Lesson 1 of 8 · Grades 4 to 5
Place value to thousands
Every digit in a number has a place, and the place decides what the digit is worth. In this lesson you will read and build four-digit numbers, write them in expanded form, and see why a zero can be just as important as any other digit.
A place for every digit
Look at the number 4,072. Four digits stand in a row, and each one has a job. The 4 counts thousands, the 0 counts hundreds, the 7 counts tens and the 2 counts ones. The position of a digit is called its place, and the whole idea is called place value: the same digit is worth different amounts in different places.
The chart below puts each digit above the name of its place. Read it from the left, the way you read a number: four thousands, zero hundreds, seven tens and two ones.
What a digit is worth
The value of a digit is the amount it gives to the number. In 4,072 the 7 stands in the tens place, so its value is 7 tens, which is 70. It is not worth 7. Now look at 7,042. The very same digit, 7, stands in the thousands place, so it is worth 7,000. One digit, two places, two very different values.
Each place is worth ten times the place on its right. Ten ones make a ten, ten tens make a hundred, and ten hundreds make a thousand. This pattern is called base ten, and it is the reason the places are named after the numbers 1, 10, 100 and 1,000.
Expanded form
Expanded form breaks a number into its digit values and adds them up. The number 4,072 expands to 4,000 + 70 + 2. The zero in the hundreds place gives nothing to the sum, so it is left out. The number 5,306 expands to 5,000 + 300 + 6. Working the other way, 2,000 + 600 + 40 + 9 builds the number 2,649.
Expanded form is a good check on your reading. If the expanded parts do not add back to the number you started with, a place was read incorrectly.
The zero that holds a place
The zero in 4,072 is doing real work. Without it the number would be 472, and the 7 would slide from the tens place into the hundreds place. Zero says "there are no hundreds here" and holds the place open so that the other digits keep their jobs. The numbers 4,072 and 4,720 use the same four digits, but they are not the same number: the zero and the seven have swapped places.
Watch out for this
A zero is not a nothing. 4,072 is four thousand and seventy-two, not four hundred and seventy-two. In 5,040 the zero in the ones place is also load-bearing: without it the number would be 54 or 540. Read the places from left to right before you say a number out loud.
Reading four-digit numbers
A comma splits a four-digit number into thousands and the rest, so 4,072 is easier to read. Say it as "four thousand and seventy-two". The number 5,040 is "five thousand and forty". The comma is a helper for the eye; it never changes the value of a digit.
Worked example
A stadium has five thousand and forty seats. Write the number, then say what the 5 is worth.
Step 1: name the places. Five thousand and forty has four places: thousands, hundreds, tens and ones.
Step 2: fill the places. The thousands digit is 5, the hundreds digit is 0, the tens digit is 4 and the ones digit is 0.
Step 3: write the number with a comma after the thousands: 5,040.
Step 4: find the value of the 5. It stands in the thousands place, so it is worth 5 thousands, which is 5,000.
Answer: 5,040 seats, and the 5 is worth 5,000.
Remember
- Every digit has a place, and the place sets its value.
- From right to left the places are ones, tens, hundreds, thousands.
- Each place is ten times the place on its right.
- Zero holds a place open so the other digits keep their values.
Try it
Answer the five questions below. Work them out first, then open each answer to check.
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In 3,586, which digit is in the hundreds place?
Show answer
5. The digits are 3 thousands, 5 hundreds, 8 tens and 6 ones.
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What is the value of the 7 in 4,071?
Show answer
70. The 7 stands in the tens place, so it is worth 7 tens, which is 70.
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Write 2,000 + 600 + 40 + 9 as one number.
Show answer
2,649. The parts are 2 thousands, 6 hundreds, 4 tens and 9 ones.
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Write 5,306 in expanded form.
Show answer
5,000 + 300 + 6. There are no hundreds in 5,306, so the hundreds part is zero and it is left out of the sum.
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In 8,842, which 8 is worth more: the first one or the second one?
Show answer
The first 8, in the thousands place. It is worth 8,000, while the second 8 is worth 800.
Puzzle · Missing digit
Puzzle time
A four-digit number uses the digits 6, ?, 4 and 9 in the thousands, hundreds, tens and ones places. The number is between 6,300 and 6,500, and the missing digit is even. Which digit is missing?
Show a hint
Try each even digit in the hundreds place and see which number lands between 6,300 and 6,500.
Show the answer
Answer: 4. With 4 in the hundreds place the number is 6,449, which is between 6,300 and 6,500. The other even digit, 6, would give 6,649, which is too big.