Study case: comparing decimals using place value In this Year 7 Decimal Place Value Problem Tutor, I use one clear study case to help students understand what decimals actually mean. The problem is: put 0.7, 0.67 and 0.706 in ascending order. The answer is 0.67, 0.7, 0.706. I like this example because many students think that the decimal with more digits must automatically be bigger, but place value shows why that is not true. Before solving, I ask the student to line up the decimal points. This is the most important habit. I write 0.700, 0.670 and 0.706 so all three numbers have the same number of decimal places. Now the comparison is much clearer. 0.670 is smaller than 0.700, and 0.700 is smaller than 0.706. Therefore the ascending order is 0.67, 0.7, 0.706. Method 1 is the place value table method. I write each number in columns for ones, tenths, hundredths and thousandths. The ones are all zero, so I compare the tenths. 0.67 has 6 tenths, while 0.7 and 0.706 have 7 tenths. That means 0.67 is the smallest. Then I compare 0.700 and 0.706. They both have 7 tenths and 0 hundredths, but 0.706 has 6 thousandths while 0.700 has none. So 0.706 is bigger than 0.700. Method 2 is the zero-fill method. I rewrite the numbers with the same number of decimal places: 0.700, 0.670 and 0.706. This does not change the values because zeros at the end of a decimal do not change the number. Then I compare them like whole numbers after the decimal point: 670, 700 and 706. This shows the order 0.670, 0.700, 0.706. Method 3 is the number line method. I ask the student to imagine the numbers between 0 and 1. 0.67 is just over two-thirds, 0.7 is seven tenths, and 0.706 is slightly more than 0.7. This visual method helps students understand that 0.706 is not less than 0.7 just because it has extra digits. It is slightly greater because it is 0.700 plus 0.006. After the three methods, I compare them. The place value table gives the clearest understanding. The zero-fill method is efficient. The number line method helps students develop number sense. I want students to know all three because decimal questions appear in rounding, money, measures, coordinates and calculator work. The most common mistakes are ignoring place value, comparing decimals as if they were words, thinking 0.67 is bigger than 0.7 because 67 is bigger than 7, and forgetting that trailing zeros do not change the value. I use these mistakes as teaching opportunities. If a student says 0.67 is bigger than 0.7, I ask them to compare 0.670 and 0.700 instead. This topic is important for KS3 because decimal understanding supports percentages, fractions, standard form, money and measurement. A student who is confident with place value is less likely to make errors when rounding, estimating or interpreting calculator answers. A useful extension is to order 0.304, 0.34, 0.3 and 0.034. Another extension is to place decimals on a number line between 0 and 1. These exercises develop accuracy and confidence. In one-to-one tutoring, I would finish by asking the student to explain why 0.7 and 0.700 are equal. If the student can explain that zeros at the end of a decimal do not change the value, they are building real understanding rather than memorising a rule. For support with this topic, students can book one-to-one tutor services: https://www.mastermathstutoring.co.uk/services. For the wider course page, visit KS3 Maths tutoring: https://www.mastermathstutoring.co.uk/ks3. To ask about lessons or availability, use contact MasterMaths Tutoring: https://www.mastermathstutoring.co.uk/contact-me.