Question

write each number in scientific notation or in standard form.
(9) a. 36000000
b. 105000
c. 4200000
d. 198000
e. 2350000
f. 4090000
h. 81000
g. 3300000
i. 271000000
(10) a. 4.6×10³
c. 6.4×10⁴
e. 1.06×10³
g. 6.3×10⁶
i. 3.9×10⁷
b. 8.6×10⁵
d. 9.7×10⁶
f. 4.08×10⁷
h. 2.07×10⁸
j. 4.29×10⁷
look at the list of prices for each item. circle the most expensive one on each list.
(11) car price ($)
a 1.5×10⁵
b 1.05×10⁵
c 1.5×10⁴
(12) house price ($)
a 9×10⁵
b 1.9×10⁴
c 1×10⁶
(13) ring price ($)
a 1.4×10⁷
b 4.1×10⁶
c 4×10⁶

Explanation:

Step1: Recall scientific - notation rules

Scientific notation is of the form $a\times10^{n}$, where $1\leq a<10$ and $n$ is an integer. To convert a large number to scientific notation, move the decimal point to the left until $a$ is in the correct range, and $n$ is the number of places the decimal is moved. To convert from scientific notation to standard form, move the decimal point $n$ places according to the sign of $n$.

Step2: Convert numbers to scientific notation (9)

a.

For $36000000$, move the decimal 7 places to the left. So, $36000000 = 3.6\times10^{7}$.

b.

For $105000$, move the decimal 5 places to the left. So, $105000=1.05\times 10^{5}$.

c.

For $4200000$, move the decimal 6 places to the left. So, $4200000 = 4.2\times10^{6}$.

d.

For $198000$, move the decimal 5 places to the left. So, $198000=1.98\times 10^{5}$.

e.

For $2350000$, move the decimal 6 places to the left. So, $2350000 = 2.35\times10^{6}$.

f.

For $4090000$, move the decimal 6 places to the left. So, $4090000=4.09\times 10^{6}$.

g.

For $3300000$, move the decimal 6 places to the left. So, $3300000 = 3.3\times10^{6}$.

h.

For $81000$, move the decimal 4 places to the left. So, $81000 = 8.1\times10^{4}$.

i.

For $271000000$, move the decimal 8 places to the left. So, $271000000=2.71\times 10^{8}$.

Step3: Convert numbers from scientific notation to standard form (10)

a.

For $4.6\times10^{3}$, move the decimal 3 places to the right. So, $4.6\times10^{3}=4600$.

b.

For $8.6\times10^{5}$, move the decimal 5 places to the right. So, $8.6\times10^{5}=860000$.

c.

For $6.4\times10^{4}$, move the decimal 4 places to the right. So, $6.4\times10^{4}=64000$.

d.

For $9.7\times10^{6}$, move the decimal 6 places to the right. So, $9.7\times10^{6}=9700000$.

e.

For $1.06\times10^{3}$, move the decimal 3 places to the right. So, $1.06\times10^{3}=1060$.

f.

For $4.08\times10^{7}$, move the decimal 7 places to the right. So, $4.08\times10^{7}=40800000$.

g.

For $6.3\times10^{6}$, move the decimal 6 places to the right. So, $6.3\times10^{6}=6300000$.

h.

For $2.07\times10^{8}$, move the decimal 8 places to the right. So, $2.07\times10^{8}=207000000$.

i.

For $3.9\times10^{7}$, move the decimal 7 places to the right. So, $3.9\times10^{7}=39000000$.

j.

For $4.29\times10^{7}$, move the decimal 7 places to the right. So, $4.29\times10^{7}=42900000$.

Step4: Compare prices in scientific - notation (11 - 13)

Car

$A:1.5\times10^{5}=150000$, $B:1.05\times10^{5}=105000$, $C:1.5\times10^{4}=15000$. The most expensive car is $A$.

House

$A:9\times10^{5}=900000$, $B:1.9\times10^{4}=19000$, $C:1\times10^{6}=1000000$. The most expensive house is $C$.

Ring

$A:1.4\times10^{7}=14000000$, $B:4.1\times10^{6}=4100000$, $C:4\times10^{6}=4000000$. The most expensive ring is $A$.

Answer:

9a. $3.6\times10^{7}$
9b. $1.05\times 10^{5}$
9c. $4.2\times10^{6}$
9d. $1.98\times 10^{5}$
9e. $2.35\times10^{6}$
9f. $4.09\times 10^{6}$
9g. $3.3\times10^{6}$
9h. $8.1\times10^{4}$
9i. $2.71\times 10^{8}$
10a. $4600$
10b. $860000$
10c. $64000$
10d. $9700000$
10e. $1060$
10f. $40800000$
10g. $6300000$
10h. $207000000$
10i. $39000000$
10j. $42900000$

1. A
2. C
3. A