---
title: "Numbers to 1000"
book: "Primary & Middle School Mathematics"
subject: math
language: en
chapter: 7
exercises: 10
source: https://one-course.com/books/math/1/en/chapter/7-numbers-to-1000
---

# Chapter 7 — Numbers to 1000

Grade 1 bundled units into tens ([Chapter 4](https://one-course.com/books/math/1/en/chapter/4-numbers-to-100#ch-g1-tens)); now ten tens bundle into a *hundred*, and the numbers stretch all the way to $1000$. Three digits, three jobs: hundreds, tens, units.

## 7.1 Hundreds, tens, units

**Definition 7.1 (Three places).**

A *hundred* is ten tens, that is ten bundles of ten. The number $346$ has three parts:

$$
346 = 3 \text{ hundreds} + 4 \text{ tens} + 6 \text{ units}
= 300 + 40 + 6 .
$$

![The place table of 346, read “three hundred forty-six”. (Bigger numbers wait for .)](https://one-course.com/images/onecourse/chapters/math-1/g2-numbers/fig-37c59d5f967c.svg)

*The place table of $346$, read “three hundred forty-six”. (Bigger numbers wait for [Chapter 14](https://one-course.com/books/math/1/en/chapter/14-numbers-up-to-10-000#ch-g3-numbers).)*

**Example 7.2 (The zero holds the place).**

“Three hundred and five” is $305$: three hundreds, *no* tens, five units. The $0$ keeps the $5$ in the units place. Without it, $35$ would be a completely different number.

**Example 7.3 (Exchanging).**

Ten units make a ten, ten tens make a hundred. So $10$ tens $= 100$, and $2$ hundreds $= 20$ tens. The number $250$ contains $25$ tens, not just the digit $5$.

## 7.2 Comparing and ordering

**Method 7.4 (Comparing three-digit numbers).**

1. More digits wins: $103 > 98$ ;
2. same length: compare from the left — hundreds first, then tens, then units. The first difference decides: $472 > 468$ because at the tens, $7 > 6$ .

**Example 7.5.**

Order $530$, $305$, $503$: hundreds first ($5$, $3$, $5$), so $305$ leads; between $530$ and $503$, the tens decide ($3 > 0$):

$$
305 < 503 < 530 .
$$

## 7.3 Jumps on the number line

**Method 7.6 (Adding tens and hundreds).**

On the line:

1. $+1$ / $-1$ : change the units;
2. $+10$ / $-10$ : change the tens ( $362 + 10 = 372$ );
3. $+100$ / $-100$ : change the hundreds ( $362 + 100 = 462$ ).

Only one digit moves each time — unless a place “fills up” and carries over, like $195 + 10 = 205$.

![Jumps from 362: a small hop of +10 changes the tens, a big hop of +100 changes the hundreds.](https://one-course.com/images/onecourse/chapters/math-1/g2-numbers/fig-60c5cceed837.svg)

*Jumps from $362$: a small hop of $+10$ changes the tens, a big hop of $+100$ changes the hundreds.*

## 7.4 Exercises

**Exercise 7.1 ★.**

How many hundreds, tens and units in: $258$; $470$; $600$; $909$?

**Solution of Exercise 7.1.**

$258$: $2$ hundreds, $5$ tens, $8$ units. $470$: $4$, $7$, $0$. $600$: $6$, $0$, $0$. $909$: $9$, $0$, $9$.

**Exercise 7.2 ★.**

Write the number: $4$ hundreds, $0$ tens, $7$ units; $6$ hundreds and $3$ tens; ten hundreds.

**Solution of Exercise 7.2.**

$407$; $630$; $1000$.

**Exercise 7.3 ★.**

Write in digits: two hundred sixteen; five hundred and four; seven hundred ninety.

**Solution of Exercise 7.3.**

$216$; $504$; $790$.

**Exercise 7.4 ★.**

Decompose as in [Definition 7.1](#def-g2-numbers-places): $438$; $702$; $560$.

**Solution of Exercise 7.4.**

$438 = 400 + 30 + 8$; $702 = 700 + 2$; $560 = 500 + 60$.

**Exercise 7.5 ★.**

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

$$
327 \;?\; 372, \qquad
580 \;?\; 508, \qquad
199 \;?\; 200, \qquad
640 \;?\; 604 .
$$

**Solution of Exercise 7.5.**

$327 < 372$; $580 > 508$; $199 < 200$; $640 > 604$.

**Exercise 7.6 ★.**

Order from smallest to biggest: $430$; $304$; $340$; $403$.

**Solution of Exercise 7.6.**

$304 < 340 < 403 < 430$.

**Exercise 7.7 ★.**

Compute by jumping on the line: $253 + 10$; $253 + 100$; $480 - 10$; $716 - 100$.

**Solution of Exercise 7.7.**

$253 + 10 = 263$; $253 + 100 = 353$; $480 - 10 = 470$; $716 - 100 = 616$.

**Exercise 7.8 ★.**

Count on: $195, 205, 215, ?, ?$. $300, 400, 500, ?, ?$. Careful with the first one!

**Solution of Exercise 7.8.**

$195, 205, 215, 225, 235$ (the first jump fills the tens and carries). $300, 400, 500, 600, 700$.

**Exercise 7.9 ★.**

A shop has $6$ boxes of $100$ pencils and $5$ loose pencils. How many pencils in all?

**Solution of Exercise 7.9.**

$6$ hundreds and $5$ units: $600 + 5 = 605$ pencils.

**Exercise 7.10 ★★.**

Using the digits $2$, $5$ and $8$ once each, write the biggest three-digit number and the smallest one. How far apart are they? (You may add them up on the line by jumps.)

**Solution of Exercise 7.10.**

Biggest: $852$. Smallest: $258$. Distance: $852 - 258 = 594$.