Try This First
Try this short activity before reading the lesson.
> Get some paper and cut ten small squares. Put them in a row and count them: that row is a ten. Make ten rows. That is a hundred. Now show $124$ with one hundred, two tens and four loose squares.
Math Lab: Too many tens
Predict first. A number has 2 hundreds, 14 tens and 3 ones. Is it more or less than 300?
<div class="math-model"><p><strong>Place-value boxes: hundreds, tens, ones.</strong></p><div class="model-bar"><span class="model-cell">2 hundreds</span><span class="model-cell">14 tens</span><span class="model-cell">3 ones</span></div><p class="model-caption">Only 0 to 9 can stay in one place.</p></div>
Model and solve. Ten of the $14$ tens make $1$ hundred, so $14$ tens is $100 + 40$. Then $200 + 100 + 40 + 3 = 343$. That is more than $300$.
Spot the mistake. Someone writes the number as 2143. Which box has too many pieces to stay in its place?
Your turn. A number has 3 hundreds, 12 tens and 5 ones. Draw the boxes, trade ten tens for a hundred, and write the number.
Check after trying. $12$ tens is $1$ hundred and $2$ tens, so $300 + 100 + 20 + 5 = 425$. In 2143 the $14$ tens were written as two digits; ten of them had to become a hundred first, giving $343$.
The Big Idea
A number up to $1{,}000$ has three places: hundreds, tens and ones. The digit tells you how many; the place tells you of what. In $630$ the $3$ is not three. It is three tens, which is thirty.
Ten ones make a ten. Ten tens make a hundred. Ten hundreds make a thousand. Every time you have ten of something, you trade it for one of the next bigger thing.
Expanded form writes the number as its parts: $358 = 300 + 50 + 8$. If a place has nothing in it, you write a $0$ to hold the place. Four hundred seven is $407$, not $47$.
A three-digit number is hundreds, tens and ones, and a hundred is ten tens. In this chapter you read and write numbers to 1,000 in digits, words and expanded form, and say what each digit is worth. The same three columns stretch to a million in Grade 4 and to decimals after that, so the habit of naming the place, not just the digit, starts here.
Words to Know
- digit: One of the symbols $0$ to $9$. The number $407$ has three digits.
- place: Where a digit sits: ones, tens or hundreds. The place says what the digit is worth.
- expanded form: The number written as its parts added together: $358 = 300 + 50 + 8$.
Worked Examples and Your Turn
Study each example, then try the paired problem.
Example 1: Say what the digit is worth
Problem: In $274$, what is the $7$ worth?
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stroke-width="0.6"/><line x1="264" y1="72" x2="272" y2="72" stroke="#333" stroke-width="0.6"/><line x1="264" y1="80" x2="272" y2="80" stroke="#333" stroke-width="0.6"/><line x1="264" y1="88" x2="272" y2="88" stroke="#333" stroke-width="0.6"/><line x1="264" y1="96" x2="272" y2="96" stroke="#333" stroke-width="0.6"/><rect x="282" y="96" width="8" height="8" fill="#f2c14e" stroke="#333" stroke-width="1"/><rect x="282" y="85.6" width="8" height="8" fill="#f2c14e" stroke="#333" stroke-width="1"/><rect x="282" y="75.2" width="8" height="8" fill="#f2c14e" stroke="#333" stroke-width="1"/><rect x="282" y="64.8" width="8" height="8" fill="#f2c14e" stroke="#333" stroke-width="1"/><text x="98" y="124" text-anchor="middle" fill="#333">2 hundreds</text><text x="218" y="124" text-anchor="middle" font-weight="bold" fill="#333">7 tens = 70</text><text x="262" y="142" text-anchor="middle" font-size="13" fill="#333">4 ones</text></svg>
Solution:
- Name the places from the right: $4$ ones, $7$ tens, $2$ hundreds.
- The $7$ is in the tens place. Seven tens is $70$. Why: a ten is ten ones, and seven of them is seventy.
Answer: The $7$ is worth $70$.
> Notice: Ask "seven of what?" every time. Seven ones, seven tens and seven hundreds are all written with a $7$.
Your Turn 1: In $593$, what is the $9$ worth?
Example 2: Words to digits, digits to words
Problem: Write six hundred fifteen in digits. Then write $290$ in words.
Solution:
- Six hundred fifteen: six hundreds, then fifteen, which is one ten and five ones. So $6$, $1$, $5$: $615$.
- $290$: two hundreds and nine tens and no ones. Say the hundreds, then the tens: two hundred ninety. Why: the $0$ means there are no ones to say.
Answer: $615$; two hundred ninety.
Your Turn 2: Write three hundred eight in digits, and $740$ in words.
Example 3: Tens and ones, when there are more than nine tens
Problem: A number is made of $12$ tens and $5$ ones. What is the number? Then write the expanded form of $809$.
Solution:
- Twelve tens is too many for one tens place. Trade ten of the tens for a hundred. Why: ten tens make a hundred. That leaves $1$ hundred and $2$ tens.
- Now the number is $1$ hundred, $2$ tens, $5$ ones: $125$.
- For $809$: eight hundreds, no tens, nine ones. Write only the parts that are there: $800 + 9$.
Answer: $125$; and $809 = 800 + 9$.
> Notice: The $0$ in $809$ is a placeholder. It keeps the $8$ in the hundreds place. It adds nothing to the expanded form.
> Verification & Check: Count twelve tens out loud: $10, 20, \ldots, 120$. Then five more is $125$.
Your Turn 3: A number is made of $14$ tens and $3$ ones. What is it? Write the expanded form of $560$.
Example 4: The trap: four hundred seven
Problem: Write four hundred seven in digits.
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 363 150" width="363" height="150" role="img" aria-label="Base-ten blocks for four hundred seven: 4 hundred flats, an empty space where the tens would go, and 7 single cubes. The empty tens place is written as 0, so the number is 407."
The chapter continues in the book.
