Show that each number is a rational number by writing it as the quotient of two integers.
1. 37
2. -3 1/5
3. 9.2
4. -0.23
37/1
-16/5
92/10 = 46/5
-23/100
To show that each number is a rational number, we need to write them as the quotient of two integers.
1. 37 can be written as the quotient of 37 and 1: 37/1.
2. -3 1/5 can be written as -16/5. To convert the mixed number -3 1/5 to a fraction, we multiply the whole number (-3) by the denominator (5) and add the numerator (1). So, we have (-3 * 5 + 1)/5 = -15 + 1/5 = -16/5.
3. 9.2 can be written as the quotient of 92 and 10: 92/10. To convert the decimal 9.2 to a fraction, we remove the decimal point and write it as the numerator (92) and put the denominator as a power of 10, which is 10 in this case.
4. -0.23 can be written as the quotient of -23 and 100: -23/100. To convert the decimal -0.23 to a fraction, we remove the decimal point and write it as the numerator (-23) and put the denominator as a power of 10, which is 100 in this case.
So, each number is a rational number expressed as the quotient of two integers.
To show that each number is a rational number, we need to express it as the quotient of two integers.
1. 37: Since 37 is an integer, it can be written as a quotient by dividing it by 1. So, 37 = 37/1.
2. -3 1/5: To write this as a quotient of two integers, we need to convert the mixed number into an improper fraction. First, multiply the whole number (-3) by the denominator (5) and then add the numerator (1) to get -3 * 5 + 1 = -14. The denominator remains the same, so -3 1/5 = -14/5.
3. 9.2: The number 9.2 can be written as a quotient by considering it as the fraction 9 + 2/10. We can simplify this fraction by multiplying the numerator and denominator by 10 to get 92/10.
4. -0.23: Similarly, we can express -0.23 as the quotient of two integers by multiplying both the numerator and denominator by 100 to get -23/100.
Therefore, each of the numbers 37, -3 1/5, 9.2, and -0.23 can be expressed as the quotient of two integers, making them rational numbers.