Maths: Place Value and Ordering

In this kind of question, you're given a number in words, like two thousand and eighty. Your job is to find how it's written in figures, from five answers. Only one is right.

Other questions ask what a figure is worth, or which order numbers go in. It all comes down to one idea: the column a figure sits in gives it its value.

In GL's papers these questions usually come early on. The video above and the worked example below work through the same question, with the options in the same order. Then both work a second question, on ordering decimals, with the same four steps.

The method

Four steps: put it in the grid, read the column, compare from the left, check the zeros.

Worked example

What is “two thousand and eighty” written in figures?

A. 280 B. 2,080 C. 2,800 D. 20,080 E. 200,080

1. Put it in the grid. Picture the columns: thousands, hundreds, tens and ones. Then put each part of the number in its column. Two thousand is a 2 in the thousands. Eighty is eight tens, so an 8 goes in the tens. The hundreds and the ones are empty, and every gap is a zero.
2. Read the column. Read the grid from the left: 2 thousands, no hundreds, 8 tens, no ones. Together, that's two thousand and eighty, and in figures it's 2,080.
3. Compare from the left. Picture each answer in the grid, and start with its biggest column. Ours is the thousands. E is two thousand and eighty written side by side, so it reaches the hundred thousands. That's far too big, so E is out. D has an extra zero, so it starts in the ten thousands. D is out. A starts in the hundreds. Its thousands column is empty, so A is too small. A is out.
4. Check the zeros. C starts in the thousands too, so look closer, column by column. C puts the 8 in the hundreds, and the zero in the tens. That's two thousand eight hundred, so C is out. B has the 2 in the thousands, the 8 in the tens, and a zero in each gap. So the answer is B.

Answer: B — 2,080 (2 thousands · 0 hundreds · 8 tens · 0 ones)

A second worked example

The same four steps work for decimals.

Which list shows these numbers in order, from smallest to largest?

0.49, 0.05, 0.325, 0.4

A. 0.325, 0.4, 0.49, 0.05

B. 0.4, 0.05, 0.49, 0.325

C. 0.49, 0.4, 0.325, 0.05

D. 0.05, 0.325, 0.4, 0.49

E. 0.325, 0.05, 0.49, 0.4

1. Put it in the grid. Line up the points, so every tenth sits under a tenth. Every gap is a zero, so now each number has three places after the point.
2. Read the column. The first column after the point is tenths: 4, none, 3 and 4 tenths. B puts them in order as if the figures after the point were whole numbers: 4, 5, 49 and 325. Columns don't work like that, so B is out.
3. Compare from the left. The first difference decides. The ones are all 0, so look at the tenths. 0.05 has no tenths, so it's the smallest. Next comes 0.325. 0.4 and 0.49 tie on tenths, so look at the hundredths: none against 9. So 0.4 comes before 0.49. C has the right order backwards, largest first, so C is out.
4. Check the zeros. Length doesn't decide. A puts 0.05 last, missing the zero straight after the point, so A is out. E puts the longest number first, as if more figures made a number smaller. With every gap filled, they're all the same length, so E is out. So D is the right order.

Answer: D — 0.05, 0.325, 0.4, 0.49

Things to watch out for

1. Every gap is a zero. Even two side by side: two empty columns need two zeros. Eight thousand and nine has an 8 in the thousands and a 9 in the ones. The hundreds and the tens are both empty, so it's 8,009. 809 has lost a zero, and 8,090 has put the 9 in the tens.
2. Tens or tenths? The “-ths” columns come after the point. A ribbon is 1.38 m long. What is the 8 worth? It's in the second column after the point, the hundredths, so it's worth 0.08. 800 is the hundreds column, on the other side of the ones, so check which side of the point you're on.
3. On a scale, find the step first. Share the gap between the labels. A number line is labelled only at its ends, 300 and 400, and goes from one to the other in 5 equal steps. The question asks for the number at point A, the second mark after 300. 100 shared into 5 is 20, so the marks go 300, 320, 340: that's point A. Counting each mark as 1 gives 302.
4. Multiply, and every figure slides. × 10, × 100 and × 1,000 slide every figure one, two and three columns to the left, and the point stays where it is. What is 6.58 × 100? 100 has two zeros, so every figure slides two columns to the left. 6.58 becomes 658. 600.58 only moved the 6.

Related

• The complete 11+ question-type guide
• Maths: Written Calculation — estimate first, then cross off by size
• Maths: Number Properties — turn each clue into a test
• Maths: Fractions — find the whole, cut it into equal parts

All example questions come from the Brainblox question bank — practise this question type inside 25+ learning games, timed mock exams and focused practice. Brainblox is an independent app: not affiliated with, endorsed by or licensed by any exam board, school or assessment publisher, and it contains no past papers.