Notes 3.3 – Exploring Decimals

PLACE VALUE The value of a digit in a decimal is determined by its ___________ or place. For example, given the decimal 0.35, the 3 is in the _________ place and the 5 is in the ________________ place. POSITION TENTHS HUNDREDTHS

TENS (10) THOUSANDTHS (0.001) TENTHS (0.1) HUNDREDS (100) ONES (1) HUNDREDTHS (0.01) TEN-THOUSANDTHS (0.0001) THOUSANDS (1,000) What is this number? _____ thousand, _____ hundred ______________ AND ____ thousand, _____ hundred ________________ ten thousandths ONE TWO THIRTY-FOUR FIVE SIX SEVENTY-EIGHT

More Fractions A ________________ is a number written with both a whole number and a fraction.     Useful Information: To enter mixed numbers on a calculator: Type in the whole number + ( fraction ) 3 ½ would be entered as 3 + (1/2) MIXED NUMBER

Write the following numbers as a decimal and a mixed number with the fraction in lowest terms. Decimal Mixed Number  a) one thousand and one hundred-thousandth   b) twenty-two and two thousand five hundred ten-thousandths

TERMINATING AND REPEATING DECIMALS A decimal is called a terminating decimal if the decimal number terminates, or _______. A decimal is called a repeating decimal if the decimal number does not terminate. It repeats a ___________. ENDS PATTERNS

Bar Notation: A bar indicates what number(s) in the decimals will repeat:   Rewrite the repeating decimals using bar notation A.) 56.11111… B.) -4.356356356…

Examples: Use division to determine whether each of the following fractions terminate or repeat. A.) B.) C.) D.)

Comparing Decimal Numerals 1.) __________ each decimal with the _______ number of decimal places 2) _______ up the decimal points 3) Write the numerals in ________. 4) Change the decimals to the ___________ form. REWRITE SAME LINE ORDER ORIGINAL

Order the decimals from least to greatest Most number of decimal places? B.) -7.11, -7.011, -7.105, -7.01, -7.1 ______________________ ______________________

Write each decimal as a fraction or mixed number in lowest terms Fraction Lowest Terms   a) .23 b) 4.015 c) 45 .45 d) 81.225

Order the numbers from least to greatest; a) b).

Homework: p. 146 #6-35, 36-47, 54-69