Representing, Comparing, Ordering, and Estimating Decimals #8

Place value can help you understand and write and compare decimal numbers. Vocabulary

Example 1: Reading and Writing Decimals Write each decimal in standard form, expanded form, and words. A B

Example 2: Reading and Writing Decimals Write the decimal in standard form and expanded form. C. fourteen and eight hundredths

Example 3: Real-World Application The star Wolf 359 has an apparent magnitude of Suppose another star has an apparent magnitude of Which star has the smaller magnitude?

Example 4: Real-World Application Marci shipped two packages. One weighed pounds and the other weighed pounds. Which package weighed less?

Additional Example 5: Comparing and Ordering Decimals Order the decimals from least to greatest , 16.6, 16.07

Example 5 Continued Graph the numbers on a number line

Example 6: Comparing and Ordering Decimals Order the decimals from greatest to least. 0.08, 0.04, 0.1

Example 6 Continued Graph the numbers on a number line

Example 7 Order the decimals 12.42, 12.4, from least to greatest , 12.4,

When numbers are about the same value, you can use clustering to estimate. Clustering means rounding the numbers to the same value. Vocabulary

Example 8: Real-World Application Nancy wants to cycle, ice skate, and water ski for 30 minutes each. About how many calories will she burn in all? (Cycling = calories, ice skating = calories, and water skiing = calories)

Example 9 Abner wants to run, roller-skate, and snow ski for 60 minutes each. About how many calories will he burn in all? (Running = calories, roller-skating = calories, and snow skiing = calories.)

Look at the digit to the right of the place to which you are rounding. If it is 5 or greater, round up. If it is less than 5, round down. Caution!

Example 10: Rounding Decimals to Estimate Sums and Differences Estimate by rounding to the indicated place value. A ; ones B – ; tenths

Example 11: Using Compatible Numbers to Estimate Products and Quotients Estimate each product or quotient. A  1.98 B ÷ 26.14

You can also use front-end estimation to estimate with decimals. Front-end estimation means to use only the whole-number part of the decimal. Vocabulary

Additional Example 12: Using Front-End Estimation Estimate a range for the sum Use front-end estimation.

Example 13 Estimate a range for the sum