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Decimals, their place values and how to write it
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- 2. How do Iknow what kind of decimal it is? ď‚— The name of a decimal is determined by the number of places to the right of the decimal point Number of Places Decimal Name Example 1 tenths 0.7 2 hundredths 0.05 3 thousandths 0.016
- 3. What are mixeddecimals?  Mixed decimals are numbers with both whole numbers and decimals  The name of a whole number is determined by the number of places to the left of the decimal point  In the number 128.765, 1 is in the hundreds place, 2 is in the tens place, 8 is in the ones place, 7 is in the tenths place, 6 is in the hundredths place, and 5 is in the thousandths place
- 4. How do youread decimals?  To read a decimal correctly, first find the decimal point  Whole numbers are to the left of the decimal point; any numbers to the right of a decimal point form a decimal fraction  Say “and” for the decimal point  The decimal 2164.511 is read as “two thousand, one hundred sixty-four and five hundred eleven thousandths”
- 5. Zeros after thedecimal point  Writing extra zeros after the decimal point does not change the value!  The decimals 0.2, 0.20, and 0.200 are equivalent decimals
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- 7. Exercise 1 Write thedecimals. 1.Five thousandths 2.Ninety-four thousandths 3.Three hundred thirty-six and sixty-nine hundredths
- 8. Exercise 2 Write eachdecimal in words. 1.7884.011 2.5592.4 3.4.203 4.612.250 5.10.44
- 9. Exercise 3 In whatplace (on the place value chart) is the underlined digit? Write the answer. 1.1.475 2.3.763 3.7780.215 4.412.407 5.902.103
- 10. Exercise 4 Write adecimal that has the same number. 1.0.2 2.5.51 3.410.6 4.753.809
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- 12. How to ConvertDecimals to Fractions Use the place value of the last digit in the number to determine what the denominator of the fraction will be.
- 13. How to ConvertDecimals to Fractions .24
- 14. How to ConvertDecimals to Fractions .5 The 5 is in the tenths place 10 5
- 15. How to ConvertDecimals to Fractions .84 The 4 is in the hundredths place 100 84
- 16. What if thereis a whole number before the decimal point? 1.589The 9 is in the thousandths place 1000 589 1
- 17. 25.5 The 5 isin the tenths place 10 5 25 What if there is a whole number before the decimal point?
- 18. How to ConvertFractions to Decimals 100 23 This is the hundredths place so the 3 needs to be in the hundredths place. 2 3 .23
- 19. How to ConvertFractions to Decimals 1000 567 This is the thousandths place so the 7 needs to be in the thousandths place. 5 6 .567 7
- 20. How to ConvertFractions to Decimals 1000 4 This is the thousandths place so the 4 needs to be in the thousandths place. 0 0 .004 4
- 21. How to ConvertFractions to Decimals 10 2 This is the tenths place so the 2 needs to be in the tenths place. 2 .2
- 22. What if thereis a whole number before the fraction? 1000 567 This is the thousandths place so the 7 needs to be in the thousandths place. 5 6 3.567 7 3 3
- 23. How to ConvertFractions to Decimals 1000 34 24.034 24 This is the thousandths place so the 4 needs to be in the thousandths place.
- 24. Suppose You Can’tUse A Denominator of 10? 6 5 Divide the Numerator by the Denominator
- 25. Suppose You Can’tUse A Denominator of 10? 6 5 6 5.0 .8 4 8 2 0 0 3 18 2 .83
- 26. Suppose You Can’tUse A Denominator of 10? 3 2 3 2.0 .6 1 8 2 .6
- 28. Try Some .. . 8 7 50 5 10 6 4 3 16 12 40 3
- 29. Try Some .. . .35 .25 .95 .6 .875 .125
- 30. Comparing Decimals How dowe compare decimals? When we compare we use terms such as:  Less than <  Greater than >  Equal to = Comparing decimals is similar to comparing whole numbers.  45<47  150>105 When we compare decimals we use place value or a number line.
