Forms of Numbers

Standard Form • Expanded Form • Word Form

🔢

Standard

5,280

➕

Expanded

(5×1,000)+(2×100)+(8×10)

📝

Word

five thousand, two hundred eighty

📋 The Three Forms

Every number can be written 3 different ways

🔢Standard Form

The "normal" way we write numbers: 6,347,052

➕Expanded Form

Shows the value of each digit added together:

(6 × 1,000,000) + (3 × 100,000) + (4 × 10,000) + (7 × 1,000) + (5 × 10) + (2 × 1)

📝Word Form

Written out in words:

six million, three hundred forty-seven thousand, fifty-two

📊 Place Value Chart

Every digit has a place and a value

The number 5,138,406 in a place value chart:

Millions		Hundred Thousands	Ten Thousands	Thousands		Hundreds	Tens	Ones
5	,	1	3	8	,	4	0	6

The 5 is in the millions place → its value is 5,000,000

The 0 is in the tens place → it's a placeholder (skip it in expanded form!)

💡Key Rule

When writing expanded form, skip any digit that is 0 — zeros are placeholders!

🔧 Writing Expanded Form

Step by step

Write 82,305 in expanded form

Step 1: Identify each digit and its place value

Ten Thous.	Thousands		Hundreds	Tens	Ones
8	2	,	3	0	5

Step 2: Write each digit × its place value (skip zeros!)

(8 × 10,000)+ (2 × 1,000)+ (3 × 100)+ (5 × 1)

⚠️ We skip the 0 in the tens place!

📝 Writing Word Form

Read by periods (groups of 3 digits)

Write 4,729,015 in word form

Step 1: Break the number into periods

4

Millions

,

729

Thousands

,

015

Ones

Step 2: Read each period, then say the period name

four million, seven hundred twenty-nine thousand, fifteen

⚠️Don't Say "And"!

For whole numbers, never say "and" — save "and" for the decimal point!

✏️ Problem 1

Write in expanded form

Write in Expanded Form

463,218

✓Solution

Hund. Thous.	Ten Thous.	Thousands		Hundreds	Tens	Ones
4	6	3	,	2	1	8

Expanded Form

(4 × 100,000) + (6 × 10,000) + (3 × 1,000) + (2 × 100) + (1 × 10) + (8 × 1)

✏️ Problem 2

Write in expanded form

Write in Expanded Form

7,050,913

✓Solution

Millions		Hund. Th.	Ten Th.	Thous.		Hund.	Tens	Ones
7	,	0	5	0	,	9	1	3

⚠️ Skip the zeros — they're placeholders!

Expanded Form

(7 × 1,000,000) + (5 × 10,000) + (9 × 100) + (1 × 10) + (3 × 1)

✏️ Problem 3

Write in word form

Write in Word Form

892,547

✓Solution

892

Thousands

,

547

Ones

Word Form

eight hundred ninety-two thousand, five hundred forty-seven

✏️ Problem 4

Write in word form

Write in Word Form

53,006,410

✓Solution

53

Millions

,

006

Thousands

,

410

Ones

⚠️ The thousands period is "006" → just say "six thousand"

Word Form

fifty-three million, six thousand, four hundred ten

✏️ Problem 5

Write in standard form

Write in Standard Form

(3 × 1,000,000) + (8 × 100,000) + (5 × 10,000) + (6 × 1,000) + (2 × 100) + (9 × 1)

✓Solution

Find the value of each term:

3,000,000 + 800,000 + 50,000 + 6,000 + 200 + 9

⚠️ Notice there's no tens term — put a 0 in the tens place!

Standard Form

3,856,209

✏️ Problem 6

Write in standard form

Write in Standard Form

(6 × 10,000,000) + (1 × 100,000) + (9 × 10,000) + (4 × 100) + (7 × 10) + (2 × 1)

✓Solution

60,000,000 + 100,000 + 90,000 + 400 + 70 + 2

⚠️ Missing: millions and thousands — fill with zeros!

Ten Mill.	Millions		Hund. Th.	Ten Th.	Thous.		Hund.	Tens	Ones
6	0	,	1	9	0	,	4	7	2

Standard Form

60,190,472

✏️ Problem 7

Write in standard form

Write in Standard Form

fourteen million, two hundred sixty-one thousand, eight hundred thirty-nine

✓Solution

fourteen

14

million

,

two hundred sixty-one

261

thousand

,

eight hundred thirty-nine

839

ones

Standard Form

14,261,839

✏️ Problem 8

Write in standard form

Write in Standard Form

two hundred six million, forty thousand, three hundred twelve

✓Solution

two hundred six

206

million

,

forty

040

thousand

,

three hundred twelve

312

ones

⚠️ "forty thousand" = 040 (pad with zeros to fill 3 digits!)

