Math / Numbers & Operations

Questionb. Select the correct choice below and, if necessary, fill in the answer box to complete your choic A. $\frac{17}{200}$ as a terminating decimal is $\square$ . (Type an integer or a decimal.) B. $\frac{17}{200}$ cannot be written as a terminating decimal.

Studdy Solution

STEP 1

1. We need to determine if the fraction $\frac{17}{200}$ can be expressed as a terminating decimal.
2. A fraction can be expressed as a terminating decimal if its denominator can be expressed in the form $2^m \times 5^n$ , where $m$ and $n$ are non-negative integers.

STEP 2

1. Simplify the fraction if necessary.
2. Determine if the denominator is in the form $2^m \times 5^n$ .
3. Convert the fraction to a decimal if it is terminating.

STEP 3

Check if $\frac{17}{200}$ can be simplified. Since 17 is a prime number and does not divide 200, the fraction is already in its simplest form.

STEP 4

Factor the denominator $200$ to check if it is in the form $2^m \times 5^n$ .
$200 = 2^3 \times 5^2$
Since the denominator is composed only of the prime factors 2 and 5, it can be expressed in the form $2^m \times 5^n$ .

STEP 5

Since the denominator is in the form $2^m \times 5^n$ , $\frac{17}{200}$ can be expressed as a terminating decimal. Now, perform the division to find the decimal form.
$\frac{17}{200} = 0.085$
The correct choice is: A. $\frac{17}{200}$ as a terminating decimal is $0.085$ .

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Questionb. Select the correct choice below and, if necessary, fill in the answer box to complete your choic A. $\frac{17}{200}$ as a terminating decimal is $\square$ . (Type an integer or a decimal.) B. $\frac{17}{200}$ cannot be written as a terminating decimal.

Studdy Solution

STEP 1

1. We need to determine if the fraction $\frac{17}{200}$ can be expressed as a terminating decimal.
2. A fraction can be expressed as a terminating decimal if its denominator can be expressed in the form $2^m \times 5^n$ , where $m$ and $n$ are non-negative integers.

STEP 2

1. Simplify the fraction if necessary.
2. Determine if the denominator is in the form $2^m \times 5^n$ .
3. Convert the fraction to a decimal if it is terminating.

STEP 3

Check if $\frac{17}{200}$ can be simplified. Since 17 is a prime number and does not divide 200, the fraction is already in its simplest form.

STEP 4

Factor the denominator $200$ to check if it is in the form $2^m \times 5^n$ .
$200 = 2^3 \times 5^2$
Since the denominator is composed only of the prime factors 2 and 5, it can be expressed in the form $2^m \times 5^n$ .

STEP 5

Since the denominator is in the form $2^m \times 5^n$ , $\frac{17}{200}$ can be expressed as a terminating decimal. Now, perform the division to find the decimal form.
$\frac{17}{200} = 0.085$
The correct choice is: A. $\frac{17}{200}$ as a terminating decimal is $0.085$ .

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Questionb. Select the correct choice below and, if necessary, fill in the answer box to complete your choic A. 17200\frac{17}{200}20017​ as a terminating decimal is □\square□ . (Type an integer or a decimal.) B. 17200\frac{17}{200}20017​ cannot be written as a terminating decimal.

Studdy Solution

STEP 1

1. We need to determine if the fraction 17200\frac{17}{200}20017​ can be expressed as a terminating decimal.2. A fraction can be expressed as a terminating decimal if its denominator can be expressed in the form 2m×5n2^m \times 5^n2m×5n, where mmm and nnn are non-negative integers.

STEP 2

1. Simplify the fraction if necessary.2. Determine if the denominator is in the form 2m×5n2^m \times 5^n2m×5n.3. Convert the fraction to a decimal if it is terminating.

STEP 3

Check if 17200\frac{17}{200}20017​ can be simplified. Since 17 is a prime number and does not divide 200, the fraction is already in its simplest form.

STEP 4

Factor the denominator 200200200 to check if it is in the form 2m×5n2^m \times 5^n2m×5n.200=23×52 200 = 2^3 \times 5^2 200=23×52Since the denominator is composed only of the prime factors 2 and 5, it can be expressed in the form 2m×5n2^m \times 5^n2m×5n.

STEP 5

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Questionb. Select the correct choice below and, if necessary, fill in the answer box to complete your choic A. $\frac{17}{200}$ as a terminating decimal is $\square$ . (Type an integer or a decimal.) B. $\frac{17}{200}$ cannot be written as a terminating decimal.

1. We need to determine if the fraction $\frac{17}{200}$ can be expressed as a terminating decimal.
2. A fraction can be expressed as a terminating decimal if its denominator can be expressed in the form $2^m \times 5^n$ , where $m$ and $n$ are non-negative integers.

1. Simplify the fraction if necessary.
2. Determine if the denominator is in the form $2^m \times 5^n$ .
3. Convert the fraction to a decimal if it is terminating.

Check if $\frac{17}{200}$ can be simplified. Since 17 is a prime number and does not divide 200, the fraction is already in its simplest form.

Factor the denominator $200$ to check if it is in the form $2^m \times 5^n$ .
$200 = 2^3 \times 5^2$
Since the denominator is composed only of the prime factors 2 and 5, it can be expressed in the form $2^m \times 5^n$ .