Question

skill practice 4
numbers practice
name:____ date:____

1. solve the following problems. write answers in scientific notation.

a) (7.430 x 10^4)(3.0 x 10^3) =
b) 8.03 x 10^6 + 4.0 x 10^4 =
c) (2.22 x 10^(-12))+(4.10x10^(-33)) =
d) (35,020)(321.0) =
e) 3.22x10^12 - 2.44x10^11 =
f) (6.32 x 10^(-32))+(8.19x10^(-36)) =

1. convert the following numbers to scientific notation:

a) 23,000,210,000 =
b) 0.00000000351 =

1. convert the following numbers to

egular\ notation:
a) 2.354 x 10^5 =
b) 3.400 x 10^(-9) =
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Explanation:

Step1: Multiply coefficients and add exponents

For $(7.430\times 10^{4})(3.0\times 10^{3})$, multiply $7.430$ and $3.0$ to get $22.29$, and add exponents $4 + 3=7$. Then rewrite as $2.229\times 10^{8}$ since scientific - notation has a single non - zero digit before the decimal.

Step2: Make exponents the same for addition

For $8.03\times 10^{6}+4.0\times 10^{4}$, rewrite $4.0\times 10^{4}$ as $0.04\times 10^{6}$. Then add $8.03 + 0.04=8.07$, so the result is $8.07\times 10^{6}$.

Step3: Divide coefficients and subtract exponents

For $(2.22\times 10^{- 12})\div(4.10\times 10^{-33})$, divide $2.22$ by $4.10\approx0.5415$, and subtract exponents $-12-(-33)=21$. Rewrite as $5.415\times 10^{20}$.

Step4: Multiply numbers and convert to scientific notation

For $(35020)(321.0)=35020\times321 = 11241420=1.124142\times 10^{7}$.

Step5: Make exponents the same for subtraction

For $3.22\times 10^{12}-2.44\times 10^{11}$, rewrite $2.44\times 10^{11}$ as $0.244\times 10^{12}$. Then subtract $3.22 - 0.244 = 2.976$, so the result is $2.976\times 10^{12}$.

Step6: Divide coefficients and subtract exponents

For $(6.32\times 10^{-32})\div(8.19\times 10^{-36})$, divide $6.32$ by $8.19\approx0.7717$, and subtract exponents $-32-(-36)=4$. Rewrite as $7.717\times 10^{3}$.

Step7: Convert to scientific notation

For $23000210000$, move the decimal 10 places to the left, so it is $2.300021\times 10^{10}$.

Step8: Convert to scientific notation

For $0.00000000351$, move the decimal 9 places to the right, so it is $3.51\times 10^{-9}$.

Step9: Convert to regular notation

For $2.354\times 10^{5}$, move the decimal 5 places to the right, so it is $235400$.

Step10: Convert to regular notation

For $3.400\times 10^{-9}$, move the decimal 9 places to the left, so it is $0.0000000034$.

Answer:

a) $2.229\times 10^{8}$
b) $8.07\times 10^{6}$
c) $5.415\times 10^{20}$
d) $1.124142\times 10^{7}$
e) $2.976\times 10^{12}$
f) $7.717\times 10^{3}$

1. a) $2.300021\times 10^{10}$

b) $3.51\times 10^{-9}$

1. a) $235400$

b) $0.0000000034$