Ten of each, again and again
Ten of the thousand cubes make ten thousand, written 10,000. Ten of those make a hundred thousand, 100,000. Ten hundred thousands make a million, 1,000,000, and ten millions make ten million, 10,000,000.
It is the same step every time: each place is worth ten of the place on its right. From the right, the places are ones, tens, hundreds, thousands, ten thousands, hundred thousands, millions and ten millions.
Ten of the thousand cubes, each one worth 1000: 10 × 1000 = 10,000.
Group the digits in threes
A long row of digits is hard to read, so the digits are put in groups of three, counting from the right, with a comma between the groups. The number 342516 is written 342,516.
The group before the comma counts thousands, and the group after it counts ones. So 342,516 is 342 thousands and 516 more.
Read the groups one at a time
To say the number, read the front group as an ordinary number, say "thousand" at the comma, then read the back group. 342,516 is three hundred forty-two thousand, five hundred sixteen.
A zero keeps a place that is empty. Two hundred five thousand, sixty is written 205,060: the front group 205 has no tens, and the back group 060 has no hundreds. Leave out a zero and the other digits slide into the wrong places.
A second comma for millions
A number with seven or eight digits has two commas. The group before the first comma counts millions, the middle group counts thousands, and the last group counts ones. 4,250,000 is read four million, two hundred fifty thousand. The last group is 000, so there is nothing more to say.
Ten million is 10,000,000: the 10 counts millions, and two empty groups of three follow it, eight digits in all.
Which place a digit is in
Name the places from the right. In 672,463, the 3 is in the ones, the 6 in the tens, the 4 in the hundreds, the 2 in the thousands, the 7 in the ten thousands and the 6 in the hundred thousands. So the 7 is worth 70,000.
The usual mistake is to count from the left. The first digit of a six-digit number is the hundred thousands, but the first digit of a five-digit number is the ten thousands: in 81,511 the 8 is worth 80,000.
Worked example: The Same Digit in Two Different Places
Question A toy shop sold 2568 toy cars last year and 5310 toy cars this year. (a) What is the value of the digit 5 in 2568, and what is its value in 5310? (b) What is the difference between the two values?
1.Write 2568 in a place-value chart. The digit 5 is in the hundreds column, so its value is 500.
In 2568 the digit 5 is in the hundreds column, so its value is 500. 2.Write 5310 in the chart. The digit 5 is in the thousands column, so its value is 5000.
In 5310 the digit 5 is in the thousands column, so its value is 5000. 3.(a) The digit 5 stands for 500 in 2568 and for 5000 in 5310.
(a) The digit 5 stands for 500 in 2568 and for 5000 in 5310. 4.(b) Subtract the smaller value from the larger value: 5000 − 500 = 4500. Check: 4500 + 500 = 5000.
(b) The difference between the two values is 5000 − 500 = 4500.
Answer: (a) 500 and 5000; (b) 4500
Common mistakes
- Saying that the digit 5 is worth 5 in both numbers. The value of a digit depends on its column: 5 hundreds are 500 and 5 thousands are 5000.
- Subtracting the two whole numbers, 5310 − 2568. The question asks for the difference between the two values of the digit 5, which are 5000 and 500.
More thousands, angles and time problems, worked step by step →
Worked example: The Greatest and the Smallest Number from Four Digit Cards
Question Ravi has four digit cards: 4, 0, 7 and 2. He uses all four cards to make a 4-digit number. (a) What is the greatest number he can make, and what is the smallest number he can make? (b) What is the difference between these two numbers?
1.For the greatest number, put the greatest digit in the thousands place. Then put the next greatest digit in each place after it: 7, 4, 2, 0. The greatest number is 7420.
The greatest digit goes in the thousands place, then the next greatest each time: 7420. 2.For the smallest number, the smallest digit should go first. But 0 cannot go first, because 0247 is only the 3-digit number 247.
0 cannot go first, because 0247 is only the 3-digit number 247. 3.So put 2 first, then 0, then 4, then 7. (a) The greatest number is 7420 and the smallest number is 2047.
(a) Put 2 first, then 0, then 4, then 7. The smallest number is 2047 and the greatest is 7420. 4.(b) Subtract the smallest number from the greatest number: 7420 − 2047 = 5373. Check: 2047 + 5373 = 7420.
(b) 7420 − 2047 = 5373.
Answer: (a) 7420 and 2047; (b) 5373
Common mistakes
- Writing 0247 as the smallest number. A 4-digit number cannot start with 0. The smallest digit that is not 0 goes first, and 0 goes second.
- Writing the smallest number as 2470, with 0 at the end. A small digit should go in a place with a great value, so 0 goes in the hundreds place: 2047.
More thousands, angles and time problems, worked step by step →