- 31. Example: Compare Sara’s scorewith Danny’s score. 1.Line Up Decimal Points  Sara: 42.1  Danny: 42.5 2.Start at the left and find the first place where the digits differ. Compare the digits  1<5  42.1<42.5 This means Sara’s score was lower than Danny’s score. Sara Sara 42.1 42.1 Danny Danny 42.5 42.5 Ross Ross 42.0 42.0 Bethan Bethan y y 40.7 40.7 Jacob Jacob 46.1 46.1 Half pipe Results
- 32. Let’s Try UsingA Number Line Sara Sara 42.1 42.1 Danny Danny 42.5 42.5 Ross Ross 42.0 42.0 Bethany Bethany 40.7 40.7 Jacob Jacob 46.1 46.1 42.0 42.1 42.5 Numbers to the right are greater than numbers to the left. Since 42.5 is to the right of 42.1 we have: 42.5>42.1
- 33. Equivalent Decimals ď‚— Decimalsthat name the same number are called equivalent decimals. 0.60 and 0.6 ď‚— Are these the same???
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- 35. Adding Zeros ď‚— Thismeans placing a zero to the right of the last digit in a decimal. ď‚— 0.6 0.60 ď‚— Although we added a zero, the value of the decimal did not change!! ď‚— Adding zeros is useful when ordering a group of decimals.
- 36. Ordering Decimals  Wecan order decimals from least to greatest or we can order from greatest to least. Let’s try this example:  Order 15, 14.95, 15.8, and 15.01 from least to greatest
- 37. ď‚—First, line upthe decimal points 15 14.95 15.8 15.01 15, 14.95, 15.8, 15.01
- 38. 15, 14.95, 15.8,15.01 ď‚—Next, add zeros so that each number has the same number of decimal places 15.00 14.95 15.80 15.01
- 39. ď‚— Finally, useplace value to compare the decimals. Always start from the left. 15.00 14.95 15.80 15.01 ď‚—14.95, 15, 15.01, 15.8 15, 14.95, 15.8, 15.01
- 40. ď‚—Order these numbersfrom greatest to least 35.06, 35.7, 35.5, 35.84
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- 49. Dividing Decimals withWhole Number Dividing decimals by whole numbers is similar to normal division. Here, the dividend is a decimal number and the divisor is a whole number, so the decimal point in the quotient will be placed according to the decimal point of the dividend. We can understand this with the help of the long division of decimals. Example: Divide 338.56 Ă· 23
- 50. Dividing Decimals withWhole Number Step 1: First, write the division in the standard form. Start by dividing the whole number part by the divisor. Step 2: Place the decimal point in the quotient above the decimal point of the dividend. Bring down the tenth digit. Step 3: Divide and bring down the other digit in sequence. Divide until 0 is obtained in the remainder. Thus, the decimal in the quotient is placed according to the decimal in the dividend.
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- 52. Dividing Decimals withDecimals For dividing decimals by another decimal, we need to convert the divisor into a whole number and then continue the division. Let us understand the conditions and rules for this method using an example. Example: Divide 48.65 Ă· 3.5
- 53. Step 1: Thedividend is 48.65 and the divisor is 3.5. We need to change the divisor to a whole number and so we will multiply it by 10 so that the decimal point shifts to the right and it becomes a whole number. This means, 3.5 Ă— 10 = 35. Step 2: We need to treat the dividend in the same way as we had treated the divisor. So, we will multiply the dividend by 10 as well. This means it will be 48.65 Ă— 10 = 486.5. In other words, we need to move both the decimal points to the right until the divisor becomes a whole number. Step 3: Now, we have 486.5 as the dividend and 35 as the divisor. This can be divided as we do the usual division and we get 13.9 as the quotient.
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- 55. Important Tips onDividing Decimals • Convert the divisor to a whole number by multiplying by the powers of 10. Multiply the dividend by the same powers of 10. • In order to divide a decimal number by 10, move the decimal point to the left by one place. For example, if we need to divide 45.67 ÷ 10, then it can be easily done by shifting the decimal point to the left and the answer will be 4.567
- 56. Important Tips onDividing Decimals • In order to divide a decimal number by 100, move the decimal point to the left by two places. For example, if we need to divide 324.6 ÷ 100, then it can be easily done by shifting the decimal point to the left and the answer will be 3.246 • In order to divide a decimal number by 1000, move the decimal point to the left by three places. For example, if we need to divide 8934.5 ÷ 1000, then it can be easily done by shifting the decimal point to the left and the answer will be 8.9345