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QuestionEvaluate the following without a calculator and express in scientific notation:
1. 0.0025×107−1.07×1050.0025 \times 10^{7}-1.07 \times 10^{5}
2. 9×106+2.4×1079 \times 10^{6}+2.4 \times 10^{7}
3. (0.0034)(2.5×10−7)(0.0034)(2.5 \times 10^{-7})
4. 1.44×10−8÷0.0000241.44 \times 10^{-8} \div 0.000024

Studdy Solution

STEP 1

Assumptions1. All the numbers are given in scientific notation. . We are to perform the operations as indicated.
3. The final answers should be expressed in scientific notation.

STEP 2

Let's start with the first expression 0.0025×107−1.07×1050.0025 \times10^{7}-1.07 \times10^{5}First, we need to express both numbers in the same power of10. We can do this by adjusting the decimal point and the exponent.

STEP 3

Express 0.0025×1070.0025 \times10^{7} in terms of 10510^{5}.
0.0025×107=2.5×1050.0025 \times10^{7} =2.5 \times10^{5}

STEP 4

Now we can subtract 1.07×101.07 \times10^{} from 2.×102. \times10^{}.
2.×10−1.07×102. \times10^{} -1.07 \times10^{}

STEP 5

Perform the subtraction.
2.5×105−1.07×105=1.43×1052.5 \times10^{5} -1.07 \times10^{5} =1.43 \times10^{5}

STEP 6

Next, let's evaluate the second expression 9×106+2.4×109 \times10^{6}+2.4 \times10^{}First, we need to express both numbers in the same power of10. We can do this by adjusting the decimal point and the exponent.

STEP 7

Express 9×1069 \times10^{6} in terms of 10710^{7}.
9×106=0.9×1079 \times10^{6} =0.9 \times10^{7}

STEP 8

Now we can add 0.×1070. \times10^{7} to 2.4×1072.4 \times10^{7}.
0.×107+2.4×1070. \times10^{7} +2.4 \times10^{7}

STEP 9

Perform the addition.
.9×7+2.4×7=3.3×7.9 \times^{7} +2.4 \times^{7} =3.3 \times^{7}

STEP 10

Next, let's evaluate the third expression (0.0034)(2.5×10−7)(0.0034)\left(2.5 \times10^{-7}\right)This is a multiplication operation. We can multiply the decimal numbers and then add the exponents of10.

STEP 11

Perform the multiplication.
(0.0034)(.5×10−7)=0.0085×10−7(0.0034)\left(.5 \times10^{-7}\right) =0.0085 \times10^{-7}

STEP 12

Express 0.0085×10−70.0085 \times10^{-7} in scientific notation.
0.0085×10−7=8.5×10−90.0085 \times10^{-7} =8.5 \times10^{-9}

STEP 13

Finally, let's evaluate the fourth expression .44×10−8÷0.000024.44 \times10^{-8} \div0.000024
This is a division operation. We can divide the decimal numbers and then subtract the exponents of10.

STEP 14

Express 0.0000240.000024 in scientific notation.
0.000024=2.4×10−0.000024 =2.4 \times10^{-}

STEP 15

Now we can divide .44×10−8.44 \times10^{-8} by 2.4×10−52.4 \times10^{-5}.
.44×10−82.4×10−5\frac{.44 \times10^{-8}}{2.4 \times10^{-5}}

STEP 16

Perform the division.
.44×10−82.4×10−5=0.6×10−3\frac{.44 \times10^{-8}}{2.4 \times10^{-5}} =0.6 \times10^{-3}

STEP 17

Express 0.6×10−30.6 \times10^{-3} in scientific notation.
0.6×10−3=6×10−40.6 \times10^{-3} =6 \times10^{-4}So, the solutions to the given expressions are33. .43×105.43 \times10^{5}
34. 3.3×1073.3 \times10^{7}
35. .5×10−9.5 \times10^{-9}
36. 6×10−46 \times10^{-4}

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