Standard Form

206,040,312

⭐ Problem 9: All Three Forms!

Write in BOTH Expanded Form AND Word Form

5,807,163

✓Solution

Expanded Form:

(5 × 1,000,000) + (8 × 100,000) + (7 × 1,000) + (1 × 100) + (6 × 10) + (3 × 1)

⚠️ Skip the 0 in ten-thousands!

Expanded Form

(5 × 1,000,000) + (8 × 100,000) + (7 × 1,000) + (1 × 100) + (6 × 10) + (3 × 1)

Word Form

five million, eight hundred seven thousand, one hundred sixty-three

🅰️ Problem 10: Multiple Choice

Which is the expanded form of 24,709?

A(2 × 10,000) + (4 × 1,000) + (7 × 100) + (9 × 1)

B(2 × 10,000) + (4 × 1,000) + (7 × 100) + (9 × 10)

C(24 × 1,000) + (7 × 100) + (9 × 1)

D(2 × 10,000) + (4 × 1,000) + (7 × 10) + (9 × 1)

✓Solution

A is correct!

24,709 → 2 ten-thousands + 4 thousands + 7 hundreds + 0 tens + 9 ones

B is wrong: puts 9 in the tens place (that would make 24,790)

C is wrong: 24 × 1,000 isn't proper expanded form

D is wrong: puts 7 in the tens place (that would make 24,079)

🅰️ Problem 11: Multiple Choice

The Nile River is 4,130 miles long. What is this in word form?

Aforty-one hundred thirty

Bfour thousand, one hundred thirty

Cfour thousand, one hundred three

Dfour thousand, thirteen

✓Solution

B is correct!

4,130 → four thousand, one hundred thirty

C is wrong: 103 ≠ 130 (be careful with the 3!)

D is wrong: 13 ≠ 130 (that would be 4,013)

🔀 Now Add Decimals!

Same rules — just extend past the decimal point

📊Decimal Place Value Chart

Thous.	Hund.	Tens	Ones	.	Tenths	Hundredths	Thousandths
8	4	1	6	.	3	7	2

The 3 is worth 3 tenths = 3 × 1/10

The 7 is worth 7 hundredths = 7 × 1/100

The 2 is worth 2 thousandths = 2 × 1/1,000

💡Decimal Place Values Use Fractions

In expanded form, decimals use × 1/10, × 1/100, and × 1/1,000 instead of × 10, × 100, × 1,000.

➕ Expanded Form: Decimals

Using fractions for decimal places

Write 5,041.63 in expanded form

Thous.		Hund.	Tens	Ones	.	Tenths	Hundredths
5	,	0	4	1	.	6	3

(5 × 1,000)+ (4 × 10)+ (1 × 1)+ (6 × 1/10)+ (3 × 1/100)

⚠️ Skip the 0 in hundreds — same rule as whole numbers!

📝 Word Form: Decimals

NOW we use the word "and"!

Write 72,308.49 in word form

72,308

Whole Number Part

.

49

Decimal Part

Step 1: Read the whole number part normally:

seventy-two thousand, three hundred eight

Step 2: Say "and" for the decimal point

Step 3: Read the decimal digits, then say the last place value name:

forty-nine hundredths

Word Form

seventy-two thousand, three hundred eight and forty-nine hundredths

⚠️Remember!

"And" = decimal point. Never say "and" anywhere else in the number!

✏️ Problem 12

Write in expanded form

Write in Expanded Form

3,629.74

✓Solution

Thous.		Hund.	Tens	Ones	.	Tenths	Hundr.
3	,	6	2	9	.	7	4

Expanded Form

(3 × 1,000) + (6 × 100) + (2 × 10) + (9 × 1) + (7 × 1/10) + (4 × 1/100)

✏️ Problem 13

Write in expanded form

Write in Expanded Form

40,805.109

✓Solution

Ten Th.		Hund.	Tens	Ones	.	Tenths	Hundr.	Thous.
4	,	8	0	5	.	1	0	9

⚠️ Skip both zeros — in tens AND hundredths!

