10.1.9 Very Big and Very Small Numbers

The calculator will convert very large numbers (numbers over a million) to scientific notation. Enter the number and click the Equals key or press Enter.

Try this with the number 123456789. Enter it into the calculator and click the Equals key. You should see the number 123456789 in the white window and written in scientific format in the black window.

Similarly, very small numbers (numbers in scientific notation which have a power of 10 that is –6 or smaller) are automatically written in scientific notation. Enter 0.000000123 into the calculator, then click the Equals key or press Enter and see what happens. You should see this:

Working with Numbers in Scientific Notation

Here are activities to practice working with numbers in scientific notation.

Activity Symbol Activity: Adding Very Big Numbers

Add 9.2 multiplication 10 super 10 to 9.5 multiplication 10 super nine by entering both numbers in scientific notation. Give your answer first in normal format, then in scientific notation.

Hint Symbol

Comment

Use the The button being shown is the power of ten key. key, remembering to close the parentheses after you have entered the power of 10.

Solution Symbol

Answer

Here is what you should see on the calculator:

The calculation is shown correctly in the black window. But be careful, because there is only space for part of the answer. The full answer is shown in the white window. Clicking on the Equals key again gives the answer in scientific notation. The calculation is shown as follows:

9.2 multiplication 10 super 10 plus 9.5 multiplication 10 super nine equals 101 comma 500 comma 000 comma 000 equals 1.015 multiplication 10 super 11

Activity Symbol Activity: Multiplying Very Small Numbers

If you multiply two very small numbers, then your answer is even smaller. Try this with the following calculation:

3.3 multiplication 10 super six minus multiplication 4.2 multiplication 10 super five minus

Hint symbol

Comment

Do you remember how to enter negative numbers? Use the The button being shown is the positive or negative value key. key.

Make sure you watch the white window as you enter the calculation. In particular, remember to close the parentheses after you have entered each power of 10.

Solution Symbol

Answer

Once again, the full answer doesn’t show in the black window but is given below. Clicking on the Equals key or pressing Enter will give the answer in scientific notation in the black window.

equation sequence 3.3 multiplication 10 super six minus multiplication 4.2 multiplication 10 super five minus equals 0.0000000001386 equals 1.386 multiplication 10 super one minus times zero

The calculator should show this:

10.1.8 The Case of the Missing Parentheses

10.1.10 How Many Bees?