Question

covering the ideas

1. what u.s. coin has each stated value?

a. 10^(-2) dollar b. 1/10 dollar
in 2 and 3, write the general rule for multiplying a decimal by the given number.

1. 0.001 3. 1/100000

in 4 - 9, rewrite each number in decimal notation.

1. 1/10×372 5. 437000×0.00001
2. 87.51×10^(-4) 7. 5^0
3. forty billionths 9. seventy - two millionths
4. what decimal can you use to multiply by 1/1000 on a calculator?
5. describe how the names of the negative integer powers of 10 correspond to the names of the positive integer powers of 10.
6. write each number as a power of 10.

a. one millionth b. 1/10000 c. one quintillionth

1. what is the general rule for multiplying a decimal by a negative integer power of 10?

applying the mathematics

1. if 895.23×10^x = 0.00089523, what is x?
2. describe the results you obtained in the activity.
3. how is 0^10 different from 10^0?
4. candace earns $35.00 per week. she decides to give 1/10 of that to charity. how much will she give per week?
5. arrange from least to greatest.

1 10^(-3) 0.0001 1/10 10^2

1. use your calculator to evaluate 1/x^4 when x is

a. 5. b. 10. c. 0.5.

1. in the metric system, all the prefixes have consistent meanings. for example, kilo - means 1000; centi - means 1/100, or 0.01; and milli - means 1/1000, or 0.001. use this information to explain the meaning of each term.

a. kilogram b. centimeter c. milliliter

Explanation:

Step1: Solve problem 1a

$10^{-2}$ dollar means 1 cent since $10^{-2}=\frac{1}{100}$ and 1 dollar = 100 cents.

Step2: Solve problem 1b

$\frac{1}{10}$ dollar means 10 cents since $\frac{1}{10}\times100 = 10$ cents.

Step3: Solve problem 2

When multiplying a decimal by 0.001 (or $10^{-3}$), move the decimal - point 3 places to the left.

Step4: Solve problem 3

When multiplying a decimal by $\frac{1}{100000}$ (or $10^{-5}$), move the decimal - point 5 places to the left.

Step5: Solve problem 4

$\frac{1}{10}\times372 = 37.2$ since multiplying by $\frac{1}{10}$ is equivalent to moving the decimal - point 1 place to the left.

Step6: Solve problem 5

$437000\times0.00001=4.37$. First, $437000 = 4.37\times10^{5}$ and $0.00001 = 10^{-5}$, then $4.37\times10^{5}\times10^{-5}=4.37\times10^{5+( - 5)}=4.37$.

Step7: Solve problem 6

$87.51\times10^{-4}=0.008751$. Move the decimal - point 4 places to the left.

Step8: Solve problem 7

$5^{0}=1$. Any non - zero number to the power of 0 is 1.

Step9: Solve problem 8

Forty billionths is written as 0.000000040 in decimal notation.

Step10: Solve problem 9

Seventy - two millionths is written as 0.000072 in decimal notation.

Step11: Solve problem 10

To multiply by $\frac{1}{1000}$ (or $10^{-3}$) on a calculator, you can use 0.001.

Step12: Solve problem 11

The names of the negative integer powers of 10 are the reciprocals of the names of the positive integer powers of 10. For example, a million is $10^{6}$ and a millionth is $10^{-6}$.

Step13: Solve problem 12a

One millionth is $10^{-6}$.

Step14: Solve problem 12b

$\frac{1}{10000}$ is $10^{-4}$.

Step15: Solve problem 12c

One quintillionth is $10^{-18}$.

Step16: Solve problem 13

When multiplying a decimal by a negative integer power of 10 ($10^{-n}$, where $n$ is a positive integer), move the decimal - point $n$ places to the left.

Step17: Solve problem 14

Given $895.23\times10^{x}=0.00089523$. Since $895.23$ becomes $0.00089523$, the decimal - point moves 6 places to the left, so $x=-6$.

Step18: Solve problem 17

Candace earns $35$ per week and gives $\frac{1}{10}$ of it to charity. So she gives $35\times\frac{1}{10}=3.5$ dollars per week.

Step19: Solve problem 18

First, convert all numbers to decimal form: $10^{-3}=0.001$, $\frac{1}{10}=0.1$, $10^{2}=100$. Arranging from least to greatest: $0.0001,10^{-3}, \frac{1}{10},1,10^{2}$.

Step20: Solve problem 19a

When $x = 5$, $\frac{1}{x^{4}}=\frac{1}{5^{4}}=\frac{1}{625}=0.0016$.

Step21: Solve problem 19b

When $x = 10$, $\frac{1}{x^{4}}=\frac{1}{10^{4}}=0.0001$.

Step22: Solve problem 19c

When $x = 0.5=\frac{1}{2}$, $\frac{1}{x^{4}}=\frac{1}{(\frac{1}{2})^{4}}=16$.

Step23: Solve problem 20a

A kilogram means 1000 grams. The prefix "kilo - " indicates a factor of 1000.

Step24: Solve problem 20b

A centimeter means $\frac{1}{100}$ of a meter. The prefix "centi - " indicates a factor of $\frac{1}{100}$ or 0.01.

Step25: Solve problem 20c

A milliliter means $\frac{1}{1000}$ of a liter. The prefix "milli - " indicates a factor of $\frac{1}{1000}$ or 0.001.

Answer:

1a. 1 cent
1b. 10 cents

1. Move the decimal - point 3 places to the left.
2. Move the decimal - point 5 places to the left.
3. 37.2
4. 4.37
5. 0.008751
6. 1
7. 0.000000040
8. 0.000072
9. 0.001
10. The names of the negative integer powers of 10 are the reciprocals of the names of the positive integer powers of 10.

12a. $10^{-6}$
12b. $10^{-4}$
12c. $10^{-18}$

1. Move the decimal - point $n$ places to the left when multiplying by $10^{-n}$ ($n$ is a positive integer).
2. $x=-6$
3. $3.5$ dollars
4. $0.0001,10^{-3}, \frac{1}{10},1,10^{2}$

19a. 0.0016
19b. 0.0001
19c. 16
20a. 1000 grams
20b. $\frac{1}{100}$ of a meter
20c. $\frac{1}{1000}$ of a liter