Place Value to Millions

🔢 Place Value to Millions

Part 1 of 5 — What Place Value Means

Topics in This Part

🔑 Key Idea: The same digit can be worth different amounts depending on where it sits in a number. The spot a digit sits in is called its place, and the amount it is worth there is its value. That is what "place value" means.

Digits vs. Numbers

A digit is one of the ten symbols we write numbers with:

$0,\ 1,\ 2,\ 3,\ 4,\ 5,\ 6,\ 7,\ 8,\ 9$

A number is built by putting digits together. The number $375$ is made from the three digits $3$, $7$, and $5$.

Here is the big secret of our number system: the position of a digit tells you how much it is worth.

💡 The same digit $5$ stands for $5$, then $50$, then $500$. Moving one spot to the left makes a digit 10 times bigger.

Concept Check 🎯

The Place Value Chart

We give each spot a name. Reading from right to left, the places get bigger and bigger:

Notice the pattern: each step to the left is $10$ times the place before it. Ten ones make one ten, ten tens make one hundred, ten hundreds make one thousand, and so on.

🔑 Key Rule: Each place to the left is 10 times the place to its right. That is why we call ours a base-ten number system.

Ten Times Bigger 🧮

Each place is $10$ times the one to its right. Fill in each blank.

1) $10$ tens make $1$ hundred. How many hundreds make $1$ thousand? 2) A digit in the thousands place is worth $1{,}000$. What is a digit worth one place to its left (ten thousands)? 3) $10 \times 100 = \,?$

Reading Each Place

Let's place the number $3{,}527{,}481$ into the chart. We line up the digits with their place names:

Now we can read each digit's place:

• The $3$ is in the millions place.
• The $5$ is in the hundred thousands place.
• The $2$ is in the ten thousands place.
• The $1$ is in the ones place.

💡 To find any digit's place, just line the number up in the chart. In Part 2, we'll turn each place into its full value (like "the $3$ is worth $3{,}000{,}000$").

Name the Place 🔽

Use the number $3{,}527{,}481$ from the chart above. Choose the place each digit sits in.

🔢 Place Value to Millions

Part 2 of 5 — The Value of a Digit

🔑 The Idea: A digit's place is its spot's name (tens, hundreds, ...). A digit's value is the full amount it stands for in that spot. The $7$ in $700$ has a value of $700$, even though the digit is just $7$.

Place vs. Value

To find a digit's value, multiply the digit by what one of that place is worth.

$\text{value} = \text{digit} \times \text{value of the place}$

Look at $4{,}716{,}203$:

⚠️ Watch out: A $0$ does not mean "nothing useful." The $0$ in the tens place is a placeholder — it keeps every other digit in its correct, larger spot.

Concept Check 🎯

Match the Value 🔽

Use the number $809{,}205$. Pick the value of each digit.

Find the Value 🧮

For the number $2{,}658{,}300$, write the value of each digit below. (Write the full number, like $700$ or $40{,}000$.)

1) The value of the $6$ ( hundred thousands place ) $= \,?$ 2) The value of the $5$ ( ten thousands place ) $= \,?$ 3) The value of the $8$ ( thousands place ) $= \,?$

The "10 Times" Connection

Because each place is $10$ times the one to its right, the same digit is worth $10$ times more each spot it moves left.

Look at the digit $5$ across three numbers:

Each time the $5$ moves one place left, its value is multiplied by $10$: $\;50 \to 500 \to 5{,}000$.

🔑 Key Fact: $5{,}000$ is exactly 10 times as much as $500$, because $5{,}000 = 10 \times 500$. Place value and "times 10" go hand in hand.

🔢 Place Value to Millions

Part 3 of 5 — Three Ways to Write a Number

🔑 The Idea: Every number can be written in three forms: standard form (the digits, like $42{,}569$), expanded form (each value added up), and word form (written out in words). Knowing all three is the heart of place value.

The Three Forms

Let's write $42{,}569$ three ways.

Standard form — the everyday way, just the digits: $42{,}569$

Expanded form — break it into the value of each digit and add: $40{,}000 + 2{,}000 + 500 + 60 + 9$

Word form — say it the way you'd read it out loud: $\text{forty-two thousand, five hundred sixty-nine}$

💡 Tip: Expanded form is just every digit's value from Part 2, added together. If a place has a $0$, you can skip it in expanded form.

