Unit 2 – Operations with Whole Numbers and Decimals Name: ___________________ Lesson 2.1 - Large Numbers Standard Notation Each place is 10 times the place to its right Each period, or group, is divided into ones, tens, hundreds Each period is separated by a comma Expanded Notation A number is written as the sum of the values of its digits 345 = 300 + 40 + 5 or 345 = (3 * 100) + (4 * 10) + (5 * 1) Number-and-Word Notation Significant digits followed by a word for the place value of the largest period 63,800,000 = 63,800,000 = 63.8 million Process 1. Choose the largest period group 2. Replace the comma with a decimal 3. Write down any other digits to the right of the decimal 4. Write the word for the largest period Lesson 2.2 - Small Numbers Small numbers: Each place is 1/10 of the place to its left Each place is 10 times the place to its right The decimal divides between the parts and whole Reading Small Numbers 1. Identify the place value of the smallest digit. 2. Read the number (ignore the decimal and zeros) and say the smallest digit’s place value Ex.: 0.0134 = 134 ten-thousandths Writing Small Numbers 1. Draw a decimal point and enough spaces for the smallest digit 2. Write the number in the spaces so the smallest digit is on the last space 3. Fill the blanks with zeros Ex. 345 thousandths = ___ . ___ ___ ___ Lesson 2.3 - Decimals: Add and Subtract Decimal computation: 1. Line up the decimals 2. Estimate whole numbers 3. Add or Subtract 4. Verify answer with estimate Example: 34.9+ 3.25 Lesson 2.4 - Powers of 10 Powers of 10 Numbers such as 0.1, 1,10, 100, 0.01 Exponential Notation numbers written with an exponent Lesson 2.5- Multiplying Decimals Estimating Products with Decimals Round each factor to its greatest place value (5.3 * 0.64 = 5 * 0.6 = 3) Remember, if one factor is less than 1, the product will be less than the other factor. For numbers less than one, use a fraction for a more accurate estimate Lesson 2.6 - Divisibility Rules Divisible by My Hypothesis I think…. Rule I learned… 2 All even numbers (end in 0, 2, 4, 6, 8) 3 Find sum of all digits (add them up)… the sum is divisible by 3. Underline last two digits of number…they are divisible by 4. 4 5 Ends in a 0 or 5 6 Is divisible by both 2 and 3 7 Take the last digit in a number. Double and subtract the last digit from the rest of the digits. Is it divisible by 7? If so, the number is. Example: 357 (Double the 7 to get 14. Subtract 14 from 35 to get 21 which is divisible by 7 8 The last 3 digits are divisible by 8 9 Add up all digits. If the sum is divisible by 9, so is the number. 10 Ends in a zero Lesson 2.7 - Rounding Rounding Rules Underline the place that you are rounding to Look at the number to the right of the place 0,1,2,3,4 – Ignore the number and leave the rounding number as it is 5,6,7,8,9 – Round up to the next number you are rounding too Lesson 2.9 - Scientific Notation Powers of 10 Scientific Notation Used for large and small numbers: First part: a number between one and nine Second part: a positive or negative power of ten that was used to get the first part 4 Ex: 5.3 * 10 -4 1.05 * 10 Exponents Negative Exponents = Divide by 10 (decimal to the left) Positive Exponents = Multiply by 10 (decimal to the right) Unit 2 Study Zone Test Date: ___________________ Parent’s Signature: ____________________ My plan to prepare for this test is: Skill Vocabulary/Process Write and compare Define the words: numbers written in Scientific Notation different notation types Standard Notation Repeated Factors Word and Number Notation Exponential Notation Write exponents Exponents Add decimals Subtract decimals Multiply decimals Divide Decimals Divide Decimals to two decimal places Process: 1. Line up decimals in problem 2. Add; carry if needed 3. Copy correctly Process: 1. Line up decimals in problem 2. Subtract; borrow if needed 3. Copy with decimal How to Study Study each notation type in your notes. Test yourself and check by looking up the definitions in the glossary Create a number; then translate it in each notation form Make 5 numbers in different notation forms, convert each to standard form to order (compare) them Practice writing numbers with positive exponents and create large numbers negative exponents and create small numbers Ideas to practice computation: Review your quizzes for types of mistakes that you made so that you will know what to watch out for Create a problem, solve it, then check answer on a calculator Copy problems that you feel more practice is need on out of the journal. Then go back and solve them. Look over your quizzes and redo any problems that were missed. Process: 1. Copy problem & estimate 2. Multiply by ones in bottom number. Remember to carry. 3. Add a space-keeper, then multiply by tens Process: Basic Facts: 1. Copy carefully www.Xtramath.com 2. Remove decimal in divisor; www.emgames.com same process in dividend 3. Place decimal in answer 4. Divide Set up the problem… 1. Remove decimal in factor and then do the same thing to the product. 2. Find where the decimal is in the product and move it into the answer 3. Make the product have two decimal places to the right of the decimal point 4. Divide and write the remainder as a fraction 5. Determine whether to round up or ignore the fraction

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# Unit 2