From standard form to scientific notation:

Practice: Write the number 28 000 in scientific notation.

Solution Steps

(a) The corresponding number between 1 and 10 is 2.8.

Next step...

(b) For 28000=28000.0 to "become" 2.8 we need to move the decimal point 4 places to the left.

Answer:

28000=2.8 \times 10^4 .

Practice: Write the number 0.003934 in scientific notation.

Solution Steps

(a) The corresponding number between 1 and 10 is 3.934.

Next step...

(b) For 0.003934 to "become" 3.934 we need to move the decimal point 3 places to the right.

Answer:

0.003934=3.934 \times 10^{-3} .

From scientific notation to standard form:

Practice: Write the number -7 \times 10^5 in standard notation.

Solution Steps

(a) A positive exponent means we are talking about a "big" number, that is a number between 0 and 1; the minus sign means we are talking about a negative number. So the result must be a big negative number.

Next step...

(b) We move the decimal point 5 places to the right.

Answer:

-7 \times 10^5 = -700\,000 .

Practice: Write the number 4.02 \times 10^{ - 3} in standard notation.

Solution Steps

(a) A negative exponent means we are talking about a "small" number.

Next step...

(b) We move the decimal point 3 places to the left.

Answer:

4.02 \times 10^{ - 3} = 0.00402 .