CCEA GCSE Mathematics

## Place value and decimals Each digit in a number has a value set by its position. In $4\,036.275$ the 4 is worth 4 thousands, the 0 is a placeholder with no hundreds, the 3 is 3 tens, and after the decimal point the 2 is 2 tenths, the 7 is 7 hundredths and the 5 is 5 thousandths. Moving a digit one place to the left makes it ten times bigger, and one place to the right makes it ten times smaller, which is why multiplying by 10, 100 or 1000 moves every digit that many places left. To compare decimals, line up the decimal points and compare digit by digit from the left, adding zeros if that helps. Comparing $0.35$, $0.305$ and $0.4$ as $0.350$, $0.305$ and $0.400$ gives the order $0.305 < 0.350 < 0.400$. The length of a decimal says nothing about its size. Decimal notation for money keeps two decimal places: £3.50, not £3.5, and £0.80 or 80p, never £0.80p. ### Adding and subtracting decimals Write the numbers underneath each other with the decimal points in a line, fill any gaps with zeros, and add or subtract as with whole numbers, putting the point straight down in the answer. $$ \begin{aligned} 12.4 + 0.375 &= 12.400 + 0.375 = 12.775 \\ 9 - 2.64 &= 9.00 - 2.64 = 6.36 \end{aligned} $$ ### Multiplying and dividing decimals To multiply, ignore the points, multiply the whole numbers, then put the point back so that the answer has as many decimal places in total as the two numbers being multiplied. For $0.6 \times 0.07$, work out $6 \times 7 = 42$; there are one and two…