# MathSphere MATHEMATICS. Equipment. Y6 Fractions 6365 Round decimals. Equivalence between decimals and fractions

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1 MATHEMATICS Y6 Fractions 6365 Round decimals. Equivalence between decimals and fractions Paper, pencil, ruler Fraction cards Calculator Equipment MathSphere

2 6365 Round decimals. Equivalence between fractions and decimals Page Concepts Children are expected to be able to round decimals with one or two decimal places to the nearest whole number. Children need reminding about their year 5 work on rounding decimals They need to be shown again which digit is important when rounding decimals. For instance, when rounding to the nearest tenth or to one decimal place, the hundredth digit is the important one to consider Further work of this kind is found in the rounding up and down after division. The relationship between fractions and decimal fractions is a crucial one to develop further. This should be done with fractions up to thousandths. Again, the calculator can be used, with the fraction e.g. 8/ being seen as a division sum: = A calculator can also be used to compare fractions. Games such as snap, or matching cards, are very good ways of building this relationship. A number of cards can be found at the end of this module. It is suggested that they are photocopied onto card to give them extra strength.

3 6365 Round decimals. Equivalence between fractions and decimals Page 3 Rounding to the nearest whole one - revision When rounding to the nearest whole one the important figure is the number of tenths. This is the first number after the decimal point. If the tenths are 5 or above round to the next whole number. If the tenths are below 5 round down - to the whole number as it already is is rounded down to is rounded up to 7 There is no need to look at the hundredths, when rounding to the nearest whole one. Round these amounts to the nearest whole one: Remember to look at the tenths - don't worry about the hundredths! Round these lengths to the nearest whole metre: m m 9..5 m 0..9 m m. 5.9 m m m m m

4 6365 Round decimals. Equivalence between fractions and decimals Page Rounding to the nearest whole one - revision Remember to look at the first digit after the decimal point to decide whether to round up or down. If it is 5 or more, round up! is rounded down to is rounded up to 7 There is no need to look at the hundredths when rounding to the nearest whole one. Round these amounts to the nearest whole one: Getting the idea of these, I hope! Round these lengths to the nearest whole metre: m m m m m..8 m m m m 6.. m

5 6365 Round decimals. Equivalence between fractions and decimals Page 5 Rounding to the nearest whole one - thousandths When rounding a number with thousandths into the nearest whole one, the important figure is still the number of tenths. This is the first number after the decimal point. If the tenths are 5 or above round to the next whole number. If the tenths are below 5 round down - to the whole number as it already is is rounded down to is rounded up to 8 There is no need to look at the hundredths, or thousandths, when rounding to the nearest whole one. Round these amounts to the nearest whole one: Remember after the decimal point it's tenths, then hundredths, then thousandths! Round these masses to the nearest whole kilogramme: kg kg kg kg..567 kg. 9.5 kg kg kg kg kg

6 6365 Round decimals. Equivalence between fractions and decimals Page 6 Rounding to the nearest whole one - revision Remember to look at the first digit after the decimal point to decide whether to round up or down. If it is 5 or more, round up! is rounded down to is rounded up to 9 There is no need to look at the hundredths or thousandths when rounding to the nearest whole one. Round these amounts to the nearest whole one: Getting the idea of these, I hope! Round these lengths to the nearest whole kilometre: km km km km..009 km..555 km km km km km

7 6365 Round decimals. Equivalence between fractions and decimals Page 7 Rounding to the nearest tenth When rounding to the nearest tenth it is the hundredth column which becomes important is rounded down to is rounded up to 6. What are these amounts to the nearest ten pence (rounding to tenths)? Now we look at the hundredths! Round these lengths to the nearest ten cm ( nearest tenth ): m 8..0 m m 0..5 m m..8 m m m m m

8 6365 Round decimals. Equivalence between fractions and decimals Page 8 Rounding to the nearest tenth When rounding to the nearest tenth it is the hundredth column which becomes important is rounded down to is rounded up to 7. What are these amounts to the nearest ten pence (rounding to tenths)? Each of your answers should have a nought in the pence column! Check to see that you have! Round these lengths to the nearest ten cm ( nearest tenth ): m 8..0 m m m. 9.8 m..06 m m. 8.0 m m m

9 6365 Round decimals. Equivalence between fractions and decimals Page 9 Rounding to the nearest tenth When rounding to the nearest tenth it is the hundredth column which becomes important is rounded down to..63 is rounded up to. What are these lengths to the nearest tenth, or to one decimal place km km Now we look at the hundredths! km km km km Round these lengths to the nearest tenth (or one decimal place)? m m m 0..3 m. 6.7 m..678 m m m m m

