---
title: "Numbers up to 10 000"
book: "Primary & Middle School Mathematics"
subject: math
language: en
chapter: 14
exercises: 11
source: https://one-course.com/books/math/1/en/chapter/14-numbers-up-to-10-000
---

# Chapter 14 — Numbers up to 10 000

One thousand, two thousand, three thousand … big numbers are built from small ones, using a wonderful idea: the *place* of a digit tells its value. This chapter teaches how to read, write, compare and order numbers up to $10\,000$.

## 14.1 Reading and writing numbers

**Definition 14.1 (Place value).**

A number is written with the digits $0, 1, 2, \dots, 9$. Reading from the right, the places are: units, tens, hundreds, thousands. In $3\,254$:

$$
3\,254 = 3 \text{ thousands} + 2 \text{ hundreds} + 5 \text{ tens}
+ 4 \text{ units}.
$$

![The place-value table of 3\,254, read “three thousand two hundred fifty-four”.](https://one-course.com/images/onecourse/chapters/math-1/g3-numbers/fig-1d25c11717b8.svg)

*The place-value table of $3\,254$, read “three thousand two hundred fifty-four”.*

**Example 14.2 (The zero that holds a place).**

“Four thousand and seven” is written $4\,007$: a $4$ in the thousands, a $7$ in the units, and *[zeros](https://one-course.com/books/math/1/en/chapter/1-counting-to-20#def-g1-counting-zero)* in between to keep each digit in its right place. Without them, $47$ would be a very different number!

**Example 14.3 (Exchanging).**

Ten units make one ten; ten tens make one hundred; ten hundreds make one thousand. So $10$ hundreds $= 1\,000$, and $32$ tens $= 320$: the number $320$ contains $32$ tens (not just the digit $2$!).

## 14.2 Comparing and ordering

**Method 14.4 (Comparing two numbers).**

1. Count the digits: more digits means a bigger number ( $1\,002 > 998$ ).
2. Same number of digits: compare digit by digit starting from the *left* . The first difference decides: $5\,614 > 5\,589$ because $6 > 5$ at the hundreds.
3. Write the answer with the signs $<$ (smaller than) or $>$ (bigger than): the open side always [faces](https://one-course.com/books/math/1/en/chapter/11-shapes-and-solids#def-g2-shapes-solids) the bigger number.

![Numbers on a line graduated in hundreds: further right means bigger. 240 < 690 < 905.](https://one-course.com/images/onecourse/chapters/math-1/g3-numbers/fig-5d8158f84e02.svg)

*Numbers on a line graduated in hundreds: further right means bigger. $240 < 690 < 905$.*

**Example 14.5.**

Order from smallest to biggest: $780$, $8\,700$, $807$, $87$. First by the number of digits: $87$ (two), then $780$ and $807$ (three), then $8\,700$ (four). Between $780$ and $807$: compare the hundreds digits, $7 < 8$, so $780 < 807$. Final order:

$$
87 < 780 < 807 < 8\,700 .
$$

## 14.3 Even and odd

**Definition 14.6 (Even, odd).**

A number is *even* when it can be split into two equal whole parts — its units digit is $0$, $2$, $4$, $6$ or $8$. Otherwise it is *odd* (units digit $1$, $3$, $5$, $7$ or $9$).

**Example 14.7.**

$46$ is [even](#def-g3-numbers-evenodd) ($46 = 23 + 23$); $47$ is [odd](#def-g3-numbers-evenodd) (two equal parts would need half an object). Only the *last* digit matters: $3\,578$ is [even](#def-g3-numbers-evenodd), $2\,341$ is [odd](#def-g3-numbers-evenodd).

![Even numbers split into two equal rows; odd numbers always leave one alone.](https://one-course.com/images/onecourse/chapters/math-1/g3-numbers/fig-8210cd04cdac.svg)

*[Even numbers](#def-g3-numbers-evenodd) split into two equal rows; [odd numbers](#def-g3-numbers-evenodd) always leave one alone.*

## 14.4 Exercises

**Exercise 14.1 ★.**

Write in digits: “two thousand three hundred forty-five”; “six thousand and fifty”; “nine thousand and one”.

**Solution of Exercise 14.1.**

$2\,345$; $6\,050$; $9\,001$.

