Patterns in multiplying by 10 - University of Idaho

[Pages:2]Patterns in multiplying by 10.

Name _______________________

Adapted from Powers of Ten, Mathematics in Context, Britannica Mathematics System.

If you multiply a number by 10, notice what happens: 8 ?1080 ?10800 ?108000 . AS

you can see from the pattern in the arrow string, every time you multiply a whole number by 10, one zero is added to the number (now why does that happen??)

Notice that 345, 982 ?100 34, 598, 200 results in the same answer as

345,982 ?103, 459,820 ?1034, 598, 200

1. Notice that we could use that idea to compute 800 ? 200 by doing the following: 800 ? 200 = 800 ? 2 ? 10 ? 10 so we get 1600 ? 10 ? 10 = 160,000 Use that idea to compute the following without using a calculator. For d and e, show how you could decompose the numbers into products of 10 so you can figure out how many zeroes your answer has.

a. 300 ?10 =

b. 3,000 ?10?10

c. 7,000 ? 2000 (show what you could do with the 2000 so it fits the pattern above of multiplying by 10s)

d. 1,000 ? 1,000 ? 100 ? 10

e. 1,000 ? 100,000

2. What if you now multiply a number with a decimal by 10. Use your calculator to do the following:

3.5 ?10 _______ ?10 ________

4.875 ?10 _______ ?10 ________ ?10 ________

3. What are the similarities and differences between multiplying a whole number by 10 and multiplying a decimal by 10?

4 . Calculate the following without using a calculator a. 2.6 ? 10 = _______ ? 10 = ________ ? 10 = _______

b. 3.125 ? 10 = ______ ? 10 = ________ ? 10 = _______

5. How many times would you have to multiply 1 by 10 to get:

a. one thousand

b. one hundred thousand

c. one million

d. 100 million

5. We use exponents to write repeated multiplication: 2 ? 2 ? 2 = 2 3.

Since 100,000 = 1 ? 10 ? 10? 10 ? 10 ? 10, you can rewrite it as 1 ? 105, or just 105. Write the

following numbers in exponential notation.

i. 1,000

ii. 1, 000,000,000

iii. 10,000,000,000

6. Write each of these exponential numbers in expanded form ? example 10 3 = 1000

a. 104

b. 106

c. 1012

7. Calculate the following and write your answer in exponential form (or notation) example: 10 3 ?

102 = 1000 ? 100 = 100000 or 105

a. 104 ? 10

b. 108 ? 100

c. 1011 ? 103.

d. What happens to the exponent of a power of 10 each time you multiply by 10?

8. Calculate the following and write the answer in exponential form.

a. 106 ? 102

b. 108 ? 107

c. 104 ? 105 ?10 2

Scientific Notation.

9. The distance of Jupiter from the sun is 778,000,000 km. There are different ways to write this

number. Fill in the missing blanks in the table below following the pattern shown.

778,000,000 ? 1 =

778,000,000 ? 100

77,800,000 ? 10 =

77,800,000 ? 101

7,780,000

? 100 =

7,780,000 ? 102

___________ ? _______ = _______________ ? ____

____________ ? _______ = _______________ ? ____

____________ ? _______ = _______________ ? ____

____________ ? _______ = ________________ ? ____

77.8

? _______ = ________________ ? ____

7.78

? _______ = ________________ ? ____ THIS LAST ONE IS CONSIDERED

AS BEING IN SCIENTIFIC NOTATION.

10. This method of writing a number as a number between 1 and 10, multiplied by 10 to a power

is referred to as scientific notation. (You may have to look up some information in the book

about this) Fill in the missing numbers in the table.

Diameter

distance from sun (km)-not in

distance from sun

( in km)

scientific notation

in scientific notation

sun earth Jupiter Mars Mercury Neptune Pluto Saturn Uranus Venus

1, 392, 000 12,760 143,000 6,790 4,900 50,000 2,300 121,000 51,000 12,100

0 778,000,000 228,000,000 4,500,000,000

2,870,000,000 108,000,000

0 1.5 ? 108

5.8 ? 107

5.9 ? 109 1.43 ? 109

a. What planet is the smallest planet in the solar system? b. The largest planet? (Note the sun is a star, not a planet)

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