Expanded Form

(4 × 10,000) + (8 × 100) + (5 × 1) + (1 × 1/10) + (9 × 1/1,000)

✏️ Problem 14

Write in word form

Write in Word Form

1,456.82

✓Solution

1,456

whole part

and

82

hundredths

Word Form

one thousand, four hundred fifty-six and eighty-two hundredths

✏️ Problem 15

Write in word form

Write in Word Form

23,070.516

✓Solution

23,070

whole part

and

516

thousandths

The last decimal digit is in the thousandths place, so say "thousandths"

Word Form

twenty-three thousand, seventy and five hundred sixteen thousandths

✏️ Problem 16

Write in standard form

Write in Standard Form

(9 × 1,000) + (2 × 100) + (6 × 10) + (5 × 1) + (8 × 1/10) + (3 × 1/1,000)

✓Solution

9,000 + 200 + 60 + 5 + 0.8 + 0.003

⚠️ No hundredths term — put a 0 in the hundredths place!

Thous.		Hund.	Tens	Ones	.	Tenths	Hundr.	Thous.
9	,	2	6	5	.	8	0	3

Standard Form

9,265.803

✏️ Problem 17

Write in standard form

Write in Standard Form

six hundred forty-three thousand, two hundred seventeen and ninety-one hundredths

✓Solution

six hundred forty-three thousand, two hundred seventeen

643,217

.

ninety-one hundredths

91

"Hundredths" → 2 decimal places

Standard Form

643,217.91

✏️ Problem 18

Write in standard form

Write in Standard Form

eight thousand, four hundred two and sixty-seven thousandths

✓Solution

eight thousand, four hundred two

8,402

.

sixty-seven thousandths

067

⚠️ "Thousandths" → 3 decimal places → 67 becomes 067 (pad with a leading zero!)

Standard Form

8,402.067

🅰️ Problem 19: Multiple Choice

Which is the expanded form of 15,302.46?

A(1 × 10,000) + (5 × 1,000) + (3 × 100) + (2 × 1) + (4 × 1/10) + (6 × 1/100)

B(1 × 10,000) + (5 × 1,000) + (3 × 100) + (2 × 10) + (4 × 1/10) + (6 × 1/100)

C(1 × 10,000) + (5 × 1,000) + (3 × 100) + (2 × 1) + (46 × 1/100)

D(15 × 1,000) + (3 × 100) + (2 × 1) + (4 × 1/10) + (6 × 1/100)

✓Solution

A is correct!

15,302 → 1 ten-thousand + 5 thousands + 3 hundreds + 0 tens + 2 ones

B is wrong: puts the 2 in the tens (would make 15,320.46)

C is wrong: 46 × 1/100 isn't proper expanded form — each digit gets its own term

D is wrong: 15 × 1,000 isn't proper expanded form

🅰️ Problem 20: Multiple Choice

A raindrop weighs 7,051.204 grams. What is this in word form?

Aseven thousand, fifty-one and two hundred four tenths

Bseven thousand, fifty-one and two hundred four thousandths

Cseven thousand, fifty-one and twenty-four hundredths

Dseven hundred fifty-one and two hundred four thousandths

✓Solution

B is correct!

7,051 → seven thousand, fifty-one

.204 → the last digit is in the thousandths place, so read as "two hundred four thousandths"

A is wrong: "tenths" has only 1 decimal digit

C is wrong: .24 ≠ .204

D is wrong: 751 ≠ 7,051

⭐ Problem 21: All Three Forms!

Write in BOTH Expanded Form AND Word Form

16,530.72

✓Solution

Ten Th.	Thous.		Hund.	Tens	Ones	.	Tenths	Hundr.
1	6	,	5	3	0	.	7	2

Expanded Form

(1 × 10,000) + (6 × 1,000) + (5 × 100) + (3 × 10) + (7 × 1/10) + (2 × 1/100)

Word Form

sixteen thousand, five hundred thirty and seventy-two hundredths

🏆 Great Work! Key Takeaways

✅DO Remember

Skip zeros in expanded form — they're placeholders
Use × 1/10, × 1/100, × 1/1,000 for decimal places
"And" means the decimal point in word form
Name the last decimal place (tenths, hundredths, thousandths)
Fill missing places with zero when going from expanded → standard

❌DON'T Forget

Don't say "and" for whole numbers — save it for the decimal!
Don't forget placeholders when converting to standard form
Don't write 67 thousandths as .67 — it's .067 (3 decimal places!)
Don't combine digits like (24 × 1,000) — each digit gets its OWN term
Don't confuse "hundreds" with "hundredths"!