QuestionDecide if these statements are true or false and explain: $1.67\% = 3.67$ and $0.12 < 1 \frac{7}{10}$ .

Studdy Solution

STEP 1

Assumptions1. The statements are mathematical comparisons between two numbers. . We need to determine if the comparisons are true or false.
3. We will use basic mathematical operations and principles to evaluate the statements.

STEP 2

Let's evaluate the first statement $1.67 \% =.67$ .

STEP 3

First, we need to convert the percentage to a decimal value. We can do this by dividing the percentage by100.
$1.67\% = \frac{1.67}{100}$

STEP 4

Calculate the decimal value of the percentage.
$1.67\% = \frac{1.67}{100} =0.0167$

STEP 5

Now, compare the decimal value of the percentage to the number on the right side of the equation.
$0.0167 =3.67$

STEP 6

As we can see, $0.016$ is not equal to $3.67$ . Therefore, the first statement is false.

STEP 7

Let's evaluate the second statement $0.12 <1 \frac{7}{10}$ .

STEP 8

First, we need to convert the mixed number to a decimal. We can do this by adding the whole number to the fraction converted to a decimal.
$1 \frac{7}{10} =1 + \frac{7}{10}$

STEP 9

Calculate the decimal value of the fraction.
$\frac{7}{} =.7$

STEP 10

Now, add the whole number to the decimal value of the fraction.
$\frac{7}{10} = +0.7 =.7$

STEP 11

Now, compare the number on the left side of the inequality to the decimal value of the mixed number.
$0. <.7$

STEP 12

As we can see, $0.12$ is less than $.7$ . Therefore, the second statement is true.
In conclusion, the first statement is false and the second statement is true.

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QuestionDecide if these statements are true or false and explain: $1.67\% = 3.67$ and $0.12 < 1 \frac{7}{10}$ .

Studdy Solution

STEP 1

Assumptions1. The statements are mathematical comparisons between two numbers. . We need to determine if the comparisons are true or false.
3. We will use basic mathematical operations and principles to evaluate the statements.

STEP 2

Let's evaluate the first statement $1.67 \% =.67$ .

STEP 3

First, we need to convert the percentage to a decimal value. We can do this by dividing the percentage by100.
$1.67\% = \frac{1.67}{100}$

STEP 4

Calculate the decimal value of the percentage.
$1.67\% = \frac{1.67}{100} =0.0167$

STEP 5

Now, compare the decimal value of the percentage to the number on the right side of the equation.
$0.0167 =3.67$

STEP 6

As we can see, $0.016$ is not equal to $3.67$ . Therefore, the first statement is false.

STEP 7

Let's evaluate the second statement $0.12 <1 \frac{7}{10}$ .

STEP 8

First, we need to convert the mixed number to a decimal. We can do this by adding the whole number to the fraction converted to a decimal.
$1 \frac{7}{10} =1 + \frac{7}{10}$

STEP 9

Calculate the decimal value of the fraction.
$\frac{7}{} =.7$

STEP 10

Now, add the whole number to the decimal value of the fraction.
$\frac{7}{10} = +0.7 =.7$

STEP 11

Now, compare the number on the left side of the inequality to the decimal value of the mixed number.
$0. <.7$

STEP 12

As we can see, $0.12$ is less than $.7$ . Therefore, the second statement is true.
In conclusion, the first statement is false and the second statement is true.

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QuestionDecide if these statements are true or false and explain: 1.67%=3.671.67\% = 3.671.67%=3.67 and 0.12<17100.12 < 1 \frac{7}{10}0.12<1107​.

Studdy Solution

STEP 1

Assumptions1. The statements are mathematical comparisons between two numbers. . We need to determine if the comparisons are true or false.3. We will use basic mathematical operations and principles to evaluate the statements.

STEP 2

Let's evaluate the first statement 1.67%=.671.67 \% =.671.67%=.67.

STEP 3

First, we need to convert the percentage to a decimal value. We can do this by dividing the percentage by100.1.67%=1.671001.67\% = \frac{1.67}{100}1.67%=1001.67​

STEP 4

Calculate the decimal value of the percentage.1.67%=1.67100=0.01671.67\% = \frac{1.67}{100} =0.01671.67%=1001.67​=0.0167

STEP 5

Now, compare the decimal value of the percentage to the number on the right side of the equation.0.0167=3.670.0167 =3.670.0167=3.67

STEP 6

As we can see, 0.0160.0160.016 is not equal to 3.673.673.67. Therefore, the first statement is false.

STEP 7

Let's evaluate the second statement 0.12<17100.12 <1 \frac{7}{10}0.12<1107​.

STEP 8

First, we need to convert the mixed number to a decimal. We can do this by adding the whole number to the fraction converted to a decimal.1710=1+7101 \frac{7}{10} =1 + \frac{7}{10}1107​=1+107​

STEP 9

Calculate the decimal value of the fraction.7=.7\frac{7}{} =.77​=.7

STEP 10

Now, add the whole number to the decimal value of the fraction.710=+0.7=.7 \frac{7}{10} = +0.7 =.7107​=+0.7=.7

STEP 11

Now, compare the number on the left side of the inequality to the decimal value of the mixed number.0.<.70. <.70.<.7

STEP 12

As we can see, 0.120.120.12 is less than .7.7.7. Therefore, the second statement is true.In conclusion, the first statement is false and the second statement is true.

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QuestionDecide if these statements are true or false and explain: $1.67\% = 3.67$ and $0.12 < 1 \frac{7}{10}$ .

Assumptions1. The statements are mathematical comparisons between two numbers. . We need to determine if the comparisons are true or false.
3. We will use basic mathematical operations and principles to evaluate the statements.

Let's evaluate the first statement $1.67 \% =.67$ .

First, we need to convert the percentage to a decimal value. We can do this by dividing the percentage by100.
$1.67\% = \frac{1.67}{100}$

Calculate the decimal value of the percentage.
$1.67\% = \frac{1.67}{100} =0.0167$

Now, compare the decimal value of the percentage to the number on the right side of the equation.
$0.0167 =3.67$

As we can see, $0.016$ is not equal to $3.67$ . Therefore, the first statement is false.

Let's evaluate the second statement $0.12 <1 \frac{7}{10}$ .

First, we need to convert the mixed number to a decimal. We can do this by adding the whole number to the fraction converted to a decimal.
$1 \frac{7}{10} =1 + \frac{7}{10}$

Calculate the decimal value of the fraction.
$\frac{7}{} =.7$

Now, add the whole number to the decimal value of the fraction.
$\frac{7}{10} = +0.7 =.7$

Now, compare the number on the left side of the inequality to the decimal value of the mixed number.
$0. <.7$

As we can see, $0.12$ is less than $.7$ . Therefore, the second statement is true.
In conclusion, the first statement is false and the second statement is true.