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Fractions, Decimals, Percents , & Scientific Notation

Fractions, Decimals, Percents , & Scientific Notation. Converting, Comparing, & Ordering SOL 7.1. Fractions. A fraction is a way of representing division of a ‘ whole ’ into ‘ parts ’. Part. Whole. Examples. A graphical example of fraction is shown by the marching

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Fractions, Decimals, Percents , & Scientific Notation

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  1. Fractions, Decimals, Percents, & Scientific Notation Converting, Comparing, & Ordering SOL 7.1

  2. Fractions A fractionis a way of representing division of a ‘whole’ into ‘parts’. Part Whole

  3. Examples A graphical example of fraction is shown by the marching men below. There are five marching men in the illustration. There are 2 men in orange uniform, thus . Is there another fraction that can be made from the picture below? Create a fraction for the pictures below.

  4. Ordering Fractions There are three major ways to order fractions: Drawing a picture Converting Thinking about it!!! Before we start ordering we need to learn/review … • Vocabulary: • Descending: Greatest to Least • Ascending: Least to Greatest • Numerator: the part, the top of the fraction • Denominator: the whole, the bottom of the fraction • Quotient: answer to a division problem

  5. Ordering by Drawing a Picture Least to Greatest! Suppose you have to place the following in ascendingorder… 1. Draw a box. 2. Draw lines in your box to create rows. You need as many rows as you have fractions. 3. Now break each row up into the number of whole parts of each fraction…the denominator. 1 3 4. Now shade each part of the whole…the numerator. 2 5. The row with the least color is the smallest and so on.

  6. You try it! Place in descending order:

  7. Ordering by Converting Fractions can be converted into fractions for easy ordering. To convert a fraction, like into a decimal you must… Divide the numerator (2) by the denominator (5). The quotient is your decimal. Do this for each fraction you have! 0 . 4 0 -0 2 0 -20 0 But first…

  8. Common Fraction Conversions Chart Copy these down and learn them…it’ll save you some time!

  9. Once you have your fractions converted… 0.4, 0.111, 0.1 1. Line the decimals up by their decimal points. 0 .4 0 .1 1 1 0 .1 0 2. Look at the numbers in the first column, the smallest number corresponds to the smallest fraction. 3. If the numbers are the same, move on to the next column… then the next, and the next. They were already in descending order!

  10. Try It! Place in order from least to greatest. 0 . 7 5 0 . 1 6 7 0 . 3 7 5

  11. Ordering by Thinking! Fractions can arranged in 4 categories when it comes to size…. Less than half! Half! More than half! A Whole! Placing your fractions in these categories can help you order them quickly!

  12. How do you know if a Fraction is… Less Than Half? Half? More Than Half? A Whole?

  13. Try It! Place in ascending order! 5 is more than half of 8! 3 is half of 6! 1 is less than half of 9! So…

  14. Your Assignment… Order the following fractions from greatest to least by drawing a picture! Place the following fractions in ascending order by converting! Order the following fractions from least to greatest by thinking about it!

  15. Decimals A decimal is similar to a fraction in that it is not a whole number. It is a part of a number. 13.032 Whole Number Decimal Decimal Point

  16. Place Value In our decimal number system, the value of a digit depends on its place, or position, in the number. Each place has a value of 10 times the place to its right. Decimals can be named and ordered by their place value! Always line decimals up to the chart and each other by their decimal point. Decimal Point (.) Thousands Ones Hundredths Thousandths Hundreds Tens Ten Thousandths Tenths The decimal with biggest number that is farthest left is the largest! Let’s try it!

  17. Ordering Decimals Remember Descending- Greatest to Least Ascending- Least to Greatest Let’s place 0.45, 0.123, and 0.1045 in ascending order! 1. Line up your decimals by the decimal point. 0 . 4 5 0 . 1 2 3 0 . 1 0 4 5 You cannot tell which decimal is biggest by which is longest! 2. Since the first digits are all zeros, we can look to the right of the decimal point The largest decimal will have the largest number in the tenths place! 3. The same rule applies for the hundredthsplace and so on. 0.1045, 0.123, 0.45

  18. Let’s Try Some… 1) 0.42, 0.31, 0.402 Place in descending order. 0.42, 0.402, 0.31 2) 0.2, 0.11, 0.3 Place in ascending order. 0.11, 0.2, 0.3 3) 1.02, 0.57, 1.201 Order least to greatest. 0.57, 1.02, 1.201 4) -0.42, 0.01, -0.2 Place in descending order. 0.01, -0.2, -0.42

  19. Percent A ratio that compares a number to 100. A ratio compares two numbers using division! 15% = = Percent Symbol

  20. Percents and Fractions Percents and fractions are directly connected…with one you can change to the other. Percent to Fraction: Drop the percent sign. Make the number that was before the percent sign your numerator. Make 100 your denominator. Simplify! Your answer is INCORRECTif your fraction is not in simplest form! 25% = = How do you simplify?!

  21. How to Find the Simplest Form of a Fraction 1. Find the greatest common factor of the numerator and the denominator. 2. Divide both the numerator and the denominator by that number. The greatest common factor is the largest factor between two numbers. A factor, in this case, is a number that divides evenly into another. 12 6 2 ÷ = 18 6 3

  22. Let’s trying turning some percents to fractions! Remember: Drop the percent sign. Make the number that was in front of the percent sign the numerator! Make 100 your denominator. Simplify. 45 9 5 ÷ = 45% 5 100 20 To simplify or reduce: Find the Greatest Common Factor. Divide the numerator and denominator by that GCF!

