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This page sets out the method for place value in the order you would use it, then walks through the full lesson explanation. For three complete worked examples with the slips that cost marks, see the Place value topic page.
When you see 'write down the value of the digit …', find which column the digit sits in.
When you see a list of decimals to put in order, make them all the same length first.
Start at the ones. Move left for tens, hundreds, then thousands.
The same digit 4 means 4, 40, 400, or 4 000 depending on the column.
The face of a digit is the symbol you see. The value is the face times the column.
In 174 the face of the 7 is 7, but its value is 70.
In 406 the 0 means there are no tens. It is not “no digit”.
Without the 0, 406 would be read as 46.
4 208 = 4 000 + 200 + 8. There are no tens, so that part is 0.
You can rebuild the number by adding those parts back together.
Compare thousands first, then hundreds, then tens, then ones.
3 420 is larger than 3 390 because 4 hundreds beats 3 hundreds.
Digits shift one column left when you multiply by 10. 37 × 10 = 370.
Dividing by 10 shifts one column right. 370 ÷ 10 = 37.
Find the decimal point first. If there is no decimal point, it sits just after the units digit. From there, columns to the left are units, tens, hundreds, thousands, ten thousands, hundred thousands. Columns to the right are tenths, hundredths, thousandths. Write the column name, then write the digit with the zeros that column needs.
Worked habit: in 46082, cover the 6 and count how many digits sit to its right before the decimal point. There are three (0, 8 and 2), so the 6 is thousands and its value is 6 × 1000 = 6000. In 3.047 the 4 is the second digit after the point, so it is hundredths: 4 × 0.01 = 0.04.
Give the value as a number unless the question asks for the column name. 'Hundreds' on its own is not the value of the 7 in 4726. The value is 700. If the question says 'write down the value of the digit', the mark is for 700, not for the word hundreds.
Method: 1. Find the decimal point, or put it just after the units digit. 2. Name the column the digit sits in. 3. Attach the zeros that show what that column is worth.
Sometimes the question gives the parts already split: 50000 + 800 + 7. Add them by columns. Fifty thousand has a 5 in the ten-thousands column. 800 puts an 8 in the hundreds column. 7 is units. Every empty column is a zero, so the number is 50807. It is not 587 and it is not 500008007.
Check by reading it back. 50807 is 50000 + 0 × 1000 + 8 × 100 + 0 × 10 + 7. If a part such as 40 is missing from your reading, you dropped a column. A useful check is that the biggest part decides the size: an answer near 50000 can be right; an answer near 800 cannot.
Large whole numbers are often written with a small space or a comma between groups of three digits: 50 800 and 50,800 both mean fifty thousand eight hundred. A decimal point is different: 50.8 means fifty point eight.
Method: 1. Put each part into its column, starting with the largest. 2. Write a zero in every column that has no part. 3. Read the number back and check the largest part is still there.
Line the decimal points up, or pad with zeros so every number has the same number of decimal places. Then compare from the left, one column at a time. Whole numbers first, then tenths, then hundredths, then thousandths. Stop at the first column that differs.
Take 0.62, 0.6, 0.602 and 0.7. Pad to three places: 0.620, 0.600, 0.602, 0.700. Tenths are 6, 6, 6 and 7, so 0.7 is the largest. Among the three that start 0.6, hundredths are 2, 0 and 0. So 0.620 is the largest of the three. Between 0.600 and 0.602, thousandths are 0 and 2, so 0.600 is smaller. The order from smallest is 0.6, 0.602, 0.62, 0.7.
Write the originals back, not the padded forms, unless the question used the padded forms. Read the instruction: 'smallest first' and 'largest first' are different questions. A correct list written backwards scores nothing for the order.
Method: 1. Pad the decimals with zeros so they have the same number of places. 2. Compare from the left until one digit is bigger. 3. Write the original numbers in the order you found.
When you may use each card once, sort with a rule for the end digit first if there is one. An even number must end in 0, 2, 4, 6 or 8. An odd number must end in 1, 3, 5, 7 or 9. A number greater than 5000 must start with 5 or more. Lock that constrained digit, then sort the rest.
