QuestionCalculate the following: (a) $1.600 \times 10^{-7} \times 2.1 \times 10^{3}$ , (b) $(1.33)^{3}$ , (c) $1.93 \times 2.651$ , (d) $4.4 / 2.200$ .

Studdy Solution

STEP 1

Assumptions1. We are performing basic arithmetic operations (multiplication, exponentiation, and division) on the given numbers. . We are using standard rules of arithmetic to solve the problems.

STEP 2

For part (a), we are multiplying two numbers in scientific notation. The rule for multiplying numbers in scientific notation is to multiply the coefficients and add the exponents.
$\left(1.600 \times10^{-7}\right)\left(2.1 \times10^{}\right) = (1.600 \times2.1) \times10^{-7+}$

STEP 3

Calculate the coefficient and the exponent separately.
$Coefficient =1.600 \times2.1 =3.36$ $Exponent = -7 +3 = -$

STEP 4

Combine the coefficient and the exponent to write the answer in scientific notation.
$Answer =3.36 \times10^{-4}$

STEP 5

For part (b), we are raising a number to a power. The rule for this is to multiply the number by itself for the number of times indicated by the power.
$(1.33)^{3} =1.33 \times1.33 \times1.33$

STEP 6

Calculate the result of the exponentiation.
$(1.33)^{3} =1.33 \times1.33 \times1.33 =2.35237$

STEP 7

For part (c), we are multiplying two decimal numbers. The rule for this is to perform the multiplication as if they were whole numbers and then count the number of digits after the decimal point in the original numbers and place the decimal point in the product so that there is the same number of digits after it.
$1.93 \times2.651 =5.11343$

STEP 8

For part (d), we are dividing two decimal numbers. The rule for this is to perform the division as if they were whole numbers and then place the decimal point in the quotient directly above its place in the dividend.
$4.4 /2.200 =2$

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QuestionCalculate the following: (a) $1.600 \times 10^{-7} \times 2.1 \times 10^{3}$ , (b) $(1.33)^{3}$ , (c) $1.93 \times 2.651$ , (d) $4.4 / 2.200$ .

Studdy Solution

STEP 1

Assumptions1. We are performing basic arithmetic operations (multiplication, exponentiation, and division) on the given numbers. . We are using standard rules of arithmetic to solve the problems.

STEP 2

For part (a), we are multiplying two numbers in scientific notation. The rule for multiplying numbers in scientific notation is to multiply the coefficients and add the exponents.
$\left(1.600 \times10^{-7}\right)\left(2.1 \times10^{}\right) = (1.600 \times2.1) \times10^{-7+}$

STEP 3

Calculate the coefficient and the exponent separately.
$Coefficient =1.600 \times2.1 =3.36$ $Exponent = -7 +3 = -$

STEP 4

Combine the coefficient and the exponent to write the answer in scientific notation.
$Answer =3.36 \times10^{-4}$

STEP 5

For part (b), we are raising a number to a power. The rule for this is to multiply the number by itself for the number of times indicated by the power.
$(1.33)^{3} =1.33 \times1.33 \times1.33$

STEP 6

Calculate the result of the exponentiation.
$(1.33)^{3} =1.33 \times1.33 \times1.33 =2.35237$

STEP 7

STEP 8

For part (d), we are dividing two decimal numbers. The rule for this is to perform the division as if they were whole numbers and then place the decimal point in the quotient directly above its place in the dividend.
$4.4 /2.200 =2$

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QuestionCalculate the following: (a) 1.600×10−7×2.1×1031.600 \times 10^{-7} \times 2.1 \times 10^{3}1.600×10−7×2.1×103, (b) (1.33)3(1.33)^{3}(1.33)3, (c) 1.93×2.6511.93 \times 2.6511.93×2.651, (d) 4.4/2.2004.4 / 2.2004.4/2.200.

Studdy Solution

STEP 1

Assumptions1. We are performing basic arithmetic operations (multiplication, exponentiation, and division) on the given numbers. . We are using standard rules of arithmetic to solve the problems.

STEP 2

STEP 3

Calculate the coefficient and the exponent separately.Coefficient=1.600×2.1=3.36Coefficient =1.600 \times2.1 =3.36Coefficient=1.600×2.1=3.36Exponent=−7+3=−Exponent = -7 +3 = -Exponent=−7+3=−

STEP 4

Combine the coefficient and the exponent to write the answer in scientific notation.Answer=3.36×10−4Answer =3.36 \times10^{-4}Answer=3.36×10−4

STEP 5

For part (b), we are raising a number to a power. The rule for this is to multiply the number by itself for the number of times indicated by the power.(1.33)3=1.33×1.33×1.33(1.33)^{3} =1.33 \times1.33 \times1.33(1.33)3=1.33×1.33×1.33

STEP 6

Calculate the result of the exponentiation.(1.33)3=1.33×1.33×1.33=2.35237(1.33)^{3} =1.33 \times1.33 \times1.33 =2.35237(1.33)3=1.33×1.33×1.33=2.35237

STEP 7

STEP 8

For part (d), we are dividing two decimal numbers. The rule for this is to perform the division as if they were whole numbers and then place the decimal point in the quotient directly above its place in the dividend.4.4/2.200=24.4 /2.200 =24.4/2.200=2

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QuestionCalculate the following: (a) $1.600 \times 10^{-7} \times 2.1 \times 10^{3}$ , (b) $(1.33)^{3}$ , (c) $1.93 \times 2.651$ , (d) $4.4 / 2.200$ .

Calculate the coefficient and the exponent separately.
$Coefficient =1.600 \times2.1 =3.36$ $Exponent = -7 +3 = -$

Combine the coefficient and the exponent to write the answer in scientific notation.
$Answer =3.36 \times10^{-4}$

For part (b), we are raising a number to a power. The rule for this is to multiply the number by itself for the number of times indicated by the power.
$(1.33)^{3} =1.33 \times1.33 \times1.33$

Calculate the result of the exponentiation.
$(1.33)^{3} =1.33 \times1.33 \times1.33 =2.35237$

For part (d), we are dividing two decimal numbers. The rule for this is to perform the division as if they were whole numbers and then place the decimal point in the quotient directly above its place in the dividend.
$4.4 /2.200 =2$