Solution to

In problem "b" of the previous frame, the zero between the four and the

Frame 5-15.

one is not dropped. Only zeroes following the last non-zero digit can be

7

dropped without changing the value of the number.

a. 3.8 x 10

4

However, you may want to round the number to make it easier to use;

b. 4.01 x10

that is, you do not need a high degree of accuracy. For example,

4.01 x 10 4 rounded to the nearest ten-thousand can be expressed as 4

x 10 4.

4

Note: If you rounded 4.01 x 10

to the nearest thousand, you would

also get 4 x 10 4.

a. Change 3,756 to scientific notation. ________________

b. Change 3,756 to scientific notation

rounded to the nearest thousand.

________________

(Hint: Round first, then change to scientific notation.)

_______________________________________________________________________________________

Solution to

The preceding frames work fine for large numbers, but how about small

Frame 5-16.

numbers, like. 0.000000000065?

3

a. 3.756 x 10

Begin at the decimal point.

3

b. 4 x10

Move the decimal point to the right until it passes the first non-zero

number (the "6"). Count the number of places you are moving the

decimal.

You moved the decimal point 11 places to the right to obtain 6.5.

Therefore "P" equals "-11." Remember, if you move the decimal point to

the right, the exponent will be negative.

0.000000000065 = 6.5 x 10 11 .

Convert the following numbers to scientific notation.

a. 0.0072 _____________

b. 0.101

_____________

c. 3.9

_____________

[Note: Remember that 10 (or any number) raised to the zero power is

"1" and that any number times "1" remains the original number.]

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MD0900

5-10

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