For the largest number, put the biggest remaining digits on the left. For the smallest, put the smallest remaining digits on the left. Never start with zero: 0385 is just 385, a three-digit number. If zero is a card and you want the smallest four-digit number, put zero in the second place, not the first.
After you build two numbers, a difference question is ordinary subtraction. Keep the larger number on top. The place-value work is choosing the digits; the last line is just column subtraction.
Method: 1. Lock the digit that the rule needs, such as the even units digit. 2. Then place the remaining digits to make the number as large or as small as asked. 3. Do not start a number with zero.
Place value explains what happens when you multiply or divide by 10, 100 or 1000. The decimal point stays where it is and every digit moves. Multiplying by 10 moves each digit one column to the left, so it becomes worth ten times as much. Dividing moves digits to the right. A real exam question might ask for the value of a digit in the answer to 36 000 ÷ 100.
Work out the answer first: 36 000 ÷ 100 = 360. Then read the column of the digit you are asked about. In 360 the 6 is in the tens column, so its value is 60, not 6. Always write the value in full, with its zeros. When digits move into a column that had nothing in it, a zero is put in as a placeholder, and that zero keeps every other digit in its correct column.
Method: 1. Do the multiplication or division, moving every digit the right number of places. 2. Fill any gaps with zeros as placeholders. 3. Find the column of the digit named in the question. 4. Write the value of that digit in full, for example 60 and not 6.
Tip: Dividing by 100 is the same as moving every digit two columns to the right.
Questions ask you to turn words into figures and figures into words. Break big numbers at the thousands: "four hundred and six thousand and fifty-two" is 406 thousand and 52, so it is 406 052. Between the groups, put a zero in any column that is not mentioned. Here there are no hundreds and no tens besides the fifty, so the group after the thousand is 052.
Going the other way, split a number such as 23 508 into groups of three digits from the right. Say the left group followed by "thousand", then the right group: "twenty-three thousand, five hundred and eight". A common slip is to write 400 000 + 3000 + 70 as 4 373, joining the numbers instead of placing each in its own column. Draw a column grid if you need one: hundred thousands, ten thousands, thousands, hundreds, tens, units.
Method: 1. Split the number at the thousand. Work out each group separately. 2. Write the left group, then the right group as three digits, using zeros for empty columns. 3. Check that the number of digits makes sense for the size in words. 4. Read your answer back in words to make sure it matches the question.
After the decimal point the columns are tenths, hundredths, thousandths. In 12.083 the 0 is in the tenths column, the 8 is in the hundredths column and the 3 is in the thousandths column. So the value of the 8 is 0.08, which is 8/100. Students often say it is 0.8, which would put the digit in the tenths column.
Adding a small step uses the same idea. The number that is 0.01 more than 12.083 increases the hundredths column by one, so it is 12.093. To compare decimals, line up the points and fill with zeros: 12.4, 12.04 and 12.41 become 12.400, 12.040 and 12.410. The smallest is 12.040. Never judge by the number of digits.
Method: 1. Write the decimal with a column heading: tenths, hundredths, thousandths. 2. Find the digit and read the name of its column to get the value. 3. For comparisons, write every number to the same number of decimal places. 4. Compare from the left, column by column.
Tip: The value of a digit in the hundredths column is that digit divided by 100.
Digit-card questions say "Use each card once". For the largest number, put the biggest digit in the highest column. For the smallest number, put the smallest digit first, but a number cannot begin with a zero, so use the smallest non-zero digit first and then zero. With the cards 2, 5, 0 and 9, the largest number is 9520 and the smallest four-digit number is 2059.
A "closest to" puzzle needs more thought. To get close to 5000 with the same cards, start with the 5 so the number begins with 5, then keep the next digits small: 5029 is only 29 away. Compare it with 5092, which is 92 away. For clue puzzles, write the digits in a row of boxes and fill them in as each clue is read. Check that every clue is true once the number is complete.
Method: 1. Decide what the target is: largest, smallest, even, or closest to a value. 2. Place the digits column by column, starting from the highest column. 3. Check any extra condition, such as even or no leading zero. 4. Try one other arrangement to show your answer is best.
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