10 6365 Round decimals. Equivalence between fractions and decimals Page 0 Rounding to the nearest tenth - revision When rounding to the nearest tenth it is the hundredth column which becomes important is rounded down to is rounded up to 7.3 What are these lengths to the nearest tenth (or one decimal place)?..66 km..09 km.66 km is kilometres and 66 metres. That's a long way for someone like me!! km km km km Round these lengths to the nearest ten cm ( nearest tenth ): m m m m. 0.7 m. 6.7 m m..09 m 5.. m m

11 6365 Round decimals. Equivalence between fractions and decimals Page Fractions and decimal fractions Most calculators do not display fractions as you usually write them. Remember it is easy to change fractions into decimal fractions using a calculator. means divided by or. Do this on a calculator: enter = The answer 0.5 will come up. This means that is the same as 0.5 In the same way, using a calculator, find the decimal fraction for these fractions. Complete all parts of the table below. FRACTION DECIMAL FRACTION DECIMAL Can you see a pattern? 3 Can you see a pattern?

12 6365 Round decimals. Equivalence between fractions and decimals Page Converting fractions to decimals Complete the table below, putting in the fractions and decimal equivalence. Look for patterns all the time - some interesting numbers come up on your calculator! FRACTION DECIMAL FRACTION DECIMAL Can you see a pattern? 6 Look hard for a pattern in the sevenths! 8 What is the pattern in the sixths? 8 8

13 6365 Round decimals. Equivalence between fractions and decimals Page 3 Converting fractions to decimals Continue using your calculator to find the decimal equivalence of ninths and tenths. Fill in all the table for one ninth to nine ninths and one tenth to ten tenths. Look for patterns all the time - some interesting numbers come up on your calculator with the ninths! FRACTION DECIMAL FRACTION DECIMAL Can you explain the pattern in the ninths? 0 Can you explain the pattern in the tenths?

14 6365 Round decimals. Equivalence between fractions and decimals Page Equivalent Fractions 0 Having found all the decimals for fractions from to you 0 might have noticed that some fractions give the same decimal. For example: = 0.5 and also = 0.5 This means that and are equal. In the box below write down all the fractions, up to ten tenths, that are equal to those on the left: FRACTION EQUIVALENT FRACTIONS 3 5

15 6365 Round decimals. Equivalence between fractions and decimals Page 5 Fractions and decimal fractions. Remember it is easy to change fractions into decimal fractions using a calculator. This can also be done with fractions with thousandths. means divided by or Do this on a calculator: enter 000 = The answer 0.00 will come up. This means that is the same as 0.00 (one thousandth) In the same way, using a calculator, find the decimal fraction for these fractions. Complete all parts of the table below. FRACTION DECIMAL FRACTION DECIMAL Can you see a pattern? Can you see a pattern?

16 6365 Round decimals. Equivalence between fractions and decimals Page 6 Converting decimals to fractions 0. is one tenth and can be written as is one hundredth and can be written as is one thousandth and can be written as In the same way convert these decimals into fractions: decimal written as fraction. 0.7 is seven tenths is is is is is is is

17 6365 Round decimals. Equivalence between fractions and decimals Page 7 Converting decimals to fractions 0. is twenty one hundredths or is four hundred and fifty six thousandths or is twenty one thousandths or In the same way convert these decimals into fractions: decimal written as fraction. 0.5 is fifteen hundredths is is. 0.8 is is is is is

18 6365 Round decimals. Equivalence between fractions and decimals Page 8 Mixed numbers as decimals 55 5 can be written as 5.55 when using a calculator. Write these mixed numbers as decimal fractions: = = Not as difficult as it looks! I'll finish these in a couple of minutes! = 5. 6 = 5. 3 = 6. = 0 7. = =

19 6365 Round decimals. Equivalence between fractions and decimals Page 9 Mixed numbers as decimal fractions - extension 3 5 can be written as 5.3 when using a calculator. 00 Write these mixed numbers as decimal fractions: is sixty five hundredths is five hundredths

20 6365 Round decimals. Equivalence between fractions and decimals Page 0 Using calculator to decide size of fractions When faced with fractions with different denominators ( bottom numbers) it is often difficult to tell which is the larger fraction. If the fractions are treated as division sums, then it is easy to use a calculator to work out which is the larger. For example: which is larger; 3 or is 0.75 whilst is 0.7 so 5 is larger than 8 5 Work out which is the larger fraction in each of these pairs of fractions:. 5 9 or or or 8 9. or or or Use your calculator to place these fractions in order of size (smallest first):

