Data, Large Numbers and Scientific Notation

Ms. Stewart

Grade 7 MathCOPY SLIDES WHEN YOU SEE THIS

There are many ways to represent one million forty-five thousand six

hundred.

Can you think of a way we can represent this number?

Strategies for Writing Large Numbers

You can write the number in standard form:

Put each digit in its place value position and put zeros in the remaining places.

Millions Thousands Hundreds

H T O H T O H T O

1 0 4 5 6 0 0

You can write the number in expanded form:

You can use powers of 10 in the expanded form.

1 000 000 + 40 000 + 5000 + 600

= (1 X 1 000 000) + (4 X 10 000) + (5 X 1000) + (6 X 100)

= (1 X 106) + (4 X 104) + (5 X 103) + (6 X 102)

You can use 1 million as a benchmark.

What is a benchmark?

A standard against which things (numbers in our case) may be compared.

1 045 600 is more than a million but less than 2 million, therefore we can write:

1.0456 million

You can write the number in scientific notation:

Express the number as a number between 1 and 10 multiplied by a power of ten.

1 045 600

= 1.0456 X 106

Writing a Number in Scientific NotationWrite 48 200 000 in scientific notation.

Step 1:Move the decimal point to the LEFT until the

number is between 1 and 104.8200000 4.82

Count how many places you have moved the decimal point.

We moved the decimal 7 places.

Writing a Number in Scientific Notation

Step 2:

We stated that we moved the decimal 7 places therefore our power of 10 would be 107

So we would then state:

48 200 000 = 4.82 X 107

Using Negative Powers of 10

Can I write this number in scientific notation?

0.000092

YES! I can write this number in scientific notation by using negative powers of 10.

Using Negative Powers of 10

Step 1:

Move the decimal point to the RIGHT until the number is between 1 and 10

0.000092 9.2

Count how many places you have moved the decimal point.

We moved the decimal 5 places.

Writing a Number in Scientific Notation

Step 2:

We stated that we moved the decimal 5 places therefore our power of 10 would be 10-5

So we would then state:

0.000092 = 9.2 X 10-5