Year 7 Fractions, Decimal, Percentages Dr J Frost

Year 7 Fractions, Decimal, Percentages Dr J Frost ([email protected]) www.drfrostmaths.com Objectives: Convert between fractions, decimals and percentages, including fractions to recurring decimals. Be able to order fractions. Last modified: 2nd February 2016

RECAP :: Basic Decimal-Fraction conversions Fraction Decimal Percentage ? Fill in the table with the missing decimals/fractions/%s, and place the fractions all on a single number line as pictured. ? ? (Copying note: don’t waste time drawing lots of lines for your table!) ? ? ? ? ? ? ? ? ? ? ? ? 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1 8 1 72 1 4 205 2 73 7 104 8

Ordering Bro Tip: Picture a number line in your head. [JMC 2002 Q15] In which of the following lists are the terms not increasing? A B C D E A B C D E [JMC 1998 Q11] Which is the smallest of these fractions? A B C D E A B C D E [JMC 2005 Q14] If the following fractions are arranged in increasing order of size, which one is in the middle? A B C D E A B C D E

Decimals Fractions Is there a method for converting any arbitrary decimal to a fraction? 45 9 0.45 ? ? 100 20 We used hundred because the last digit was the hundredths digit. 12 6 63 0.126 ? ? 1000 500 255 51 0.255 ? ? 1000 200 85 17 0.85 ? ? 100 20 612 153 0.612 ? ? 1000 250 16 4 5 1 0.16 ? ? ? ? 100 25 0.0005 10000 2000

Check Your Understanding 𝟑 0.03 𝟏𝟎𝟎 ? ? ? ? N If that’s too easy: ?

Fractions Decimals just means . So we could use long division to convert it to a decimal. 8 0 . 3 7 5 3 . 30 60 40 Uh oh. We’ve run out of digits and hence have nowhere to put the remainder. What can we do to the 3 without changing its value?

Fractions Decimals 4 ¿ 0. 3̇ 6̇ 11 11 0 . 3 6 3 6 4 . 40 70 40 70

Use of recurring dot What do the following represent? 0. 2̇ 0.22222222 ? ? ? ?

Check Your Understanding 7 0.4? 6̇ 15 5 ? 0. 5̇ 9 6 ? 0. 8̇ 5714 2̇ 7

Exercise 1 1 a b c d What are the following decimals as fractions in their simplest form? ? e ? ? f ? ? g ? ? h numbers in ? Put the following 4 [JMC 2009 Q9] How many different digits appear when is written as a recurring decimal? A 2 B 3 C 4 D 5 E 6 Solution: A ? 5 [JMO 2001 A5] Find the 100th digit after the decimal point in the decimal representation of . Solution: 5 ? 6 a [IMC 2008 Q18] When the following values are put in ascending order, which is in the middle? A B C D E Solution: C 7 3 [Kangaroo Pink 2009 Q15] Which of these decimals is less than but greater than ? A 1.01 B 1.001 C 1.0001 D 1.00001 E 1.000001 ascending order: 2 c to (potentially d b Convert the fractions recurring) decimals. a b c ? ? ? d e f ? ? ? Solution: C. . Since 2008 2000, this is slightly less than 1.0005. Similarly . 1. ? ?