11 plus Decimals questions
Most marks lost on decimals come from one habit: reading the longer decimal as the bigger number. The rest come from a decimal point that was not lined up. Neither takes long to fix once a child can see it happening.
What a Decimals question looks like
A decimals question in the 11 plus hands your child a number with a decimal point in it and asks what the digits are worth. The number stays in decimal form from the first line to the answer: which of five decimals is largest, what the 4 in 3.47 stands for, where the point ends up after multiplying or dividing by 10 or 100, how much juice is left in a 2.5 litre jug after 0.75 litres is poured out. That is what marks this skill out from its neighbours in the same corner of maths, which turn a number into another form or take a share of an amount: nothing here asks for a percentage, and only one question asks for a fraction.
The range runs from one quick step to two linked ones. At the easy end sit place value, times and divide by 10 and 100, and rounding to one decimal place. In the middle come ordering four or five decimals, finding the number halfway between two others, and working backwards from a result to the number behind it. The harder end is nearly all word problems in money, metres, litres and kilograms, where two calculations have to be done in the right order. A few questions put the decimals into a table of parcel masses, onto a number line, or into a bar chart or a line graph, and ask the same comparing or subtracting question about those values.
Every question has five options, and each wrong one is built on a slip a child really makes.
Example one: order these decimals from smallest to largest, 0.099, 0.9, 0.19, 0.109
The numbers have different numbers of digits after the point, which is the whole difficulty. Give them all the same number of digits by writing zeros on the end, which changes nothing about a decimal’s size: 0.099, 0.109, 0.190, 0.900. Now they can be read almost like whole numbers, from the left. The answer is 0.099, 0.109, 0.19, 0.9.
One option puts 0.9 third and 0.19 last. It tempts because 0.19 has more digits, and for whole numbers more digits does mean a bigger number. After a decimal point it does not: 0.9 is nine tenths, and 0.19 is not even two tenths.
Example two: a number multiplied by 100 gives 46.5. What is the number divided by 10?
Two steps here, and the first runs backwards. Something times 100 came to 46.5, so to get back to it, divide by 100: every digit moves two places right, giving 0.465. That is the number, but not yet the answer. Divide it by 10, one more place right, and the answer is 0.0465.
The wrong option that catches most children is 0.465. It is the number itself, worked out correctly, with the second half of the question forgotten once a sensible value appeared. Another option is 4.65, which is 46.5 divided by 10, from doing the operation the question mentions last and never undoing the times 100.
Example three: Lena buys 3 pens at £1.35 each and a notebook for £2.80. She pays with a £10 note. How much change does she receive?
One step at a time, writing each answer down. Three pens: three lots of £1 is £3, three lots of 35p is £1.05, so the pens cost £4.05. Add the notebook: £4.05 plus £2.80 is £6.85. Now take that away from ten, lining the points up: £10.00 minus £6.85 leaves £3.15. The answer is £3.15.
The option to watch is £5.95, which is £10 take away £4.05. It answers a question that stopped after the pens, and it looks entirely reasonable. A second wrong option, £4.15, comes from working the pounds and the pence apart and mislaying the pound the pence carried into, making three pens cost £3.05.
How to answer it
- Read to the end and note how many steps are wanted. Money and measures questions nearly always need a second calculation after the first.
- Before adding or taking away, write the shorter number with a zero on the end so both have the same number of digits after the point, then line the points up. Write 1.2 as 1.20, and 2.5 as 2.50.
- Before comparing or ordering, do the same to every number in the list, then compare from the left: whole numbers, then tenths, then hundredths, stopping at the first column where they differ.
- To multiply or divide by 10 or 100, count the zeros. One zero moves every digit one place, two zeros move every digit two places. Multiplying makes the number bigger, dividing makes it smaller.
- Check the size of the answer against the question. Change from a £10 note cannot be more than £10, and a number divided by 100 has to end up smaller than it started.
Common mistakes
- Reading the longer decimal as the bigger one. 0.404 chosen over 0.44, or a 2.405 kg parcel over a 2.45 kg one. Counting digits is a habit from whole numbers that stops working after the point.
- Not lining the points up. 0.02 plus 7.8 answered as 7.802, the digits pushed together rather than added, or 3.45 minus 1.2 answered as 2.33.
- Moving one digit instead of all of them. 3.6 times 10 given as 3.06, or 45 divided by 10 given as 4.05. A zero gets dropped into the tenths column instead of the whole number shifting across.
- Repeating the operation instead of undoing it. Given that a number divided by 10 comes to 0.56, dividing again gives 0.056. Working backwards means doing the opposite: multiply by 10 and the number is 5.6.
- Stopping after the first step, or rounding before the end. Four lots of 0.75 kg is 3 kg, but the question asked how much more flour is needed on top of the 2.8 kg already there, which is 0.2 kg. Rounding 0.75 up to 0.8 first turns that into 0.4 kg.
How to practise 11 plus Decimals questions
Two things carry most of the marks, and neither needs a worksheet. The first is saying decimals out loud in tenths and hundredths, so 0.19 is heard as nineteen hundredths rather than seen as a long number. The second is writing the zero in before adding, taking away or comparing, until it happens without being asked. Reading prices, packet weights and road signs does more for both than an hour of drill.
After that, what builds accuracy is meeting the shapes mixed up rather than blocked together, because in the eleven plus a comparing question and a two-step money question sit side by side. 11+ Daily has a Decimals project that mixes them in that order, and it sits with the rest of 11 plus maths practice so it comes round again rather than being covered once. Every question is original to 11+ Daily, nothing is a past paper, nothing is licensed, and the bank is re-checked in rounds. We have also written about how much 11 plus practice a child needs each day.
Questions parents ask
What is a decimals question in the 11 plus?
Why does my child think 0.19 is bigger than 0.9?
What happens to a decimal when you multiply or divide by 10 or 100?
How do you add or subtract decimals that have different numbers of digits?
Practise Decimals in 11+ Daily
Decimals is one of the 78 skill projects in 11+ Daily. The Today screen brings it round when it is the right thing to revise, and a wrong answer comes back in a later session until it is right. 14-day free trial, no card needed.