Scientific notation

Three quick questions from earlier lessons.

The Sun is about 150,000,000 km from Earth. Which is the same number?

Scientific notation: one digit before the point, times a power of 10.

A number is in scientific notation when it is written

a \times 10^n

with

1 \le a < 10

and

n

an integer. Large numbers have positive

n

; numbers between 0 and 1 have negative

n

. Comparing: first compare the powers of 10.

$0.00042$ .

4.2

Move the point 4 places right.

4.2 \times 10^{-4}

Small number: negative exponent.

Your turn: $6{,}000{,}000 = 6 \times 10^{?}$ .

6

Six zeros.

Write $900000000$ in scientific notation as $9 \times 10^{?}$ . What is the exponent?
Write $8000000$ in scientific notation as $8 \times 10^{?}$ . What is the exponent?

When $2 \times 10^{-6}$ is written as a decimal, how many zeros are there between the decimal point and the digit 2?
When $6 \times 10^{-8}$ is written as a decimal, how many zeros are there between the decimal point and the digit 6?

Three questions to check you have got it.

Write $900000000$ in scientific notation as $9 \times 10^{?}$ . What is the exponent?
Write $8000000$ in scientific notation as $8 \times 10^{?}$ . What is the exponent?
Write $800000000$ in scientific notation as $8 \times 10^{?}$ . What is the exponent?

Scientific notation

$a \times 10^n$ with $1 \le a < 10$ .

Watch out: count the places the point moves, not the digits.

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