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Scientific Notation

Scientific notation is used to express very large numbers.

Scientific Notation

A positive number is written in scientific notation if it is written in the form:

a × 10

r

where a is a number between 1 and 10 and r is a power of 10.

In other words, a number in scientific notation is written as the product of a number and a power

of 10. The number has one digit to the left of the decimal point. The power of ten indicates how

many places the decimal point was moved.

The decimal number 650,000 written in scientific notation would be 6.5 × 10

5

because the

decimal point was moved 5 places to the left to form the number 6.5. It is equivalent to

6.5(10)(10)(10)(10)(10).

Example: Write the decimal number 235,000 in scientific notation.

Solution: Place a decimal point in 235 (the non-zero part of 235,000) so that it is a number

between 1 and 10.

2.35

Count the number of decimal places required to move the decimal point back to its

original position.

2.35000

5 places

Write in scientific notation with 5 as the power of 10.

2.35 × 10

5

Practice: Write the numbers in scientific notation.

a) 256,000,000,000,000

b) 600,000

Solution: a) 256,000,000,000,000 = 2.56 × 10

14

b) 600,000 = 6 × 10

5

To convert a number from scientific notation to decimal form we reverse the previous steps.

Example: Write 4.27 × 10

7

in decimal form.

Solution: 4 2700000

= 42,700,000

7 places

Practice: Write the numbers in decimal form.

a) 2.3 × 10

5

b) 4.5 × 10

9

Solution: a) 230,000

b) 4,500,000,000

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Parent category: Education