Seahorse Series · Quiz 1 · Place Value

The Guide

Before you begin

This quiz is about place value: what each digit in a number is worth, depending on where it stands. The quiz has one job: to show us where to begin. Nothing in it is a trick, and no calculator is needed — that's the point. Read this guide first, look over the worked examples, then take the ten questions. Whatever the quiz shows is useful news.

Numbers live in families of three

Big numbers are read in groups of three digits. The groups are called periods; this quiz calls them families: the ones family, the thousands family, the millions family. Commas mark where one family ends and the next begins. Inside every family the three places are always the same: hundreds, tens, ones.

Take the number 4,257,309. Here is that same number, opened up so every digit shows the place it stands on — the commas still standing right where they stand in the numeral:

ones		hundreds	tens	ones		hundreds	tens	ones
Millions		Thousands				Ones
4	,	2	5	7	,	3	0	9

The chart is wider than your screen — slide it sideways with your finger, or turn your phone.

To read a number, say what is inside each family, then say the family's name — here: four million, two hundred fifty-seven thousand, three hundred nine. The ones family never says its name — it just finishes the number.

Picture it: a long street of houses, three rooms each. The comma is the wall between houses. When you read the number, you name what's in each house and then say the house's name — million, thousand — before moving on.

Zeros are silent, but they hold their places

A zero says: nothing lives in this place — but the place is still here. In 5,006,090 you never say the zeros out loud — five million, six thousand, ninety — but without them, every other digit would slide into the wrong place and the number would collapse. Writing zeros is how you keep each digit standing where it belongs.

A digit and its value are two different things

The digit is the symbol you see. Its value is what it is worth where it stands. In 583,000, the digit 8 stands in the ten-thousands place, so it is worth 80,000. The same digit, standing in a different place, is worth a different amount — the way an 8 on a price tag means eight dollars, but slid one place to the left it means eighty.

Expanded form: stretching a number out

Expanded form pulls a number apart to show what each digit is worth: 4,257,309 = 4,000,000 + 200,000 + 50,000 + 7,000 + 300 + 9. The zeros contribute nothing, so they are left out of the expanded form.

Two customs of written numbers

First: no and inside a whole number. In everyday speech we all say "two hundred and five" — but on paper, and on the GED, the word and is saved for the decimal point. Second: the numbers from twenty-one to ninety-nine take a hyphen when written out — fifty-seven, ninety-two.

Worked Examples

Three to study before you start

Example 1 · Reading

Read 4,257,309. Family by family: the millions house holds 4, the thousands house holds 257, the ones house holds 309. Say each amount, then the house name: four million, two hundred fifty-seven thousand, three hundred nine.

Example 2 · Writing — the family-of-three rule

Write sixty-two thousand, forty as a numeral. The thousands family holds 62. Now the ones family: it must have three places, and "forty" only fills two of them — so a zero takes the empty hundreds place: 040. The answer is 62,040.

The tempting wrong answer is 6,240 — squeezing "forty" against the 62. Once a family sits to the right of another, it must be written with all three of its places, zeros and all.

Example 3 · Value of a digit

What is the value of the 8 in 583,000? Walk from the comma: 3 is in the thousands place, 8 is in the ten-thousands place. So the 8 is worth 80,000 — not 8, and not 800.

The Quiz · Ten Questions

Now you

Work without a calculator. Write your answers on the lines. Questions 1 and 6 are multiple choice — choose the one best answer.

In the number 3,748,562, which digit is in the ten-thousands place?
- A) 7
- B) 4
- C) 8
- D) 5
Write 6,215,430 in words.
Write 5,006,090 in words.
Write as a numeral: two hundred four thousand, seventeen.
Write as a numeral: eight million, five hundred.
What is the value of the 7 in 2,761,948?
- A) 7
- B) 70,000
- C) 700,000
- D) 7,000,000
Write 903,250 in expanded form.
Denise is writing her rent check for $1,275. Write the amount in words, the way it should appear on the written line of the check.
The population of New York City is about 8,300,000 people. Write this number in words.
A newspaper reports that the city's new budget is twelve million, forty thousand dollars. Write that amount as a numeral.

Answer Key

Check your work

Open the key — after you've finished all ten

1 B — the digit 4.

Start at the comma after 748 and walk to the left: 8 stands in the thousands place, 4 in the ten-thousands, 7 in the hundred-thousands. If you chose A, you counted one place too far left; if C, one place too far right. Always count outward from the nearest comma.

2 Six million, two hundred fifteen thousand, four hundred thirty.

Family by family: 6 | 215 | 430. Each family says its amount, then its name — and no and anywhere.

3 Five million, six thousand, ninety.

The zeros are silent — you never say them, but they hold the 6 in the thousands family and the 9 in the tens place. The common slip is "five million, six hundred thousand, ninety" — that moves the 6 two places up and changes the number by almost six hundred thousand.

4 204,017

The thousands family holds 204. Then the ones family must be written with all three of its places — "seventeen" fills only two, so a zero takes the hundreds place: 017. If you wrote 20,417 or 2,417, revisit Example 2: the family-of-three rule.

5 8,000,500

The hardest one here, on purpose. Between "eight million" and "five hundred" there is silence — the entire thousands family is empty. But an empty family still gets written: 000. If you wrote 8,500, the empty family collapsed, and 8,500 is smaller than the true number by almost eight million.

6 C: 700,000.

The 7 stands in the hundred-thousands place. A is the digit itself, not its worth. B stops one place short. D promotes the 7 into the millions family. A digit's value is the digit times the place it stands on.

7 900,000 + 3,000 + 200 + 50

The 9 is worth 900,000, the 3 is worth 3,000, the 2 is worth 200, the 5 is worth 50. The zeros in the ten-thousands and ones places add nothing, so custom leaves them out — though if you wrote "+ 0" for them, your understanding is fine.

8 One thousand, two hundred seventy-five

Note the hyphen in seventy-five. On a real check you would finish the line with "and 00/100" — and that is exactly why and stays out of the whole-number part: it is reserved to mark where the cents begin.

9 Eight million, three hundred thousand.

The millions family holds 8, the thousands family holds 300, and the ones family is all zeros — silent, but holding all three of their places. Five zeros, not one of them spoken.

10 $12,040,000

Millions family: 12. Thousands family: "forty" fills two places, so a zero goes in front: 040. Ones family: empty, so 000. Every family to the right must be written in full before the number is done. If you wrote $1,240,000 or $12,400,000, the forty landed in the wrong seat inside its family.

Reading your results

Questions	The skill they test	If they gave trouble
1, 6	Naming places and the value of a digit	Return to the chart in The Guide; practice walking digits outward from the comma.
2, 8	Writing numbers in words	Steady practice — say the family, then its name. Watch the hyphens and the missing and.
3, 9	Reading numbers with zeros inside	Reread "Zeros are silent, but they hold their places."
4, 5, 10	Writing numbers with empty places	Example 2 is the one to study: the family-of-three rule.
7	Expanded form	Reread "Stretching a number out"; write three more of your own.

Eight or more right: place value is solid — move on to Quiz 2. Five to seven: review the rows flagged above and retake this quiz in a few days. Fewer than five: good news — we've found the right place to start. Work through The Guide slowly with your teacher, then come back to these same ten questions.