Primary & Middle School Mathematics · Grades 1–9

7Numbers to 1000

Grade 1 bundled units into tens (Chapter 4); 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 .) — The place table of $346$ , read “three hundred forty-six”. (Bigger numbers wait for Chapter 14.)

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)

More digits wins: $103 > 98$ ;
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:

$+1$ / $-1$ : change the units;
$+10$ / $-10$ : change the tens ( $362 + 10 = 372$ );
$+100$ / $-100$ : 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. — 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

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

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

Solution of Exercise 7.3.

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

Exercise 7.4 ★

Decompose as in Definition 7.1: $438$ ; $702$ ; $560$ .

Solution

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

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

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

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

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

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

Solution of Exercise 7.10.

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