AQA GCSE Mathematics

## Place value and ordering Each digit in a number is worth ten times the digit to its right, so in $4\,706.35$ the 7 stands for 700 and the 5 for five hundredths. Place value is what lets you compare decimals and multiply or divide by powers of ten: multiplying by 10 moves every digit one place to the left, and dividing by 100 moves it two places to the right. To order decimals, write them with the same number of decimal places and compare digit by digit from the left. To order fractions, either convert each to a decimal or rewrite them over a common denominator. Negative numbers order from the number line: the further left, the smaller, so $-8 < -3 < 0$. ### Worked example Put $0.45,\ 0.405,\ \tfrac{4}{9},\ 0.5$ in ascending order. $$ \begin{aligned} \tfrac{4}{9} &= 0.444\ldots \\ 0.405 &< 0.444\ldots < 0.45 < 0.5 \end{aligned} $$ So the order is $0.405,\ \tfrac{4}{9},\ 0.45,\ 0.5$. ### Inequality symbols | Symbol | Meaning | |---|---| | $=$ | is equal to | | $\neq$ | is not equal to | | $<$ | is less than | | $>$ | is greater than | | $\le$ | is less than or equal to | | $\ge$ | is greater than or equal to | The open end of the symbol faces the larger number. The statement $-2 \le x < 5$ means $x$ can equal $-2$ but cannot equal 5. ## The four operations with integers and decimals ### Adding and subtracting negatives Subtracting a negative number is the same as adding the positive: $-7 - (-3) = -7 + 3 = -4$. Two like signs in a product or quotient give a positive result…