**Exercise 14.2 ★.**

Write in words: $1\,208$; $4\,070$; $9\,999$.

**Solution of Exercise 14.2.**

$1\,208$: one thousand two hundred eight. $4\,070$: four thousand seventy. $9\,999$: nine thousand nine hundred ninety-nine.

**Exercise 14.3 ★.**

In $7\,382$: which digit is in the tens place? In the thousands place? How many *hundreds* does the number contain in total (careful: not just the hundreds digit — think of [Example 14.3](#ex-g3-numbers-exchange))?

**Solution of Exercise 14.3.**

Tens digit: $8$. Thousands digit: $7$. Hundreds contained in total: $73$ (because $7\,382 = 73$ hundreds $+ 82$, i.e. $73 \times 100 + 82$).

**Exercise 14.4 ★.**

Decompose as in [Definition 14.1](#def-g3-numbers-place): $5\,631$; $2\,046$; $8\,500$.

**Solution of Exercise 14.4.**

$5\,631 = 5$ thousands $+ 6$ hundreds $+ 3$ tens $+ 1$ unit.

$2\,046 = 2$ thousands $+ 0$ hundreds $+ 4$ tens $+ 6$ units.

$8\,500 = 8$ thousands $+ 5$ hundreds.

**Exercise 14.5 ★.**

Copy and complete with $<$ or $>$:

$$
456 \;?\; 465, \qquad
1\,203 \;?\; 989, \qquad
6\,090 \;?\; 6\,009, \qquad
9\,999 \;?\; 10\,000 .
$$

**Solution of Exercise 14.5.**

$456 < 465$ (tens: $5 < 6$); $1\,203 > 989$ (four digits beat three); $6\,090 > 6\,009$ (tens: $9 > 0$); $9\,999 < 10\,000$.

**Exercise 14.6 ★.**

Order from smallest to biggest: $530$; $3\,500$; $353$; $5\,033$; $503$.

**Solution of Exercise 14.6.**

$353 < 503 < 530 < 3\,500 < 5\,033$.

**Exercise 14.7 ★.**

On a number line graduated in hundreds from $0$ to $1\,000$, place (approximately) the numbers $150$, $480$, $820$ and $990$.

**Solution of Exercise 14.7.**

$150$ sits halfway between $100$ and $200$; $480$ just before $500$; $820$ just after $800$; $990$ almost at $1\,000$.

**Exercise 14.8 ★.**

[Even](#def-g3-numbers-evenodd) or [odd](#def-g3-numbers-evenodd)? $34$; $57$; $70$; $2\,481$; $6\,548$.

**Solution of Exercise 14.8.**

[Even](#def-g3-numbers-evenodd): $34$, $70$, $6\,548$ (last digit $4$, $0$, $8$). [Odd](#def-g3-numbers-evenodd): $57$, $2\,481$ (last digit $7$, $1$).

**Exercise 14.9 ★.**

Count by steps: from $2\,970$, count five steps of $10$; from $860$, count four steps of $100$; from $9\,996$, count four steps of $1$. What do you notice at the end of the last one?

**Solution of Exercise 14.9.**

From $2\,970$: $2\,980$, $2\,990$, $3\,000$, $3\,010$, $3\,020$.

From $860$: $960$, $1\,060$, $1\,160$, $1\,260$.

From $9\,996$: $9\,997$, $9\,998$, $9\,999$, $10\,000$ — the last step crosses into a five-digit number: our whole chapter’s limit!

**Exercise 14.10 ★★.**

Using each of the digits $3$, $7$, $0$, $5$ exactly once, write the biggest possible four-digit number, then the smallest one (a number cannot start with $0$).

**Solution of Exercise 14.10.**

Biggest: $7\,530$ (digits in decreasing order). Smallest: $3\,057$ (smallest nonzero digit first, then the rest increasing — the $0$ right after the $3$).

**Exercise 14.11 ★★.**

I am a three-digit number. My digits are $2$, $5$ and $8$, I am [even](#def-g3-numbers-evenodd), and I am bigger than $800$. Who am I?

**Solution of Exercise 14.11.**

Bigger than $800$: the hundreds digit is $8$. [Even](#def-g3-numbers-evenodd): the units digit must be $2$ (using each of $2$, $5$, $8$ once). So the number is $852$.