Chapter 4 Decimal Multiplication and Division
4.5 Multiplying and Dividing by Powers of Ten
Pages­ 193­197
Title: Jan 30­8:38 AM (1 of 5)
NOTES (4.5) Multiplying & Dividing by Powers of Ten
* Key Concept p. 193* Multiplying by whole # 10’s
move the decimal point to the right for every zero in the power of 10
2.795 x 10 = 27.95
2.795 x 1000 = 2795
Multiplying by Decimal Powers of 10
move the decimal point to the left for each decimal place in the power of 10
2.795 x 0.0 1 = 0.02795
_ _ _ 2. 795 x 0.0 0 0 1 = 0.0002795
*Key Concept p. 194*
In division, move opposite direction of the multiplication rule.
Title: Jan 23­6:42 PM (2 of 5)
Dividing by whole # 10's
move decimal pt to the left for every zero in the power of 10
2.795 ÷ 10 = 0.2795
_ _ 2.795 ÷ 1 0 0 0 = 0.002795
Dividing by Decimal Powers of 10
move decimal point to the right for each decimal
place in the power of 10
2. 7 9 5 ÷ 0. 0 1 = 279.5
2. 7 9 5 _ ÷ 0. 0 0 0 1 = 27950
Use notes ↑ to complete # 16­19 all
Do #26­30 even like this
25) 8.3x = 8300
8.3 * 1 0 0 0
8. 3 0 0 Title: Jan 23­6:51 PM (3 of 5)
27) 5 ÷ x + 0.2 = 0.25
5 ÷ 1 0 0 + 0.2
0. 0 5 0.05 + 0.2
29) 3 (6 ÷x ) = 1800
3 ( 6 ÷ 0.0 1)
3( 6 _ _ )
3 * 600
To write numbers in scientific notation
1) Write number without the commas
2) Put a decimal point between first two digits
3) Count all numbers to the right of the decimal point
4) Rewrite # as a product of the decimal # you created & a power
of 10 (as found in step 3 above)
Title: Jan 23­7:02 PM (4 of 5)
Do #36 & 38 like this
37) 49,200
4.9 2 0 0 4.92 x 104
39) 93,000,000
9.3 0 0 0 0 0 0
9.3 x 107
To change from scientific notation to standard form, move the decimal point to the right the same number of places as the exponent.
Do #40 & 42 like this
41) 2.1 x 1018
2. 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2,100,000,000,000,000,000
43) 1.7 x 1010
1. 7 0 0 0 0 0 0 0 0 0 17,000,000,000
Title: Jan 23­7:27 PM (5 of 5)