  23. Let’s try a few more examples! 15% 15 12 75 3 3 3 4 25 5 ÷ ÷ ÷ = = = 75% 4 25 5 4 100 100 100 25 20 12%

  24. Percents and Decimals Percents and decimals are directly connected…with one you can change to the other. Percent to Decimal: Drop the percent sign. Move the decimal to the left twice…this is the same as dividing by 100! What about percents with decimals in them, like 25.5%? The percent sign supersedes the decimal! Even though, 25.5 is indeed a decimal it is more importantly a percent. The same steps need to be followed to make it a “real” decimal!

  25. Let’s trying turning some percents to decimals! Remember: Drop the percent sign. Move the decimal to the left twice! 4.5 one .45 two 45. 45% .5 one .05 two 5. 5% 1.0 one .10 two 10. 10%

  26. Now that you can go from percent to decimal… Can you go from decimal to percent? Decimal to percent: Move the decimal to the right twice…this is the same as multiplying by 100! Tack on a percent sign. 7.6 one 76% 76. two 0.76 10.5 one 1.05 105% 105. two

  27. Ordering Percents Remember Descending- Greatest to Least Ascending- Least to Greatest Let’s place 46%, 12.3%, and 26% in descending order! 1. Look at the numbers and ignore the percent sign. 4 6 1 2 . 3 2 6 2. The larger the number, the larger a percent it is. 46%, 26%, 12.3% Percents can also be turned into decimals for ordering...follow the decimal rules for ordering.

  28. Your assignment… Convert the following percents to fractions. 24% b) 4% c) 19% d) 98% a) b) c) d) 2. Convert the following percents to decimals and decimals to percents. 2% b) .14 c) 32.5% d) .08 a) 0.02 b) 14% c) .325 d) 8% 3. Place the following percents in descending order. 2.4% b) 48% c) 99% d) 9.8% 99%, 48%, 9.8%, 2.4% 4. Place the following percents in ascending order. 1% b) 100% c) 10% d) 10.1% 1%, 10%, 10.1%, 100%

  29. Scientific Notation A more convenient way to express really large or small numbers. How old is the Earth? 4, 600, 000, 000 years old This number is written in decimal notation or standard form. When numbers get this large, it is easier to write them in scientific notation

  30. What does Scientific Notation look like? # 10 x # A number between 1 and 10 Times (multiplication) BASE- In scientific notation there will always be a base of 10! EXPONENT- Power of ten is always an integer.

  31. How do you put a number into Scientific Notation? Where is the decimal point now? After the last zero. Where would you put the decimal to make this number be between 1 and 10? Between the 4 and the 6. 4, 600, 000, 000 years old

  32. The Steps 4, 600, 000, 000 years old Place a decimal point after the first natural number (counting numbers). 4.6 0 0 0 0 0 0 0 0 2. Count the number of spaces you moved the decimal point! 4.6 3. Drop all zeros AFTER the LAST natural number. 4. Write your “x 10”. 4.6 x 10 5. Tack on your exponent (step 2). Remember, numbers larger than 1 will have positive exponents! 4.6 x 10 9

  33. The Steps 0. 0 0 0 0 0 0 0 2 0 4 Place a decimal point after the first natural number (counting numbers). 0 . 0 0 0 0 0 0 0 2.0 4 2. Count the number of spaces you moved the decimal point! 2.0 4 3. Drop all zeros BEFORE the FIRST natural number. 4. Write your “x 10”. 2.04 x 10 5. Tack on your exponent (step 2). Remember, numbers smaller than 1 will have negative exponents! 2.04 x 10 -8

  34. Remember!!! Numbers before “x 10” must be between 1 and 10! Numbers bigger than 1 will give you a positive exponent! Numbers smaller than 1 will give you a negative exponent!

  35. Let’s try some! 2, 000, 000, 000 0.0043 1, 203, 000, 000 0. 5 0.030201

  36. Ordering Scientific Notation Order by the exponent! The bigger the exponent, the bigger the number and vice versus! If the exponents are the same, then order by the number in front of the “x 10”!

  37. Place in ascending order!

  38. From Scientific Notation to Standard Form! Write down the number before the “x 10”. Move the decimal point the number of spaces that the exponent tells you. Remember: Positive moves Right Negative moves Left a) • Try these! c) b) d)

  39. Your Assignment Course 2 Textbook Chapter 1 1. Page 45 (10-34 EVEN) 2. Place the numbers written in scientific notation in descending order. Use the numbers from problems 10-17 on page 45.

  40. Ordering Fractions, Decimals, Percents, and Scientific Notation! Now that you know how to order these numbers separately let’s order them all together! 1. Convert all the numbers to decimal or standard form. 2. Order them the way you order decimals. 3. Place all answers back in ORIGINAL form.

  41. Let’s Try Placing the Following Numbers in Descending Order! 1. Convert all the numbers to decimal or standard form. Move the decimal point left twice or divide by 100! No need to change anything! Numerator divided by the denominator! The exponent is negative, so we moved left.

  42. Let’s Try Placing the Following Numbers in Descending Order! 2. Order them the way you order decimals. Let’s move on to the next column. Start with first column, right now all of the 3’s are equal. The two sevens are tied for largest! Looking at the next column, we can see 5 is larger than 0, making 0.375 the largest decimal. Start from the first column again to find the next largest!

  43. Let’s Try Placing the Following Numbers in Descending Order! 2 4 1 3 3. Place all answers back in ORIGINAL form.

  44. Let’s try some… Least to Greatest 0.03215 0.32 0.302 1.25 Greatest to Least 0.404 0.0411 0.04 0.4

  45. Your Assignment… Complete the Ordering Practice Sheet!

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