Concept Check 🎯

Build the Number 🧮

Add up the expanded form to find the standard-form number. (Type just the digits, no commas — like $40500$.)

1) $40{,}000 + 2{,}000 + 500 + 60 + 9 = \,?$ 2) $600{,}000 + 5{,}000 + 30 = \,?$ 3) $1{,}000{,}000 + 300{,}000 + 2{,}000 + 7 = \,?$

Reading Big Numbers in Words

Commas split a number into groups of three, and each group has a name. Read each group, then say its group's name.

$\underbrace{2}_{\text{millions}},\ \underbrace{084}_{\text{thousands}},\ \underbrace{500}_{\text{ones}}$

Read it group by group:

• $2$ → "two million"
• $084$ → "eighty-four thousand"
• $500$ → "five hundred"

Put it together: two million, eighty-four thousand, five hundred.

⚠️ Common mistake: Don't say "and" between groups. We write $2{,}084{,}500$ as "two million, eighty-four thousand, five hundred" — no "and." We also never name the ones group, we just say its digits.

Read It in Words 🔽

Build the word form of $3{,}450{,}016$ by choosing each group.

$\underbrace{3}_{\text{millions}},\ \underbrace{450}_{\text{thousands}},\ \underbrace{016}_{\text{ones}}$

🔢 Place Value to Millions

Part 4 of 5 — Comparing & Rounding

🔑 The Idea: Place value lets us compare two big numbers (which is bigger?) and round a number to a nearby, friendlier number. Both tricks start by lining up the digits by their places.

Comparing Big Numbers

To compare two numbers, line them up by place and compare from the left (the biggest place) first.

We use three symbols:

Example: Compare $548{,}000$ and $548{,}200$.

1. Same millions/hundred-thousands/ten-thousands/thousands: $548$ matches $548$.
2. First difference is in the hundreds place: $0$ vs. $2$.
3. Since $0 < 2$, we get $548{,}000 < 548{,}200$.

💡 Shortcut: A number with more digits is always bigger (for whole numbers). $1{,}200{,}000$ has 7 digits and $912{,}345$ has 6 digits, so $1{,}200{,}000 > 912{,}345$ — you don't even have to check each place.

Greater, Less, or Equal? 🔽

Choose the correct symbol for each pair.

Rounding to a Place

Rounding swaps a number for a nearby, simpler one. Here are the steps to round to a given place:

1. Underline the digit in the place you're rounding to.
2. Look at the digit just to its right (the "neighbor").
3. If the neighbor is $5$ or more, round up (add $1$ to the underlined digit). If it's $4$ or less, keep it the same.
4. Change every digit to the right of the underlined place into a $0$.

Example: Round $84{,}627$ to the nearest thousand.

• The thousands digit is $4$ (in $8\underline{4}{,}627$).
• Its neighbor (hundreds place) is $6$. Since $6 \ge 5$, round up: $4 \to 5$.
• Zero out the rest: $\;85{,}000$.

$84{,}627 \approx 85{,}000$

⚠️ Remember: You only look at the one digit to the right of your place — not the whole rest of the number. The neighbor decides everything.

Concept Check 🎯

Round It 🧮

Round each number as asked. (Type just the digits, no commas.)

1) Round $3{,}527{,}481$ to the nearest hundred thousand. 2) Round $5{,}450{,}000$ to the nearest million.

🔢 Place Value to Millions

Part 5 of 5 — Mixed Practice & Mastery Check

You can now (1) name each place, (2) find a digit's value, (3) write numbers in standard, expanded, and word form, and (4) compare and round. Let's put it all together.

Quick Reference

🔑 Big takeaway: Every place is 10 times the place to its right. That one rule explains naming places, finding values, comparing, and rounding. Place value is the backbone of the whole number system.

Mixed Practice 🔽

Use the number $6{,}205{,}038$ to answer each part.

Mixed Practice 🧮

Type just the digits (no commas).

1) Write the standard form of "one million, four hundred thousand, twenty-five." 2) What is the value of the $9$ in $1{,}392{,}640$? 3) Round $682{,}500$ to the nearest hundred thousand.

Exit Quiz ✅

Answer all three to finish the lesson.