B. Number · Number Sense: Big Numbers, Square Roots and Rational Numbers

Comparing, Ordering and Using Big Numbers

B1.1 A1About 40 minutes

Learning goals

I can compare and order whole numbers up to one billion.
I can compare numbers written in expanded form with powers of ten.
I can round big numbers to make them easier to understand.
I can describe ways that big numbers are used in everyday life.

Words to know

compare
Decide which of two numbers is greater, or if they are equal. Use >, < or =.

order
Put numbers from least to greatest, or greatest to least.

round
Change a number to a nearby, simpler number, like 487 302 115 → about 487 million.

estimate
A number that is close to the exact amount.

Remember from Grade 6

In Grade 6 you compared numbers up to one million: first count the digits, then compare place by place from the left. The same steps work all the way up to one billion.

Which song is more popular?

Here are some made-up numbers of plays for songs on a music app.

Song A: 487 302 115 plays
Song B: 92 845 300 plays
Song C: 487 320 015 plays
Song D: 1 000 000 000 plays

Which song has the most plays? Which has the fewest? Songs A and C look almost the same. How can you tell which is greater?

Steps to compare big numbers

Count the digits. A number with more digits is greater. (Song D has 10 digits, so it is the greatest. Song B has only 8 digits, so it is the least.)
If they have the same number of digits, line them up by place value.
Compare from the left. The first place where the digits are different decides.

	Hundred millions	Ten millions	Millions	Hundred thousands	Ten thousands	Thousands	Hundreds	Tens	Ones
Song A	4	8	7	3	0	2	1	1	5
Song C	4	8	7	3	2	0	0	1	5

The first difference is in the ten thousands place: 2 > 0, so Song C has more plays.

Plays shown in millions. Song B is near 93 million. Songs A and C are almost on top of each other near 487 million. Song D is at 1000 million, which is one billion.

Worked example

Example 1: Order the songs

Order the songs from least to greatest number of plays.

Song B has 8 digits, so it is the least.
Song D has 10 digits, so it is the greatest.
Songs A and C both have 9 digits. In the ten thousands place, C has 2 and A has 0, so C > A.

B (92 845 300) < A (487 302 115) < C (487 320 015) < D (1 000 000 000)

Worked example

Example 2: Compare with powers of ten

Which is greater: 7 × 10⁸ or 8 × 10⁷?

7 × 10⁸ = 700 000 000 (seven hundred million).
8 × 10⁷ = 80 000 000 (eighty million).
Look at the power of ten first. 10⁸ is bigger than 10⁷, so 7 × 10⁸ wins even though 7 < 8.

7 × 10⁸ > 8 × 10⁷

Drawn to scale: 7 × 10⁸ is almost 9 times as long as 8 × 10⁷. The power of ten matters more than the digit in front of it.

Worked example

Example 3: Round to make sense of a number

Round 487 302 115 to the nearest million and to the nearest hundred million.

Nearest million: the millions digit is 7. Look at the digit to its right (hundred thousands): 3. 3 is less than 5, so keep 7 and change the rest to zeros: 487 000 000.
Nearest hundred million: the hundred millions digit is 4. Look at the ten millions digit: 8. 8 is 5 or more, so round up: 500 000 000.

About 487 million, or about 500 million. A news story might say "almost half a billion plays".

Big numbers in everyday life

Big numbers describe:

Distances in space. Earth is about 150 million km from the Sun. (The exact distance changes a little during the year.)
Areas of large places. Canada's total area is about 9 984 670 km², almost 10 million square kilometres.
Money for big projects, like a city's yearly budget or building a new hospital.
Computer storage. A gigabyte is about one billion bytes.
Populations of countries and cities.

People often round big numbers or write them as "2.5 million" because exact numbers are hard to read and often not needed.

Be a good sport, be a good checker

When you compare with a partner, explain which place decided the answer. If you disagree, line the numbers up in a place value chart together. Finding a mistake is a win for both of you.

Hands-on activity

Big numbers in the news

You need: a newspaper, a news website or magazine (with a grown-up), paper and a pencil.

With your grown-up, find five numbers in the millions or close to a billion. Look for words like "million", "billion", populations, budgets, distances or views.
For each one, write it in standard form (for example, $4.5 million → $4 500 000).
Order your five numbers from least to greatest.
Round each one to the nearest million.
Talk about it: Why did the writer round the number (or not)? Would the exact number be better?

If you can't find a news source, use these: 3.2 million, 850 000, 47 million, 0.5 billion, 12 600 000.

Just for fun

What did 487 302 115 say to 487 320 015?

"We're practically twins... until the ten thousands place!"

Your turn

Use >, < or =: 76 450 000 ___ 8 950 000

Use >, < or =: 503 120 400 ___ 503 102 400

Order from least to greatest: 64 000 000, 640 000 000, 6 400 000, 46 000 000

Round 238 649 000 to the nearest million.

A headline says 4.7 million. Write it in standard form.

Which is greater: 7 × 10⁸ or 8 × 10⁷?

Earth is about 150 million km from the Sun. Write this in standard form and in expanded form with powers of ten.

More practice: warm-up

Use >, < or =: 9 000 000 ___ 10 000 000

Use >, < or =: 450 000 000 ___ 405 000 000

Which is greatest: 99 999 999, 100 000 000 or 98 765 432?

Round 61 200 000 to the nearest ten million.

Write 2.5 million in standard form.

More practice: on your own

Order from greatest to least: 1 000 000 000, 999 999 999, 1 × 10⁸, 9 × 10⁷ + 9 × 10⁶

What number is halfway between 300 million and 400 million?

A made-up city budget is $846 500 000. Round it to the nearest hundred million and to the nearest million. Which is more useful in a news headline?

Is 7 345 000 closer to 7 million or 8 million? How do you know?

Two made-up videos have 58 096 410 and 58 960 140 views. Which has more? About how many more?

Challenge

Write a 9-digit number that rounds to 500 000 000 (nearest hundred million) and to 450 000 000 (nearest ten million).

Suppose one photo file uses 4 000 000 bytes. About how many photos fit in 1 000 000 000 bytes?

Canada's total area is about 9 984 670 km². Kai says this rounds to 9 000 000 to the nearest million, because 9 is in the millions place. Is he right?

Check your understanding

Quiz

Which number is the greatest?

Round 345 678 912 to the nearest million.

Write 3.2 million in standard form.

Which sign makes this true? 602 041 000 ___ 602 401 000

Which is the largest?

Why might a news report say Earth is "about 150 million km" from the Sun?

For parents and teachers

Big idea: B1.1 also asks students to compare numbers up to one billion and describe various ways they are used in everyday life. Your child should be able to say which place decides a comparison and why we often round big numbers.

Common difficulties:

Comparing only the first digit (thinking 98 000 000 > 809 000 000). Always count digits first.
Comparing the digit instead of the power in 7 × 10⁸ vs. 8 × 10⁷.
Rounding by looking at the wrong digit. Only the digit just to the right of the rounding place decides.

How to help: Do the news activity together and talk about where big numbers show up (space, money, populations, computer storage). This lesson also builds A1 skills: communicating clearly, and treating mistakes as useful information.