.5 12.6 12.7 12.8 12.9 13 The numbers are ordered when you read the number line from left to right. The numbers in order from least to greatest are 12.02, 12.4, and 12.42.

Lesson Quiz: Part I Write each in standard form, expanded form and words. 1. 8.0342 2. 10 + 8 + 0.3 + 0.006 3. eight and twelve hundredths 8 + 0.03 + 0.004 + 0.0002; eight and three hundred forty-two ten thousandths 18.306; eighteen and three hundred six thousandths 8.12; 8 + 0.1 + 0.02

Lesson Quiz: Part II 4. It takes Pluto 246.7 years to orbit the Sun, and it takes Neptune 164.8 years. Which planet takes longer to orbit the Sun? 5. Order the decimals from least to greatest: 16.35, 16.3, 16.5. Pluto 16.3, 16.35, 16.5