Understanding other powers of 10 within one million

Mathematics - Integers and Decimals

Miss Rodda-Winden

In this lesson, you will need:

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Exercise book or paper

Pencil

Ruler

s

s

s

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Image credit: Pixabay

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Starter quiz

Place value review

What is one million?

Powers of 10 within one million

Exit quiz

Keywords

Place value - the value of a digit depending on its position within a number.

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Place value chart - a visual tool for demonstrating the place value of digits within a number.

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Number line - a visual tool for showing the relationships between values. Numbers increase in value from left to right.

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Powers of 10 - the amount of times 10 is multiplied by itself, indicated by a small number to the upper-right of the 10. For example, 10³.

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Place value review

What is Place Value?

• Hindu-Arabic number system
• decimal or base-ten
• ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9
• each digit in a number has a place value depending on its position

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Place Value to the Millions

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Here is the number 1 345 127 represented using a place value chart:

Because the value of each digit within the number depends on its place or position, the 1 in the millions place has a different value to the 1 in the hundreds place.

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Place Value to the Millions

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Here is the number 1 345 127 represented using a place value chart:

• The 1 in the millions place has a value of 1 000 000 or one million.
• The 1 in the hundreds place has a value of 100 or one hundred.

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In the number 1 345 127 the 5 is in the tens of thousands place.

The 5 is in the thousands place.

True

False

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Expanded Notation

• Numbers beyond the thousands place value cannot easily be represented using base-10 blocks.

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• Instead, we can represent these numbers using expanded notation.

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Expanded Notation

Here is the number 1 345 127 represented using the additive approach to expanded notation.

1 000 000 +

300 000 +

40 000 +

20 +

7

100 +

5 000 +

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Expanded Notation

Here is the number 1 345 127 represented using the multiplicative approach to expanded notation.

(1x1 000 000) +

(3x100 000) +

(4x10 000) +

(2x10) +

(7x1)

(1x100) +

(5x1,000) +

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Expanded Notation

What similarities and differences do you notice between the additive approach and the multiplicative approach?

(1x1 000 000) +

(3x100 000) +

(4x10 000) +

(2x10) +

(7x1)

(1x100) +

(5x1 000) +

1 000 000 +

300 000 +

40 000 +

20 +

7

100 +

5 000 +

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What is one million?

What do you know about the number one million?

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What do you know about the number one million?

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7 digits

$1 000 000

Populations are often counted in millions

What is one million?

How long would it take to count from one to one million?

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How large would a fish tank need to be to hold one million goldfish?

One million is a big number… but just how big is it?

How long is one million millimeters?

How heavy is one million grams?

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What is one million?

One million represented on a number line.

Draw this number line and locate the following numbers:

• 200 000
• 900 000
• 650 000

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0

500 000

1 000 000

100 000

700 000

200 000

300 000

400 000

600 000

800 000

900 000

650 000

What is one million?

One million represented on a number line.

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Draw this number line and locate the following numbers:

• 750 000
• 250 000
• 900 000

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0

500 000

1 000 000

250 000

750 000

900 000

What is one-million?

One-million represented on a number line.

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Draw this number line and locate the following numbers:

• 500 000
• 750 000
• 300 000

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750 000

0

500 000

1 000 000

300 000

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Powers of 10 within one million

Place value to millions

• The value of each digit within a number depends on its position.
• The value of each place increases from right to left, multiplied by 10.

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x10

x10

x10

x10

x10

x10

Place value to millions

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x10

1

1 x 10 = 10

10 x 10 = 100

x10

x10

10 x 10 x 10 = 1000

Place value to millions

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x10

2

3 x 10 = 30

8 x 10 x 10 = 800

x10

x10

3 x 10 x 10 x 10 = 3000

Place value increases by multiples of 10 from right to left.

True

False

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Powers of 10

• Representing larger numbers using multiplication number sentences takes up a lot of space.
• Powers of 10 is a handy method of writing down very large numbers.

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Powers of 10

10³

The exponent tells us how many times we need to multiply 10 by itself

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10 x 10 x 10

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1,000

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Powers of 10

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• Representing larger numbers using multiplication number sentences takes up a lot of space.
• Powers of 10 is a handy method of writing down very large numbers.

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Powers of 10 in action

• NASA estimates the mass of the Earth to be approximately 5,970,000,000,000,000,000,000,000kg
• We can use powers of 10 to represent this number in a more manageable way

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Image credit: Pixabay

Powers of 10 in action

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5,970,000,000,000,000,000,000,000

5.97 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10

5.97 x 10²⁴

Image credit: Pixabay

Powers of 10

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1. Divide the number by its place value

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600 000 ÷ 100 000 = 6

• Multiply by the appropriate power of 10

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600 000 = 6 x 10⁵

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How do we represent numbers using powers of 10? Let’s take the number 600 000.

Powers of 10

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• Divide the number by its place value

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467 000 ÷ 100 000 = 4.67

• Multiply by the appropriate power of 10

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467 000 = 4.67 x 10⁵

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Let’s use the same process to represent 467 000 using powers of 10.

Powers of 10

Match the powers of 10 with the correct number

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1 000 000

10⁵

1 000

10⁴

100 000

10⁶

10 000

10³

Powers of 10

Match the powers of 10 with the correct number

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1 000 000

10⁶

1 000

10³

100 000

10⁵

10 000

10⁴

Powers of 10

Match the powers of 10 with the correct number

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8 000

2 x 10⁵

15 000

1.5 x 10⁴

200 000

9 x 10⁶

9 000 000

8 x 10³

Powers of 10

Match the powers of 10 with the correct number

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8 000

2 x 10⁵

15 000

1.5 x 10⁴

200 000

9 x 10⁶

9 000 000

8 x 10³

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Independent Activity

Independent activity

1. Represent 3 457 845 using:
1. a place value chart
2. expanded notation - additive approach
3. expanded notation - multiplicative approach
2. Draw a number line from zero to one million. Show these numbers on it:
• 550 000
• 200 000
• 800 000
3. Represent the following numbers using powers of 10:
• 300 000
• 75 000
• 987 000

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Independent activity - answers

1. Represent 3 457 845 using:
• place value chart

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• expanded notation - additive approach

3 000 000 + 400 000 + 50 000 + 7 000 + 800 + 40 + 5

• expanded notation - multiplicative approach

(3 x 1 000 000) + (4 x 100 000) + (5 x 10 000) + (7 x 1 000) + (8 x 100) + (4 x 10) + (5 x 1)

Independent activity - answers

• Draw a number line from zero to one-million. Show these numbers on it:
• 550 000
• 200 000
• 800 000

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40

550 000

0

500 000

1 000 000

200 000

800 000

Independent activity - answers

• Represent the following numbers using powers of 10:
• 300 000

3 x 10⁵

• 75 000

7.5 x 10⁴

• 987 000

9.87 x 10⁵

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42

Starter quiz

Place value review

What is one million?

Powers of 10 within one million

Exit quiz

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