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Understanding Decimals: Concepts, Computation, and Applications in Everyday Scenarios

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Explore the fundamental concepts of decimals, their computation, and real-world applications. This guide covers whole numbers, fractions, and percentages, illustrating how to apply these concepts in practical settings like measuring gas, comparing attendance figures, and calculating discounts. Learn how decimals are structured, the significance of place value, and the steps to convert fractions into decimals. Engage with exercises designed to strengthen your understanding of decimals, comparing and ordering them effectively.

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Understanding Decimals: Concepts, Computation, and Applications in Everyday Scenarios

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  1. Decimals(Concepts & Computation) Nov. 30

  2. Number Sense • Whole number; number of people attending an event (305) • Decimal; number of gallons of gasoline (3.65) • Ratio; number of men compared to number of women (2:5) • Fraction; measurement of diameter (¾) • Percent; discount rate, interest rate (14.5%)

  3. Decimals and Place Value • A decimal is a number with a decimal point in it (6.52, 0.5, 0.01) • The value of digits in a decimal is based on the number 10 • The digits to the left of the decimal point represent whole number • The numbers to the right of the decimal point represent some part of 1

  4. Exercise • In what place is the underlined digit? 4.068 64.183 4.1065.832 5.134 • What number does the underlined name? 5.839 24.935 328.407 840.019 247.893 • Circle the number in which the 3 has the greater value. 73.249 856.634 1,420.038 52.243 78.329 865.463 1,240.308 49.321

  5. Thousandths • 2 1 6 4. 5 7 8 • 2; thousands • 1; hundreds • 6; tens • 4; ones • 5; tenths • 7; hundredths • 8; thousandths

  6. Exercise • Write the decimals. • 609 89 3 5 125 • ------ 4 ----- 86 ----- --- 2 ----- • 1000 1000 1000 10 1000 • Fifty-two thousandths • Four and four thousandths • Eight thousandths • One hundred fifty-nine and twelve hundredths

  7. Comparing and Ordering Decimals • Compare the decimals 0.27 and 0.25 • Compare number of ones (0 = 0) • Compare number of tenths (2 = 2) • Compare number of hundredths (7 > 5)

  8. Exercise • Write <, =, or >. 0.45 0.045 0.25 0.250 0.31 0.310 0.9 0.09 0.07 0.70 0.6 0.600 0.66 0.6 0.503 0.53 0.129 0.12 • Write in order from the least to the greatest 4.4 ; 4.7 ; 4.38 0.63 ; 0.6 ; 0.3 5.01 ; 4.98 ; 5 17.182 ; 1.728 ; 17.218

  9. Changing Fraction to Decimal • You can change a fraction to a decimal by dividing the numerator by the denominator • Numerator; the top part of a fraction • Denominator; the bottom part of a fraction • When you divide until the remainder is zero, the decimal is a terminating decimal

  10. Exercise • Change each fraction to a decimal. • 18 3 9 7 9 • --- --- --- --- --- • 25 40 8 32 20 • Write each decimal as a mixed number or fraction in simplest form • 0.65 0.225 0.006 1.4 0.625

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