QuestionConvert 0.000006 and 300 to scientific notation, then find and express the quotient in scientific notation.
0.000006 =
300 =
$\frac{0.000006}{300}=$

Studdy Solution

STEP 1

Assumptions1. We need to express the numbers in scientific notation. . Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form. It is commonly used by scientists, mathematicians, and engineers.
3. The format for writing a number in scientific notation is $a \\times10^n$ , where $1 \\leq |a| <10$ and $n$ is an integer.

STEP 2

First, we need to express the number0.000006 in scientific notation. To do this, we need to move the decimal point to the right until we have a number between1 and10. We count the number of places we moved the decimal point, which will be our exponent, $n$ .

STEP 3

We moved the decimal point6 places to the right, so $n = -6$ (negative because we moved the decimal point to the right). Thus,0.000006 in scientific notation is $6 \\times10^{-6}$ .

STEP 4

Next, we need to express the number300 in scientific notation. To do this, we need to move the decimal point to the left until we have a number between1 and10. We count the number of places we moved the decimal point, which will be our exponent, $n$ .

STEP 5

We moved the decimal point2 places to the left, so $n =2$ (positive because we moved the decimal point to the left). Thus,300 in scientific notation is $3 \\times10^{2}$ .

STEP 6

Now that we have both numbers in scientific notation, we can perform the division operation. When dividing numbers in scientific notation, we divide the coefficients (the numbers in front of the multiplication symbol) and subtract the exponents.
$\frac{a \\times10^n}{b \\times10^m} = \frac{a}{b} \\times10^{n-m}$

STEP 7

Substitute the given values into the formula.
$\frac{6 \\times10^{-6}}{3 \\times10^{2}} = \frac{6}{3} \\times10^{-6-2}$

STEP 8

Perform the division and subtraction operations.
$\frac{6 \\times10^{-6}}{3 \\times10^{2}} =2 \\times10^{-8}$ So, the quotient of0.000006 and300 in scientific notation is $2 \\times10^{-8}$ .

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QuestionConvert 0.000006 and 300 to scientific notation, then find and express the quotient in scientific notation.
0.000006 =
300 =
$\frac{0.000006}{300}=$

Studdy Solution

STEP 1

STEP 2

First, we need to express the number0.000006 in scientific notation. To do this, we need to move the decimal point to the right until we have a number between1 and10. We count the number of places we moved the decimal point, which will be our exponent, $n$ .

STEP 3

We moved the decimal point6 places to the right, so $n = -6$ (negative because we moved the decimal point to the right). Thus,0.000006 in scientific notation is $6 \\times10^{-6}$ .

STEP 4

Next, we need to express the number300 in scientific notation. To do this, we need to move the decimal point to the left until we have a number between1 and10. We count the number of places we moved the decimal point, which will be our exponent, $n$ .

STEP 5

We moved the decimal point2 places to the left, so $n =2$ (positive because we moved the decimal point to the left). Thus,300 in scientific notation is $3 \\times10^{2}$ .

STEP 6

STEP 7

Substitute the given values into the formula.
$\frac{6 \\times10^{-6}}{3 \\times10^{2}} = \frac{6}{3} \\times10^{-6-2}$

STEP 8

Perform the division and subtraction operations.
$\frac{6 \\times10^{-6}}{3 \\times10^{2}} =2 \\times10^{-8}$ So, the quotient of0.000006 and300 in scientific notation is $2 \\times10^{-8}$ .

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QuestionConvert 0.000006 and 300 to scientific notation, then find and express the quotient in scientific notation. 0.000006 = 300 = 0.000006300= \frac{0.000006}{300}= 3000.000006​=

Studdy Solution

STEP 1

STEP 2

First, we need to express the number0.000006 in scientific notation. To do this, we need to move the decimal point to the right until we have a number between1 and10. We count the number of places we moved the decimal point, which will be our exponent, nnn.

STEP 3

We moved the decimal point6 places to the right, so n=−6n = -6n=−6 (negative because we moved the decimal point to the right). Thus,0.000006 in scientific notation is 6times10−66 \\times10^{-6}6times10−6.

STEP 4

Next, we need to express the number300 in scientific notation. To do this, we need to move the decimal point to the left until we have a number between1 and10. We count the number of places we moved the decimal point, which will be our exponent, nnn.

STEP 5

We moved the decimal point2 places to the left, so n=2n =2n=2 (positive because we moved the decimal point to the left). Thus,300 in scientific notation is 3times1023 \\times10^{2}3times102.

STEP 6

STEP 7

Substitute the given values into the formula.6times10−63times102=63times10−6−2\frac{6 \\times10^{-6}}{3 \\times10^{2}} = \frac{6}{3} \\times10^{-6-2}3times1026times10−6​=36​times10−6−2

STEP 8

Perform the division and subtraction operations.6times10−63times102=2times10−8\frac{6 \\times10^{-6}}{3 \\times10^{2}} =2 \\times10^{-8}3times1026times10−6​=2times10−8So, the quotient of0.000006 and300 in scientific notation is 2times10−82 \\times10^{-8}2times10−8.

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QuestionConvert 0.000006 and 300 to scientific notation, then find and express the quotient in scientific notation.
0.000006 =
300 =
$\frac{0.000006}{300}=$

First, we need to express the number0.000006 in scientific notation. To do this, we need to move the decimal point to the right until we have a number between1 and10. We count the number of places we moved the decimal point, which will be our exponent, $n$ .

We moved the decimal point6 places to the right, so $n = -6$ (negative because we moved the decimal point to the right). Thus,0.000006 in scientific notation is $6 \\times10^{-6}$ .

Next, we need to express the number300 in scientific notation. To do this, we need to move the decimal point to the left until we have a number between1 and10. We count the number of places we moved the decimal point, which will be our exponent, $n$ .

We moved the decimal point2 places to the left, so $n =2$ (positive because we moved the decimal point to the left). Thus,300 in scientific notation is $3 \\times10^{2}$ .

Substitute the given values into the formula.
$\frac{6 \\times10^{-6}}{3 \\times10^{2}} = \frac{6}{3} \\times10^{-6-2}$

Perform the division and subtraction operations.
$\frac{6 \\times10^{-6}}{3 \\times10^{2}} =2 \\times10^{-8}$ So, the quotient of0.000006 and300 in scientific notation is $2 \\times10^{-8}$ .