21 6365 Round decimals. Equivalence between fractions and decimals Page Using calculator to decide size of fractions When faced with fractions with different denominators ( bottom numbers) it is often difficult to tell which is the larger fraction. If the fractions are treated as division sums, then it is easy to use a calculator to work out which is the larger. For example: which is larger; 9 or is 0. whilst 38 is 0.7 so 7 38 is larger than 9 Work out which is the larger fraction in each of these pairs of fractions:. 6 or or or or or or 300 Use your calculator to place these fractions in order of size, beginning with the smallest:

22 6365 Round decimals. Equivalence between fractions and decimals Page Answers Page m 8. 8m 9. m 0. 3m. 7m. 6m 3. 8m. 8m 5. 3m 6. 0m Page m 8. 3m 9. 7m 0. m. 7m. m 3. 0m. 77m 5. 6m 6. m Page kg 8. 6 kg 9. kg 0. 3 kg. 5 kg. 0 kg 3. 7 kg. 7 kg 5. 9 kg 6. 9 kg Page km 8. km 9. 7 km 0. 6 km. km. 3 km 3. 6 km. 7 km 5. 6 km 6. 7 km Page m 8..0m m 0..5m. 8.0m..8m m. 87.0m m 6. 3.m Page m 8..0m 9. 9.m m. 9.m..m m. 8.0m m m Page km. 3.3 km km. 8.5 km km km m m m 0.. m. 6. m..7 m 3..5 m. 7.3 m m m Page 0..6 km..0 km km. 8.9 km km km m m m m. 0. m. 6.7 m m.. m 5.. m m Page (recurring numbers after the decimal will depend on calculator) / = 0.5 / = /3 = /3 = /3 = / = 0.5 / = 0.5 3/ = 0.75 / = Discuss patterns of numbers

23 6365 Round decimals. Equivalence between fractions and decimals Page 3 Page /5 = 0. /5 = 0. 3/5 = 0.6 /5 = 0.8 5/5 = /6 = /6 = /6 = 0.5 /6 = /6 = /6 = /7 = /7 = /7 = /7 = /7 = /7 = /7 = /8 = 0.5 /8 = 0.5 3/8 = /8 = 0.5 5/8 = /8 = /8 = /8 = Discuss patterns in decimals Page 3 /9 = 0. /9 = 0. 3/9 = /9 = 0. 5/9 = /9 = /9 = /9 = /9 = /0 = 0. /0 = 0. 3/0 = 0.3 /0 = 0. 5/0 = 0.5 6/0 = 0.6 7/0 = 0.7 8/0 = 0.8 9/0 = 0.9 0/0 = Discuss patterns in decimals Page / = / = 3/6 = /8 = 5/0 / = 3/3 = / = 5/5 = 6/6 = 7/7 = 8/8 = 9/9 = 0/0 = /3 = /6 = 3/9 / = /8 /5 = /0 Page 5 (recurring numbers after the decimal will depend on calculator) / = 0.00 / = / = / = / = discuss pattern shown / = 0.0 3/ = 0.03 / = 0.0 5/ = 0.05 discuss Page is seven tenths 7/ is five tenths 5/ is three hundredths 3/ is four thousandths / is nine hundredths 9/ is three hundredths 3/ is nine thousandths 9/ is four hundredths /00 Page is fifteen hundredths 5/ is thirty five hundredths 35/ is eight hundredths 8/ is twenty eight hundredths 8/ is one hundred and twenty three thousandths 3/ is two hundred and thirty five thousandths 35/ is one hundred and five thousandths 05/ is four hundred and forty four thousandths / Page Page

24 6365 Round decimals. Equivalence between fractions and decimals Page Page 0. 67/ / /60. 7/ / / /8 /50 /9 3/90 67/ /7 9/0 3/300 79/350 8/0 Page. 6/. 353/ 3. 5/9. / /5 6. 9/ /69 0/7 3/90 5/9 /7 8. /3 33/ 3/ /58 5/7

25 606 Round decimals. Equivalence between fractions and decimals Page

26 606 Round decimals. Equivalence between fractions and decimals Page 6 /00 /00 3/00 /00 5/00 6/00 7/00 8/00 9/00 0/00 /00 /00

27 606 Round decimals. Equivalence between fractions and decimals Page 7 3/00 /00 5/00 6/00 7/00 8/00 9/00 0/00 /00 /00 3/00 /00

28 606 Round decimals. Equivalence between fractions and decimals Page

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